Economic Growth (continued)

ECON3301 : Sobey School of Business, SMU, MD.

The Globe and Mail: Income inequality rising quickly in Canada

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September 13, 2011

Income inequality rising quickly in CanadaBy TAVIA GRANTGlobe and Mail Blog

Conference Board of Canada says gap between rich and poor has beenrising more rapidly in Canada than in the U.S. since the mid-1990s

The gap between the rich and the rest is growing ever wider - with the chasmincreasing at a faster pace in Canada than in the United States.

That's the conclusion of a Conference Board of Canada study Tuesday, whichsays income inequality has been rising more rapidly in Canada than in the U.S.since the mid-1990s.

Its global analysis found that Canada has had the fourth-largest increase inincome inequality among its peers. Between the mid-nineties and late 2000s,income inequality rose in 10 of 17 peer countries - including Canada. It remainedunchanged in Japan and Norway, and declined in five countries.

"Even though the U.S. currently has the largest rich-poor income gap amongthese countries, the gap in Canada has been rising at a faster rate," noted AnneGolden, president and chief executive, adding that high inequality raises both "amoral question about fairness and can contribute to social tensions."

Of total world income, 42 per cent goes to those who make up the richest 10 percent of the world's population, while 1 per cent goes to those who comprise thepoorest 10 per cent, it says.

Tuesday's report landed on the same day the U.S. Census Bureau said the 46.2million Americans in poverty last year was the largest in the 52 years that data hasbeen published.

Countries with very high inequality are clustered in South America and southern

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Africa. Countries with low inequality are mostly in Europe. Canada and the U.S.have medium income inequality, the report says.

While plenty of prominent economists in the U.S., including Nobel Prize winnerJoseph Stiglitz and University of Chicago professor Raghuram Rajan, havedevoted much analysis to the growing income gap south of the border and itseconomic impact, the issue has not garnered much attention in Canada.

Today's report offers little explanation on why the income gap is growing morerapidly in Canada than elsewhere. Broadly, it says market forces and globalizationare increasing disparity, along with institutional shifts such as dwindlingunionization rates and stagnating minimum wages.

It also doesn't delve much into what's happened with the gap in recent years. Partof the challenge is finding solid statistics - national data on income levels istypically two years out of date. The most recent figures, for 2009, show Canadianpoverty rates started to rise again in the recession after a decade of improvement.

Canada's income gap is a worry to several business leaders, as discussed in thisstory [http://www.theglobeandmail.com/news/politics/how-paying-peoples-way-out-of-poverty-can-help-us-all/article2011940] I wrote with Anna Mehler Papernyin May.

A separate Conference Board report published in July showed the richest segmentof Canadians increased their share of total national income while poor andmiddle-income individuals have lost ground since 1993.

The Conference Board uses a measure of income inequality called the Gini index.It calculates how the distribution of income deviates from a perfectly equaldistribution. A Gini index of 0 means that every person in the society has the sameamount of income while 1 would show that one person has all the income.

A country with low inequality has a Gini index of 0.3 or less while those above 0.4point to a high-disparity country. Canada's Gini index hit 0.320 in the late 2000sfrom 0.293 in the mid-1990s. During the same period, the United States' Gini indexrose to 0.378 from 0.361.

Income inequality, along with corruption, were named as the two most seriouschallenges facing the world at this year's World Economic Forum in Davos.

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ECON3301-Fall 2011 SMU-Sobey SB

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Notes on Economic Growth in Canada

1. What is Economic Growth?

Economic growth is the increase of aggregate production in a given economy.

2. How can we measure Economic Growth?

Economic Growth is the increase of per capita gross domestic product (GDP) as a measure of

aggregate income. Usually, the annual rate of change in real GDP is taken as the indicator of the

annual rate of growth.

2.1. GDP as an indicator of economic growth

Gross domestic product (GDP) refers to the market value of all final goods and services

produced within a country in a given period. GDP per capita and its changes over time is often

considered an indicator of a country's standard of living and economic growth.

2.2. Measuring GDP

GDP can be determined in three ways, all of which should, in principle, give the same result.

They are the product (or output) approach, the income approach, and the expenditure approach.

The most direct of the three is the product approach, which sums the outputs of every class of

enterprise to arrive at the total. The expenditure approach works on the principle that all of the

product must be bought by somebody, therefore the value of the total product must be equal to

people's total expenditures in buying things.

The income approach works on the principle that the incomes of the productive factors

("producers," colloquially) must be equal to the value of their product, and determines GDP by

finding the sum of all producers' incomes.

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Example: the expenditure method:

GDP = Value of private consumption (C) + Value of gross investment (I) + Value of government spending (G) + Value of exports in national currency -imports

𝐺𝐷𝑃 = 𝐶 + 𝐼 + 𝐺 + 𝜀𝑋 −𝑀

Note:

"Gross" means that GDP measures production regardless of the various uses to which that

production can be put. Production can be used for immediate consumption, for investment in

new fixed assets or inventories, or for replacing depreciated fixed assets. "Domestic" means that

GDP measures production that takes place within the country's borders. In the expenditure-

method equation given above, the exports-minus-imports term is necessary in order to null out

expenditures on things not produced in the country (imports) and add in things produced but not

sold in the country (exports).

2.3. Shortcomings of GDP as an indicator of economic performance

Wealth distribution

Non-market transactions

Underground economy

Non-monetary economy

Quality improvements and inclusion of new products

3. Main factors behind Economics Growth

Economic growth is primarily driven by improvements in productivity, which involves

producing more goods and services with the same inputs of labour, capital, energy and materials.

4. Temporal Horizon for Measuring Economic Growth

The long-run path of economic growth is one of the central questions of economics; despite

some problems of measurement, an increase in GDP of a country greater than population growth

is generally taken as an increase in the standard of living of its inhabitants. Over long periods of

ECON3301-Fall 2011 SMU-Sobey SB

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time, even small rates of annual growth can have large effects through compounding (see

exponential growth).

A growth rate of 2.5% per annum will lead to a doubling of GDP within 29 years, whilst a

growth rate of 8% per annum (experienced by some Four Asian Tigers) will lead to a doubling of

GDP within 10 years. This exponential characteristic can exacerbate differences across nations.

5. Short-run versus long-run considerations

Economists draw a distinction between short-term economic stabilization and long-term economic

growth. The topic of economic growth is primarily concerned with the long run. The short-run variation

of economic growth is termed the business cycle.

6. Principal Theories of Economic Growth

6.1.Exogenous growth model (Solow–Swan growth model) 6.2.Ramsey-Cass-Koopmans model

The Ramsey model differs from the Solow model in that it explicitly models the choice of consumption at a point in time and so endogenizes the saving rate.

6.3.Endogenous growth theory

In economics, endogenous growth theory or new growth theory was developed in the 1980s as

a response to criticism of the neo-classical growth model. The endogenous growth theory holds

that policy measures can have an impact on the long-run growth rate of an economy. For

example, subsidies on research and development or education increase the growth rate in some

endogenous growth models by increasing the incentive to innovate.

In neo-classical growth models, the long-run rate of growth is exogenously determined by either

assuming a savings rate or a rate of technical progress (Solow model). However, the savings rate

and rate of technological progress remain unexplained. Endogenous growth theory tries to

overcome this shortcoming by building macroeconomic models out of microeconomic

foundations. Households are assumed to maximize utility subject to budget constraints while

firms maximize profits.

ECON3301-Fall 2011 SMU-Sobey SB

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Crucial importance is usually given to the production of new technologies and human capital.

The engine for growth can be as simple as a constant return to scale production function (the AK

model) or more complicated set ups with spillover effects (spillovers are positive externalities,

benefits that are attributed to costs from other firms), increasing numbers of goods, increasing

qualities, etc.

7. Economic Growth in Canada

ECON3301-Fall 2011 SMU-Sobey SB

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Notes on Solow Growth Model

Dr. Maryam Dilmaghani

The notes are set to complement textbook on Solow Growth Model (Chapter 4). Chapter 5 is dropped.

Summary of Solow Growth Model

Solow Model is set to provide an understanding into the Steady State (long-run equilibrium) level of income per capita in a given economy, using simple assumptions of production function.

1. On Production Function

𝑌 = 𝐹(𝐿,𝐾) = 𝐴𝐿∝𝐾𝛽 (1)

with 0 <∝ 𝑎𝑛𝑑 𝛽 < 1

Y is output, L is labour force and K is capital investment. Cobb-Douglas version:

𝑌 = 𝐹(𝐿,𝐾) = 𝐴𝐿∝𝐾𝛽 (i)

with 0 < 𝛼𝑎𝑛𝑑 𝛽 < 1

and 𝛂+𝛽 = 1

2. Transforming production function to ‘per worker’ (with some approximation per capita):

We divide both sides of (1) by L:

𝑌𝐿 =

𝐴𝐿∝𝐾𝛽

𝐿 ⇒

Using y for income per capita (𝑌𝐿) and simplifying:

𝑦 = 𝐴𝐾𝛽 𝐿𝛼

𝐿= 𝐴𝐾𝛽𝐿𝛼−1

Since α+β=1⤇β=1-α and α=1-β so we have:

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𝑦 = 𝐴𝐾𝛽𝐿(1−𝛽)−1 = 𝐴𝐾𝛽𝐿−𝛽=𝐴.𝐾𝛽 1𝐿𝛽

= 𝐴 �𝐾𝐿�𝛽

Using k for 𝐾𝐿, meaning investment per worker (approximately investment per

capita), we get:

𝒚 = 𝑨𝒌𝜷

3. Adding other factors

(i) Saving rate, s, is the portion of income (output) per capita that us saved, hence can be invested.

(ii) Depreciation rate, δ: the portion of investment that must be replaced at each point in time so that the stock of capital does not fall.

(iii) rate of population hence labour force, growth: n

4. Deriving force of increase in output = increase in capital per worker.

5. Increase in capital per worker is possible when the Gross Investment, saving rate× 𝑜𝑢𝑡𝑝𝑢𝑡 𝑝𝑒𝑟 𝑐𝑎𝑝𝑖𝑡𝑎 (𝑠 × 𝑦), is larger than the capital per capita decline due to Depreciation and Population Growth: (δ+n)× 𝒌.

In other words:

Change in stock of capital= 𝒔 × 𝒚 − [(𝛅 + 𝐧) × 𝒌]

5. Steady state, meaning the long run equilibrium level of income per capita is achieved when there is no change in the stock of capital per capita, or:

Change in stock of capital=0⤇

𝒔 × 𝒚 = [(𝛅 + 𝐧) × 𝒌]

ECON3301-Fall 2011 SMU-Sobey SB

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6. Figures

(i) Output per capita as a function of capital per capita

(ii) Adding saving rate and gross investment (Green Line)

K/L

Y/L

K/L

Y/L

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(iii) Adding depreciation and population growth

Consumption at each point in time is Output-Gross investment= the difference between the Red and Green curves.

Net investment= change in the stock of capital is the difference between Gross Investment and Depreciation (distance between the Green curve and Back line).

At the steady state, Net investment=0, it means that the stick of capital, hence the output will remain constant forever.

K/L

Y/L

K/L

Y/LSteady State y Consumption

ECON3301-Fall 2011 SMU-Sobey SB

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(iv) Increase in saving rate: The Green curve shifts upward

For your practice:

Label this figure live the one in (iii) and discuss the impact of increase in saving rate on steady state level of output per capita, consumption and stock of capital per capita.

K/L

Y/L

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Notes 3

Economic General Equilibrium Theory (mainly from Wikipedia)

Note:

It goes beyond the lecture and also what I expect you. I will post another note, more focused on

equations and illustrations.

General equilibrium theory is a branch of theoretical economics. It seeks to explain the

behavior of supply, demand and prices in a whole economy with several or many interacting

markets, by seeking to prove that a set of prices exists that will result in an overall equilibrium,

hence general equilibrium, in contrast to partial equilibrium, which only analyzes single

markets. As with all models, this is an abstraction from a real economy; it is proposed as being a

useful model, both by considering equilibrium prices as long-term prices and by considering

actual prices as deviations from equilibrium.

General equilibrium theory both studies economies using the model of equilibrium pricing and

seeks to determine in which circumstances the assumptions of general equilibrium will hold. The

theory dates to the 1870s, particularly the work of French economist Léon Walras.

It is often assumed that (representative) agents are price takers, and under that assumption two

common notions of equilibrium exist.

Overview

Broadly speaking, general equilibrium tries to give an understanding of the whole economy

using a "bottom-up" approach, starting with individual markets and agents. Macroeconomics, as

developed by the Keynesian economists, focused on a "top-down" approach, where the analysis

starts with larger aggregates, the "big picture". Therefore, general equilibrium theory has

traditionally been classified as part of microeconomics.

The difference is not as clear as it used to be, since much of modern macroeconomics has

emphasized microeconomic foundations, and has constructed general equilibrium models of

ECON3301-Fall 2011 SMU-Sobey SB

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macroeconomic fluctuations. General equilibrium macroeconomic models usually have a

simplified structure that only incorporates a few markets, like a "goods market" and a "financial

market". In contrast, general equilibrium models in the microeconomic tradition typically

involve a multitude of different goods markets. They are usually complex and require computers

to help with numerical solutions.

In a market system the prices and production of all goods, including the price of money and

interest, are interrelated. A change in the price of one good, say bread, may affect another price,

such as bakers' wages. If bakers differ in tastes from others, the demand for bread might be

affected by a change in bakers' wages, with a consequent effect on the price of bread. Calculating

the equilibrium price of just one good, in theory, requires an analysis that accounts for all of the

millions of different goods that are available.

History of general equilibrium modeling

The first attempt in neoclassical economics to model prices for a whole economy was made by

Léon Walras. Walras' Elements of Pure Economics provides a succession of models, each

taking into account more aspects of a real economy (two commodities, many commodities,

production, growth, money). Some (for example, Eatwell (1989), see also Jaffe (1953)) think

Walras was unsuccessful and that the later models in this series are inconsistent.

(Not done in lecture besides about the concept of Government in Keynes & Real Business

Cycles models.)

In particular, Walras's model was a long-run model in which prices of capital goods are the same

whether they appear as inputs or outputs and in which the same rate of profits is earned in all

lines of industry. This is inconsistent with the quantities of capital goods being taken as data. But

when Walras introduced capital goods in his later models, he took their quantities as given, in

arbitrary ratios. (In contrast, Kenneth Arrow and Gerard Debreu continued to take the initial

quantities of capital goods as given, but adopted a short run model in which the prices of capital

goods vary with time and the own rate of interest varies across capital goods.)

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Walras was the first to lay down a research program much followed by 20th-century economists.

In particular, the Walrasian agenda included the investigation of when equilibria are unique and

stable.(Walras himself: Lesson 7 shows neither Uniqueness, nor Stability, nor even Existence of

an agreement is guaranteed. Immediate after closing the deal, e.g.)

Walras also proposed a dynamic process by which general equilibrium might be reached, that of

the tâtonnement or groping process.

The tatonnement process is a model for investigating stability of equilibria. Prices are announced

(perhaps by an "auctioneer"), and agents state how much of each good they would like to offer

(supply) or purchase (demand). No transactions and no production take place at disequilibrium

prices. Instead, prices are lowered for goods with positive prices and excess supply. Prices are

raised for goods with excess demand. The question for the mathematician is under what

conditions such a process will terminate in equilibrium where demand equates to supply for

goods with positive prices and demand does not exceed supply for goods with a price of zero.

Walras was not able to provide a definitive answer to this question (see Unresolved Problems in

General Equilibrium below).

In partial equilibrium analysis, the determination of the price of a good is simplified by just

looking at the price of one good, and assuming that the prices of all other goods remain constant.

The Marshallian theory of supply and demand is an example of partial equilibrium analysis.

Partial equilibrium analysis is adequate when the first-order effects of a shift in the demand

curve do not shift the supply curve. Anglo-American economists became more interested in

general equilibrium in the late 1920s and 1930s after Piero Sraffa's demonstration that

Marshallian economists cannot account for the forces thought to account for the upward-slope of

the supply curve for a consumer good.

If an industry uses little of a factor of production, a small increase in the output of that industry

will not bid the price of that factor up. To a first-order approximation, firms in the industry will

not experience decreasing costs and the industry supply curves will not slope up. If an industry

uses an appreciable amount of that factor of production, an increase in the output of that industry

will exhibit decreasing costs. But such a factor is likely to be used in substitutes for the industry's

ECON3301-Fall 2011 SMU-Sobey SB

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product, and an increased price of that factor will have effects on the supply of those substitutes.

Consequently, Sraffa argued, the first-order effects of a shift in the demand curve of the original

industry under these assumptions includes a shift in the supply curve of substitutes for that

industry's product, and consequent shifts in the original industry's supply curve. General

equilibrium is designed to investigate such interactions between markets.

Continental European economists made important advances in the 1930s. Walras' proofs of the

existence of general equilibrium often were based on the counting of equations and variables.

Such arguments are inadequate for non-linear systems of equations and do not imply that

equilibrium prices and quantities cannot be negative, a meaningless solution for his models. The

replacement of certain equations by inequalities and the use of more rigorous mathematics

improved general equilibrium modeling.

The modern conception of general equilibrium is provided by a model developed jointly by

Kenneth Arrow, Gerard Debreu and Lionel W. McKenzie in the 1950s. Gerard Debreu presents

this model in Theory of Value (1959) as an axiomatic model, following the style of mathematics

promoted by Bourbaki. In such an approach, the interpretation of the terms in the theory (e.g.,

goods, prices) are not fixed by the axioms.

Modern concept of general equilibrium in economics

Three important interpretations of the terms of the theory have been often cited. First, suppose

commodities are distinguished by the location where they are delivered. Then the Arrow-Debreu

model is a spatial model of, for example, international trade.

Second, suppose commodities are distinguished by when they are delivered. That is, suppose all

markets equilibrate at some initial instant of time. Agents in the model purchase and sell

contracts, where a contract specifies, for example, a good to be delivered and the date at which it

is to be delivered. The Arrow-Debreu model of intertemporal equilibrium contains forward

markets for all goods at all dates. No markets exist at any future dates.

Third, suppose contracts specify states of nature which affect whether a commodity is to be

delivered: "A contract for the transfer of a commodity now specifies, in addition to its physical

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properties, its location and its date, an event on the occurrence of which the transfer is

conditional. This new definition of a commodity allows one to obtain a theory of [risk] free from

any probability concept..." (Debreu, 1959)

These interpretations can be combined. So the complete Arrow-Debreu model can be said to

apply when goods are identified by when they are to be delivered, where they are to be delivered

and under what circumstances they are to be delivered, as well as their intrinsic nature. So there

would be a complete set of prices for contracts such as "1 ton of Winter red wheat, delivered on

3rd of January in Minneapolis, if there is a hurricane in Florida during December". A general

equilibrium model with complete markets of this sort seems to be a long way from describing the

workings of real economies, however its proponents argue that it is still useful as a simplified

guide as to how a real economies function.

Some of the recent work in general equilibrium has in fact explored the implications of

incomplete markets, which is to say an intertemporal economy with uncertainty, where there do

not exist sufficiently detailed contracts that would allow agents to fully allocate their

consumption and resources through time. While it has been shown that such economies will

generally still have an equilibrium, the outcome may no longer be Pareto optimal. The basic

intuition for this result is that if consumers lack adequate means to transfer their wealth from one

time period to another and the future is risky, there is nothing to necessarily tie any price ratio

down to the relevant marginal rate of substitution, which is the standard requirement for Pareto

optimality. Under some conditions the economy may still be constrained Pareto optimal,

meaning that a central authority limited to the same type and number of contracts as the

individual agents may not be able to improve upon the outcome, what is needed is the

introduction of a full set of possible contracts. Hence, one implication of the theory of

incomplete markets is that inefficiency may be a result of underdeveloped financial institutions

or credit constraints faced by some members of the public. Research still continues in this area.

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Chapter 7: Simple 2-period Model

(Preliminary to Basic Dynamic General Equilibrium Model)

Dr. Maryam Dilmaghani

The Model is dynamic

as it do involves time explicitly.

1. Markets involved

(i) Goods Market

(ii) Labour Market

(iii) ‘Investment’ Markets: Bonds Market (financial investment) & Rental Market (investment

physical capital) combined.

2. Endogenous variables

They are, as usual, price and quantity in each market.

(i) Goods Market: output and price of output, denoted by P.

(ii) Labour Market: employment level and wage, denoted by W.

(iii) ‘Investment’ Markets: Bonds Market (financial investment) & Rental Market (investment

physical capital): rate of return on investments.

3. Exogenous variables

(i) Subjective rate of patience (propensity to consume (or save) in period 1 compared to period 2;

i.e. how to divide the present value of life time income (𝑦1 & 𝑦2) between 𝑐1 & 𝑐2).

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(ii) real interest rate denoted by i: it is the opportunity cost of consumption is period 1 ⤇ if

price of consumption in period 2 is assumed to be 1 then the ‘price of consumption in period 1 is

(1+i).

Note that later on, we will make real interest rate Endogenous, only in this preliminary

model, it is exogenous.

(iii) Technology, i.e. parameters of production function.

(iv) Population /Labour Force, i.e. assumed Labour Supply

4. Representative agents’ budget constraint

Suppose that the representative agent receives income (from different sources) in both periods.

The income is period 1 is denoted by 𝑦1 and 𝑦2.

In period 1, income, 𝑦1, can be consumed (𝑐1) or saved (S). So we have:

𝐲𝟏 = 𝐜𝟏 + 𝐒 ⤇ 𝐒 = 𝐲𝟏 − 𝐜𝟏 (1)

In period 2, income, 𝑦2 , along the saving from period 1,

𝑆 × (1 + 𝑖):𝑎𝑠 𝑠𝑎𝑣𝑖𝑛𝑔 𝑔𝑟𝑜𝑤𝑠 𝑏𝑦 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑟𝑎𝑡𝑒, can be consumed (𝑐2). There will be no saving

as period 2 is the last period. So we have:

𝐜𝟐 = 𝐲𝟐 + 𝐒(𝟏 + 𝐢) ⤇ 𝐒 = 𝐜𝟐(𝟏+𝐢)

− 𝐲𝟐(𝟏+𝐢)

(2)

Combining (1) and (2), we get:

𝐲𝟏 − 𝐜𝟏 = 𝐜𝟐

(𝟏 + 𝐢)−

𝐲𝟐(𝟏 + 𝐢)

⤇ 𝒄𝟐 = 𝒚𝟏 × (𝟏 + 𝒊) + 𝒚𝟐 − (𝟏 + 𝒊) × 𝒄𝟏

Hence, the Inter-temporal Budget constraint, IBC, is:

𝒄𝟐 = 𝒚𝟏 × (𝟏 + 𝒊) + 𝒚𝟐 − (𝟏 + 𝒊) × 𝒄𝟏

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Example:

𝑆𝑢𝑝𝑝𝑜𝑠𝑒: 𝑦1 = 5 and 𝑦2 = 5, i=10%

Hence with no saving, the representative agent can consume 5 in period 1 and 5 in period 2.

(i) x-axis intercept

Present value of total, life-time income= 𝑦1 + 𝑦2(1+𝑖)

= 5 + 51.1

= 5 + 4.55 = 9.55

This is the maximum possible consumption in period 1 (x-axis intercept).

(ii) y-axis intercept

And, if all is saved in period 1, it grows by 10%, so we have:

Total funds in period 2=𝑦1(1 + 𝑖) + 𝑦2 = 5 × (1.1) + 5 = 10.5

***&***

Adding the choice line will show the subjective ‘discount rate’ (rate of patience: how the person compares future and present).

All life-time income consumed in period 2 through saving

The intersections with axis are extreme cases where all real life time income is spend either on

consumption in period 1 (funds equal the Present Value of income in period 2 is borrowed and

and consumed in period 1) is or it is all save for period 2 (no consumption in period 1).

0 1 2 3 4 5 6 7 8 9 10 110

2

4

6

8

10

12

C1

C2

Budget Constraint Slope is –(1+i)= -1.1

No saving and no borrowing: 𝒚𝟏 =𝒄𝟏 & 𝒚𝟐 = 𝒄𝟐

All life-time income consumed in period 1 through borrowing

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**&**

Choice and ‘Relative Price’

Supposing that the income of the decision maker is m and the prices are C1 and C2, respectively,

the equation of a budget line is:

𝑃1𝐶1 + 𝑃2𝐶2 = 𝑚

Consider the choice/ budget line figure below.

The budget line tells you about what is attainable to the decision maker (here representative

agent) given prices and his income. If all his income is spent on good 1 (C1), the decision is

characterised by the intersection of the budget constraint (line: budget line or budget constraint

means that same) with the x-axis.

Supposing that the income of the decision maker is m and the prices are C1 and C2, respectively,

we have:

𝐶1 =𝑚𝑝1

& 𝐶2 = 0

0 1 2 3 4 5 6 7 8 9 10 110

2

4

6

8

10

12

C1

C2

ECON3301-Fall 2011 SMU-Sobey SB

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Likewise, all his income is spent on good 2 (C2), the decision is characterised by the intersection

of the budget constraint (budget line: budget line or budget constraint means that same) with the

y-axis.

𝐶1 = 0 & 𝐶2 =𝑚𝑝2

The points in between are the less extreme combinations (𝑪𝟏 ≠ 𝟎 𝒂𝒏𝒅 𝑪𝟐 ≠ 𝟎).

The blue line (that I called choice-line and it is valid for Cobb-Douglass preferences)

characterises the decision makers’ preferred combination for C1 and C2, for any given budget

constraint (m and P1 and P2).

Basically, it assumes a constant share of the two goods of the decision makers’ income. In our

Basic Dynamic (Static) General Equilibrium model, it can be interpreted as ‘saving ratio.

Application

Below, there are the important points for the application of the model using the figure.

1. The slope and y-axis intercept

The slope of the budget line is the relative price of the two goods.

𝑃1𝐶1 + 𝑃2𝐶2 = 𝑚 ⤇ 𝑃2𝐶2 = 𝑚 − 𝑃1𝐶1 ⤇ 𝐶2 = 𝑚 − 𝑃2𝐶2 ⤇ 𝐶2 =𝑚𝑃2−𝑃1𝑃2

𝐶1

Given that C2 s the y-axis variable and C2 is the x-axis variable, 𝑚𝑃2

is the y-axis intercept and

𝑃1𝑃2

is the slope.

You see that the slope is the ration of Price of Good1 to Price of Good 2: 𝑃1𝑃2

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2. The choice line

The choice-line passes throughout the origin and the slope of the choice line is the ratio of

Income Spent on Good 2/Income Spent on Good 1.

For instance, if the income is divided 50-50, the slope will be 1.

3. Impact of change in prices in budget line

With the changes in prices the Budget line will rotate around the point of no-saving (in Dynamic

GE).

No-saving means when all the income of period 1 in consumed in Period 1 and all the income of

period 2 is consumed in Period 2.

Recall that the slope has been 𝑃1𝑃2

, so for instance, with any increase in P1, then 𝑃1𝑃2

↑ and the

Budget line becomes steeper. Likewise, if P2 falls, 𝑃1𝑃2

𝑖𝑛𝑐𝑟𝑒𝑠𝑒𝑠 𝑎𝑛𝑑 the budget line becomes

steeper too.

4. Impact of change in prices on choice.

Income Effect:

Income effect (IE) is the change in ‘overall’ purchasing power as a result of change in any price.

If you are a seller (producer) of the good whose price has increased, the income effect is positive for you. It is like you become richer and as a result, you can consume more of all goods you have been consuming.

If you are a buyer (consumer) of the good whose price has increased, the income effect is negative for you. It is like you become poorer and as a result, you can consume less of all goods you have been consuming. (e.g. when your rent goes up it is like you are becoming poorer).

Substitution Effect:

Substitution affect (SE), is the reallocation of funds among goods by switching to the cheaper goods, as much as possible (given the tastes and the degree of substitution for the kind of goods.

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i.e. the degree of substitution is high for markers of different color; much lower for consumption is different periods).

Application to Dynamic General Equilibrium

The only particularity of the use of this model is to us the appropriate Relative Price.

If we have two-period and the interest rate is i, then 1 unit of Good in present becomes 1+i

Good in future.

It means that the same purchasing power can buy One Unit Of C1 and (1+i) Units of C2. It

means that if 𝑃1 = 1 then 𝑃2 = 11+𝑖

(it only makes sense that P2 is smaller than P1: it means that

C2 is cheaper and it is always to happen when we discount future).

So, if 𝑃1 = 1 and 𝑃2 = 11+𝑖

then 𝑃1𝑃2

= 111+𝑖�

= 1 + 𝑖

Therefore, the slope of the Inter-temporal Budget Constraint is –(1+i) .

Recall that for the static Budget constraint, is was -1 (for it was the same good to be consumed or

saved, hence its price was the same).

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An example: 𝒊 ↑ The read line is the initial Budget Constraint. (i) If 𝒊 ↑ 𝒕𝒉𝒆𝒏 𝟏 + 𝒊 ↑ ⤇ Budget Constraint becomes Steeper (the green line). All life-time income consumed in period 2 through saving

The intersections with axis are extreme cases where all real life time income is spend either on

consumption in period 1 (funds equal the Present Value of income in period 2 is borrowed and

consumed in period 1) is or it is all save for period 2 (no consumption in period 1).

(ii) The choice

The chance in interest rate, i, is a change in Price so it generates Income Effect and Substitution

Effect.

As the increase in i, in here happens to a borrower (as his choice on the red line shows

consuming less than his income in period 1. So we have:

Income Effect is Negative ⤇ C1↓ and C2↓

Substitution Effect: Relative Price = 1+i

As the Relative Price of Good 1 (that is 1+i) then C1 falls: C1 ↓

As the Relative Price of Good 2 (that is 1/1+i) falls then C2 goes up: C2↑

0 1 2 3 4 5 6 7 8 9 10 11 12 130

2

4

6

8

10

12

C1

C2

Budget Constraint Slope is –(1+i)= -1.1

No saving and no borrowing: 𝒚𝟏 =𝒄𝟏 & 𝒚𝟐 = 𝒄𝟐

All life-time income consumed in period 1 through borrowing

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The Overall Impact is then a sure in C1 (he person will save more) and ambiguous effects of C2, it depends on the magnitude of IE and SE.

**&**

0 1 2 3 4 5 6 7 8 9 10 11 12 130

2

4

6

8

10

12

C1

C2

Budget Constraint Slope is –(1+i)= -1.1

No saving and no borrowing: 𝒚𝟏 =𝒄𝟏 & 𝒚𝟐 = 𝒄𝟐

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As an exercise, you can do the case of a Saver.

The figure will be:

As the Relative Price of Good 1 (that is 1+i) then C1 falls: C1 ↓

As the Relative Price of Good 2 (that is 1/1+i) falls then C2 goes up: C2↑

0 1 2 3 4 5 6 7 8 9 10 11 12 130

2

4

6

8

10

12

C1

C2

Budget Constraint Slope is –(1+i)= -1.1

No saving and no borrowing: 𝒚𝟏 =𝒄𝟏 & 𝒚𝟐 = 𝒄𝟐

ECON3301-Fall 2011 SMU-Sobey SB

Page 1 of 1

Chapter 7: Simple 2-period Model

(Preliminary to Basic Dynamic General Equilibrium Model)

Dr. Maryam Dilmaghani

The Model is dynamic

as it do involves time explicitly.

C1

C2

ECON3301 Fall 2011 SMU-Sobey SB

Page 1 of 10

ECON3301: Intermediate Macroeconomics

Instructor: Dr. Maryam Dilmaghani

Notes on Multi-period, Dynamic General Equilibrium (Chapter 8) The goal of this chapter is to finish the development for the RBC framework of Dynamic

General Equilibrium and use the model to explain economic fluctuations.

The basis of the model is the same as the 2-period model in chapter 7 and it makes use of a more

sophisticated version of Income and Substitution effect in drawing the predictions.

1. Application of Income and Substitution Effect to consumption decision

The representative agent’s initial budget constraint in depicted by the red-line:

𝐶1 + 𝐶2 × � 11+𝑖� = 𝑦1 + 𝑦2 × � 1

1+𝑖� ⤇ 𝐶2 = (1 + 𝑖) × 𝑦1 + 𝑦2 − 𝐶1 × (1 + 𝑖)

𝐶2 = [(1 + 𝑖) × 𝑦1 + 𝑦2] − (1 + 𝑖) × 𝐶1

The y-axis intercept is [(1 + 𝑖) × 𝑦1 + 𝑦2]. The slope is −(1 + 𝑖).

Suppose interest rate, i, goes up. Given the position of income the two periods, the green line is the new budget constraint: clockwise rotation around endowment (no saving, no borrowing) point.

C1

C2

𝒚𝟏 & 𝒚𝟐

𝑪𝟏 & 𝑪𝟐

ECON3301 Fall 2011 SMU-Sobey SB

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Answer the following questions.

(i) What can you tell about the representative agents new choice (under the green budget

constraint) given the position of 𝑪𝟏 & 𝑪𝟐 and if 𝑺𝑬 > 𝑰𝑬.

Given that the figure shows𝑦1 > 𝐶1 (& 𝑦2 < 𝐶2), this agent is a saver. For a saver the IE of an

increase in interest rate is positive. Positive IE means an increase in purchasing power and as a

result the consumption of both goods increase

The interest rate has increased. It means that the relative price of consumption in period 1,

𝐶1, has increased: the opportunity cost of 𝐶1 is higher; since through saving, it can now buy a

larger amount of consumption in the future, 𝐶2).

Therefore:

𝐼𝐸 𝑖𝑠 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒 ⤇ 𝐶1 ↑ & 𝑎𝑛𝑑 𝐶2 ↑

𝑆𝐸 𝑜𝑓 𝑖 ↑ ⤇ 𝐶1 ↓ 𝑎𝑛𝑑 𝐶2 ↑

Hence, Total Effect on 𝑪𝟐 ↑ but in 𝑪𝟏 ↓ (SINCE

𝑆𝐸 > 𝐼𝐸).

C1

C2𝑵𝒆𝒘 𝑪𝟏 & 𝑪𝟐

ECON3301 Fall 2011 SMU-Sobey SB

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(ii) What can you tell about the representative agents new choice (under the green budget constraint) given the position of 𝑪𝟏 & 𝑪𝟐 and if 𝑰𝑬 > 𝑺𝑬.

You can do it yourself as an exercise.

2. Markets involved

(i) Goods Market

(ii) Labour Market

(iii) ‘Investment’ Market: Bonds Market (financial investment) & Rental Market (investment

physical capital) combined.

3. Endogenous variables

They are, as usual, price and quantity in each market.

(i) Goods Market: output and price of output, denoted by P.

(ii) Labour Market: employment level and wage, denoted by W.

(iii) ‘Investment’ Markets: Bonds Market (financial investment) & Rental Market (investment

physical capital): rate of return on investments or Interest Rate

.

3. Exogenous variables

There are two categories of Exogenous Variables in this model:

(i) Technology (Supply-side of the Goods’ market)

It refers to the productivity of the inputs (the parameters of the production function). Typically,

two different types of technological progress are considered.

ECON3301 Fall 2011 SMU-Sobey SB

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(i)-1: The technological change can affect only the total output (parallel shift of production

function:

For a progress, we need to have B> 0, 𝑡ℎ𝑒 𝑓𝑖𝑔𝑢𝑟𝑒 𝑖𝑠 𝑏𝑒𝑙𝑜𝑤.

In this case both MPL and MPK remain the same.

Mathematics, fyi:

𝑌𝑜𝑙𝑑 = 𝐹(𝐿,𝐾) = 𝐴𝐿𝛼𝐾𝛽 ⤇ 𝑀𝑃𝐿𝑜𝑙𝑑 = 𝐴𝐾𝛽 × (𝛼) × 𝐿𝛼−1 = �𝐴𝐾𝛽 × (𝛼)� × 𝐿𝛼−1

𝑌𝑛𝑒𝑤 = 𝐹(𝐿,𝐾) + 𝐵 = �𝐴𝐿𝛼𝐾𝛽� + 𝐵 ⤇ 𝑀𝑃𝐿𝑛𝑒𝑤 = 𝐴𝐾𝛽 × (𝛼) × 𝐿𝛼−1 = �𝐴𝐾𝛽 × (𝛼)� × 𝐿𝛼−1

So, you see that: 𝑀𝑃𝐿𝑜𝑙𝑑 = 𝑀𝑃𝐿𝑛𝑒𝑤

The same happens to MPK (no change).

(i)-2: it can affect Marginal Product of Inputs (proportionate shift of production function):

Total output, 𝑌 = 𝐴𝐹(𝐾, 𝐿) ⤇ 𝑁𝑒𝑤 𝑜𝑢𝑡𝑝𝑢𝑡 𝑌𝑁𝑒𝑤 = (𝐴 × 𝜀) × 𝐹(𝐾, 𝐿)

For a progress, we need to have ε> 1, 𝑡ℎ𝑒 𝑓𝑖𝑔𝑢𝑟𝑒 𝑖𝑠 𝑏𝑒𝑙𝑜𝑤.

K/L

Y/L

ECON3301 Fall 2011 SMU-Sobey SB

Page 5 of 10

And Marginal Products (MPL & MPK)

K/L

Y/L

Labour

MPL

Capital

MPK

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Mathematics, fyi:

𝑌𝑜𝑙𝑑 = 𝐹(𝐿,𝐾) = 𝐴𝐿𝛼𝐾𝛽 ⤇ 𝑀𝑃𝐿𝑜𝑙𝑑 = 𝐴𝐾𝛽 × (𝛼) × 𝐿𝛼−1 = �𝐴𝐾𝛽 × (𝛼)� × 𝐿𝛼−1

𝑌𝑛𝑒𝑤 = 𝐹(𝐿,𝐾) × 𝜀 = �𝐴𝐿𝛼𝐾𝛽� × 𝜀 ⤇

𝑀𝑃𝐿𝑛𝑒𝑤 = 𝜀 × 𝐴𝐾𝛽 × (𝛼) × 𝐿𝛼−1 = 𝜀 × �𝐴𝐾𝛽 × (𝛼)�× 𝐿𝛼−1

So, you see that: 𝑀𝑃𝐿𝑜𝑙𝑑 < 𝑀𝑃𝐿𝑛𝑒𝑤 and it translates itself to a rightward shift.

The same happens to MPK .

(ii) Preferences (Demand-side of the Goods’ market)

(ii)-1: Subjective rate of patience

Note that 𝑙1 + 𝑧1 = 𝑇𝑜𝑡𝑎𝑙 𝑡𝑖𝑚𝑒 𝑎𝑣𝑎𝑖𝑙𝑎𝑏𝑙𝑒 𝑡𝑜 𝑡ℎ𝑒 𝑎𝑔𝑒𝑛𝑡 𝑖𝑛 𝑝𝑒𝑟𝑖𝑜𝑑 1.

(propensity to consume (or save) in period 1 compared to

period 2; i.e. how to divide the present value of life time income among 𝑐1 & 𝑐2 & 𝑐3...

(consumption in different periods) and how to allocate time for leisure (whose opportunity costs

is forgone wage) among different periods; i.e. the decision about the level of 𝑧1, 𝑧2, 𝑧3 … .

This exogenous variable (parameter of preferences) determines Inter-temporal Substitution

Effect

(ii)-2: The taste (preference) over leisure and consumption. It informs of how an agent is willing

to substitute leisure (consumption) for consumption (leisure) in the same period while achieving

the same level of satisfaction (utility).

This exogenous variable (parameter of preferences) determines Intra-temporal Substitution

Effect.

4. The duration of the exogenous changes: Permanent or Temporary

All the exogenous variables can change in a permanent or temporary manner. The impact of a

permanent change is larger than a temporary change in its magnitude. It can for instance help

assuming whether IE is larger or smaller than SE.

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Application of Multi-period Dynamic General Equilibrium Model

A. Preliminaries

The goal is to use MDGE to understand the impact of exogenous changes on endogenous

variables. The main exogenous variable considered is Technological Change.

Taking the Goods Market

(i) Producers: They are the supply-side of the Goods Market. Their objective is to maximize

their Profit. In order to maximise their profit, they choose the level of inputs the want to hire

given the productivity (affected by the abstract concept of technology) and other variables (price

–cost- of inputs and price of output).

as the benchmark, he actors in this model can be put into two

categories:

Recall that 𝐿𝑎𝑏𝑜𝑢𝑟 − 𝐷𝑒𝑚𝑎𝑛𝑑: 𝐿𝑑 = 𝑀𝑃𝐿 & 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 − 𝐷𝑒𝑚𝑎𝑛𝑑: 𝐾𝑑 = 𝑀𝑃𝐾

Technological change may affect MPL and MPK hence labour and capital demand.

(ii) Consumers: They are the demand-side of the Goods Market. Their objective is to maximize

their Utility (satisfaction). Their utility comes from Consumption and Leisure and it incorporates

the agents’ time-preference (patience) and the preferences and taste over Consumption & Leisure

(the contribution of each to their satisfaction).

In order to maximise their utility hence, they must decide how to allocate the present value (PV)

of their life-time budget (we actually assume that the representative agent lives forever,

abstracting from consideration the replacement of generations by one another). It can e

summarise as follows:

1) Given their rate of patience (subjective discount rate) as well as their income and prices

(future and current) they decide on their pattern of consumption (𝐶1,𝐶2,𝐶3, … ) and leisure

𝑍1,𝑍2,𝑍3, … ) overtime.

ECON3301 Fall 2011 SMU-Sobey SB

Page 8 of 10

This decision is affected by Income Effect (IE) as well as Inter-temporal Substitution Effect

(Inter-SE).

2) Given their taste & preference for consumption and leisure as well as their income and prices

(current & future) they decide on the pattern of consumption and leisure in every given period:

(𝐶1,𝑍1), (𝐶2,𝑍2), (𝐶3,𝑍3),... .

This decision is affected by Income Effect (IE) as well as Intra-temporal Substitution Effect

(Intra-SE).

The consumption decision determines savings hence Supply of Capital, 𝐾𝑆, and the decision of

leisure determined Labour Supply, 𝐿𝑆.

B. Application

Case 1: Proportionate and Permanent Technological Progress.

Recall that a proportionate shift of production function is characterised by an upward shift of

production function is in below:

Total output, 𝑌 = 𝐴𝐹(𝐾, 𝐿) ⤇ 𝑁𝑒𝑤 𝑜𝑢𝑡𝑝𝑢𝑡 𝑌𝑁𝑒𝑤 = (𝐴 × 𝜀) × 𝐹(𝐾, 𝐿) with ε> 1

And Marginal Products (MPL & MPK) shifts rightward.

K/L

Y/L

ECON3301 Fall 2011 SMU-Sobey SB

Page 9 of 10

Step 1: Goods Market

(i) Supply-side

(i)-1: Technological Progress ⤇ Output ↑⤇ All else equal, Price (P) ↓

(i)-2: MPL↑ & MPK ↑⤇ 𝐿𝑑 𝑠ℎ𝑖𝑓𝑡 𝑟𝑖𝑔ℎ𝑡 & 𝐾𝑑 𝑠ℎ𝑖𝑓𝑡𝑠 𝑟𝑖𝑔ℎ𝑡𝑤𝑎𝑟𝑑.

The shifts in MPL and MPK are forever

(because the technological change is permanent).

(ii) Demand-side

As P ↓⤇𝑊𝑃

↑ ⤇ it generates both Income and Substitution Effect.

(ii)-1: Income Effect (IE) is positive ⤇ The agent can have more of both consumption and

leisure, forever. It means 𝐶𝑡 ↑ (𝑆𝑡 ↓) 𝑎𝑛𝑑 𝑍𝑡 ↑ (𝐿𝑡 ↓)𝑓𝑜𝑟 𝑎𝑙𝑙 𝑡, by IE.

Note that the t subscript indicates the period of time.

(ii)-2: Intra-temporal Substitution Effect (Intra-SE)

𝑊𝑃

↑ ⤇ The opportunity cost of leisure ↑⤇ 𝐶𝑡is now cheaper relative to 𝑍𝑡⤇ 𝐶𝑡↑ (𝑆𝑡 ↓) and

𝑍𝑡 ↓ (𝐿𝑡 ↑) in every given period, by Intra-SE.

(ii)-3: Inter-temporal Substitution Effect (Inter-SE) does NOT exist.

As the change is permanent, all the periods in future are identical, hence it does not make sense to have different patterns (a permanent change, as a rule, does not generate Inter-temporal Substitution Effect).

Hence, Total Effect on Labour Demand demands on the relative magnitude of IE (𝐿𝑡 ↓) and Intra-SE (𝐿𝑡 ↑).

If we suppose that 𝐼𝐸 > 𝐼𝑛𝑡𝑟𝑎 − 𝑆𝐸, then 𝐿𝑡 ↓ and 𝐿𝑑 shifts to the left, otherwise it shifts rightward.

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Step 2: Labour Market

Now, we just need to put supply and demand together and see what happens to the equilibrium real wage,�𝑊

𝑃�∗, and equilibrium level of employment, 𝐿∗.

Old curves: Dash

New Curves: Solid

The magnitude of shifts are assumed (they can be larger or smaller). As we see that both �𝑊𝑃�∗↑

and 𝐿∗ ↑. It means that Real Wage increases and the level of employment rises.

Question:

Can a Permanent and Proportionate Technological Change cause Real Wage to fall? Explain.

Can a Permanent and Proportionate Technological Change cause Level of Employment to fall? Explain.

Labour

W/P

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ECON3301: Intermediate Macroeconomics

Instructor: Dr. Maryam Dilmaghani

Notes on Multi-period, Dynamic General Equilibrium (Chapter 8) The goal of this chapter is to finish the development for the RBC framework of Dynamic

General Equilibrium and use the model to explain economic fluctuations.

The basis of the model is the same as the 2-period model in chapter 7 and it makes use of a more

sophisticated version of Income and Substitution effect in drawing the predictions.

1. Application of Income and Substitution Effect to consumption decision

The representative agent’s initial budget constraint in depicted by the red-line:

𝐶1 + 𝐶2 × � 11+𝑖� = 𝑦1 + 𝑦2 × � 1

1+𝑖� ⤇ 𝐶2 = (1 + 𝑖) × 𝑦1 + 𝑦2 − 𝐶1 × (1 + 𝑖)

𝐶2 = [(1 + 𝑖) × 𝑦1 + 𝑦2] − (1 + 𝑖) × 𝐶1

The y-axis intercept is [(1 + 𝑖) × 𝑦1 + 𝑦2]. The slope is −(1 + 𝑖).

Suppose interest rate, i, goes up. Given the position of income the two periods, the green line is the new budget constraint: clockwise rotation around endowment (no saving, no borrowing) point.

C1

C2

𝒚𝟏 & 𝒚𝟐

𝑪𝟏 & 𝑪𝟐

ECON3301 Fall 2011 SMU-Sobey SB

Page 2 of 7

Answer the following questions.

(i) What can you tell about the representative agents new choice (under the green budget

constraint) given the position of 𝑪𝟏 & 𝑪𝟐 and if 𝑺𝑬 > 𝑰𝑬.

Given that the figure shows𝑦1 > 𝐶1 (& 𝑦2 < 𝐶2), this agent is a saver. For a saver the IE of an

increase in interest rate is positive. Positive IE means an increase in purchasing power and as a

result the consumption of both goods increase

The interest rate has increased. It means that the relative price of consumption in period 1,

𝐶1, has increased: the opportunity cost of 𝐶1 is higher; since through saving, it can now buy a

larger amount of consumption in the future, 𝐶2).

Therefore:

𝐼𝐸 𝑖𝑠 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒 ⤇ 𝐶1 ↑ & 𝑎𝑛𝑑 𝐶2 ↑

𝑆𝐸 𝑜𝑓 𝑖 ↑ ⤇ 𝐶1 ↓ 𝑎𝑛𝑑 𝐶2 ↑

Hence, Total Effect on 𝐶2 ↑ but in 𝐶1 ↓ SINCE

𝑆𝐸 > 𝐼𝐸.

C1

C2𝑵𝒆𝒘 𝑪𝟏 & 𝑪𝟐

ECON3301 Fall 2011 SMU-Sobey SB

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(ii) What can you tell about the representative agents new choice (under the green budget constraint) given the position of 𝑪𝟏 & 𝑪𝟐 and if 𝑰𝑬 > 𝑺𝑬.

You can do it yourself as an exercise.

2. Markets involved

(i) Goods Market

(ii) Labour Market

(iii) ‘Investment’ Markets: Bonds Market (financial investment) & Rental Market (investment

physical capital) combined.

3. Endogenous variables

They are, as usual, price and quantity in each market.

(i) Goods Market: output and price of output, denoted by P.

(ii) Labour Market: employment level and wage, denoted by W.

(iii) ‘Investment’ Markets: Bonds Market (financial investment) & Rental Market (investment

physical capital): rate of return on investments or Interest Rate

.

3. Exogenous variables

There are two categories of Exogenous Variables in this model:

(i) Technology (Supply-side of the Goods’ market)

It refers to the productivity of the inputs (the parameters of the production function). Typically,

two different types of technological progress are considered.

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(i)-1: The technological change can affect only the total output (parallel shift of production

function:

For a progress, we need to have B> 0, 𝑡ℎ𝑒 𝑓𝑖𝑔𝑢𝑟𝑒 𝑖𝑠 𝑏𝑒𝑙𝑜𝑤.

In this case both MPL and MPK remain the same.

Mathematics, fyi:

𝑌𝑜𝑙𝑑 = 𝐹(𝐿,𝐾) = 𝐴𝐿𝛼𝐾𝛽 ⤇ 𝑀𝑃𝐿𝑜𝑙𝑑 = 𝐴𝐾𝛽 × (𝛼) × 𝐿𝛼−1 = �𝐴𝐾𝛽 × (𝛼)� × 𝐿𝛼−1

𝑌𝑛𝑒𝑤 = 𝐹(𝐿,𝐾) + 𝐵 = �𝐴𝐿𝛼𝐾𝛽� + 𝐵 ⤇ 𝑀𝑃𝐿𝑛𝑒𝑤 = 𝐴𝐾𝛽 × (𝛼) × 𝐿𝛼−1 = �𝐴𝐾𝛽 × (𝛼)� × 𝐿𝛼−1

So, you see that: 𝑀𝑃𝐿𝑜𝑙𝑑 = 𝑀𝑃𝐿𝑛𝑒𝑤

The same happens to MPK (no change).

(i)-2: it can affect Marginal Product of Inputs (parallel shift of production function:

Total output, 𝑌 = 𝐴𝐹(𝐾, 𝐿) ⤇ 𝑁𝑒𝑤 𝑜𝑢𝑡𝑝𝑢𝑡 𝑌𝑁𝑒𝑤 = (𝐴 × 𝜀) × 𝐹(𝐾, 𝐿)

For a progress, we need to have ε> 1, 𝑡ℎ𝑒 𝑓𝑖𝑔𝑢𝑟𝑒 𝑖𝑠 𝑏𝑒𝑙𝑜𝑤.

K/L

Y/L

ECON3301 Fall 2011 SMU-Sobey SB

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And Marginal Products (MPL & MPK)

K/L

Y/L

Labour

MPL

Capital

MPK

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Mathematics, fyi:

𝑌𝑜𝑙𝑑 = 𝐹(𝐿,𝐾) = 𝐴𝐿𝛼𝐾𝛽 ⤇ 𝑀𝑃𝐿𝑜𝑙𝑑 = 𝐴𝐾𝛽 × (𝛼) × 𝐿𝛼−1 = �𝐴𝐾𝛽 × (𝛼)� × 𝐿𝛼−1

𝑌𝑛𝑒𝑤 = 𝐹(𝐿,𝐾) × 𝜀 = �𝐴𝐿𝛼𝐾𝛽� × 𝜀 ⤇

𝑀𝑃𝐿𝑛𝑒𝑤 = 𝜀 × 𝐴𝐾𝛽 × (𝛼) × 𝐿𝛼−1 = 𝜀 × �𝐴𝐾𝛽 × (𝛼)�× 𝐿𝛼−1

So, you see that: 𝑀𝑃𝐿𝑜𝑙𝑑 < 𝑀𝑃𝐿𝑛𝑒𝑤 and it translates itself to a rightward shift.

The same happens to MPK .

(ii) Preferences (Demand-side of the Goods’ market)

(ii)-1: Subjective rate of patience

Note that 𝑙1 + 𝑧1 = 𝑇𝑜𝑡𝑎𝑙 𝑡𝑖𝑚𝑒 𝑎𝑣𝑎𝑖𝑙𝑎𝑏𝑙𝑒 𝑡𝑜 𝑡ℎ𝑒 𝑎𝑔𝑒𝑛𝑡 𝑖𝑛 𝑝𝑒𝑟𝑖𝑜𝑑 1.

(propensity to consume (or save) in period 1 compared to

period 2; i.e. how to divide the present value of life time income among 𝑐1 & 𝑐2 & 𝑐3...

(consumption in different periods) and how to allocate time for leisure (whose opportunity costs

is forgone wage) among different periods; i.e. the decision about the level of 𝑧1, 𝑧2, 𝑧3 … .

This exogenous variable (parameter of preferences) determines Inter-temporal Substitution

Effect

(ii)-2: The taste (preference) over leisure and consumption. It informs of how an agent is willing

to substitute leisure (consumption) for consumption (leisure) in the same period while achieving

the same level of satisfaction (utility).

This exogenous variable (parameter of preferences) determines Intra-temporal Substitution

Effect.

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4. The duration of the exogenous changes: Permanent or Temporary

All the exogenous variables can change in a permanent or temporary manner. The impact of a

permanent change is larger than a temporary change in its magnitude. It can for instance help

assuming whether IE is larger or smaller than SE.

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ECON3301: Intermediate Macroeconomics

Instructor: Dr. Maryam Dilmaghani

Notes on Multi-period, Dynamic General Equilibrium (Chapter 9)

The goal of this chapter is to finish the development for the RBC framework of Dynamic

General Equilibrium and use the model to explain economic fluctuations in Goods Market,

Labour Market and Capital Market.

A. Review of the general points

The goal is to use MDGE to understand the impact of exogenous changes on endogenous

variables. The main exogenous variable considered is Technological Change.

Taking the Goods Market

(i) Producers: They are the supply-side of the Goods Market. Their objective is to maximize

their Profit. In order to maximise their profit, they choose the level of inputs the want to hire

given the productivity (affected by the abstract concept of technology) and other variables (price

–cost- of inputs and price of output).

as the benchmark, he actors in this model can be put into two

categories:

Recall that 𝐿𝑎𝑏𝑜𝑢𝑟 − 𝐷𝑒𝑚𝑎𝑛𝑑: 𝐿𝑑 = 𝑀𝑃𝐿 & 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 − 𝐷𝑒𝑚𝑎𝑛𝑑: 𝐾𝑑 = 𝑀𝑃𝐾

Technological change may affect MPL and MPK hence labour and capital demand.

(ii) Consumers: They are the demand-side of the Goods Market. Their objective is to maximize

their Utility (satisfaction). Their utility comes from Consumption and Leisure and it incorporates

the agents’ time-preference (patience) and the preferences and taste over Consumption & Leisure

(the contribution of each to their satisfaction).

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In order to maximise their utility hence, they must decide how to allocate the present value (PV)

of their life-time budget (we actually assume that the representative agent lives forever,

abstracting from consideration the replacement of generations by one another). It can e

summarise as follows:

1) Given their rate of patience (subjective discount rate) as well as their income and prices

(future and current) they decide on their pattern of consumption (𝐶1,𝐶2,𝐶3, … ) and leisure

𝑍1,𝑍2,𝑍3, … ) overtime.

This decision is affected by Income Effect (IE) as well as Inter-temporal Substitution Effect

(Inter-SE).

2) Given their taste & preference for consumption and leisure as well as their income and prices

(current & future) they decide on the pattern of consumption and leisure in every given period:

(𝐶1,𝑍1), (𝐶2,𝑍2), (𝐶3,𝑍3),... .

This decision is affected by Income Effect (IE) as well as Intra-temporal Substitution Effect

(Intra-SE).

The consumption decision determines savings hence Supply of Capital, 𝐾𝑆, and the decision of

leisure determined Labour Supply, 𝐿𝑆.

B. Application

Case 1: Proportionate and Permanent Technological Progress:

Note: We focus on Capital market for now.

Recall that a proportionate shift of production function is characterised by an upward shift of

production function is in below:

Total output, 𝑌 = 𝐴𝐹(𝐾, 𝐿) ⤇ 𝑁𝑒𝑤 𝑜𝑢𝑡𝑝𝑢𝑡 𝑌𝑁𝑒𝑤 = (𝐴 × 𝜀) × 𝐹(𝐾, 𝐿) with ε> 1

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And Marginal Products (MPL & MPK) shift rightward.

Step 1: Goods Market

(i) Supply-side

(i)-1: Technological Progress ⤇ Output ↑⤇ All else equal, Price (P) ↓

(i)-2: MPK ↑⤇ 𝐾𝑑 𝑠ℎ𝑖𝑓𝑡𝑠 𝑟𝑖𝑔ℎ𝑡𝑤𝑎𝑟𝑑.

The shift MPK is forever

(ii) Demand-side

(because the technological change is permanent).

As P ↓⤇𝑅𝑃

↑ ⤇ it generates both Income and Substitution Effect.

(ii)-1: Income Effect (IE) is positive ⤇ The agent can have more of both consumption and

leisure, forever. It means 𝑪𝒕 ↑ 𝒂𝒏𝒅 𝑺𝒕 ↓ 𝐛𝐲 𝐈𝐄.

𝐴𝑙𝑠𝑜: 𝑎𝑛𝑑 𝑍𝑡 ↑ (𝐿𝑡 ↓)𝑓𝑜𝑟 𝑎𝑙𝑙 𝑡 (∀𝑡).

Note that ∀𝑡 mean for all periods of time (forever).

(ii)-2: Intra-temporal Substitution Effect (Intra-SE)

K/L

Y/L

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Recall: The trade-off involved with Intra-SE is to compare the sources of utility (satisfaction) in

each period with each other, i.e. 𝐶1 𝑤𝑖𝑡ℎ 𝑍1 ,𝐶2𝑤𝑖𝑡ℎ 𝑍2 …, taking into account their

(opportunity) cost.

𝑃 ↓⤇ 𝑊𝑃

↑ ⤇ The opportunity cost of leisure ↑ ⤇ 𝐶𝑡is now cheaper relative to 𝑍𝑡⤇ 𝑪𝒕↑ and

𝑺𝒕 ↓ 𝒃𝒚 𝑰𝒏𝒕𝒓𝒂 − 𝑺𝑬.

(Also: 𝑍𝑡 ↓ (𝐿𝑡 ↑) in every given period, by Intra-SE; but here we ignore labour market).

(ii)-3: Inter-temporal Substitution Effect (Inter-SE) does NOT exist.

As the change is permanent, all the periods in future are identical, hence it does not make sense to have different patterns (a permanent change, as a rule, does not generate Inter-temporal Substitution Effect).

Hence,

Total Effect on Capital Supply is negative, meaning a shift to the left.

Step 2: Capital Market

Now, we just need to put supply and demand together and see what happens to the equilibrium real rental rate,�𝑊

𝑃�∗, and equilibrium level of physical capital, 𝐾∗.

Old curves: Dash

New Curves: Solid

The magnitude of shifts are assumed (they can be larger or smaller). As we see that both �𝑅𝑃�∗↑

and 𝐾∗ ↑. It means that Real Rental Rate increases and the level of physical capital investment rises as well.

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Questions:

Can a Permanent and Proportionate Technological Change cause Real Rental Rate �𝑅𝑃�∗ to fall?

Explain how and comment.

Can a Permanent and Proportionate Technological Change cause Level of Physical Investment (𝐾∗) to fall? Explain how and comment.

Capital

R/P

ECON3301-Fall 2011 SMU-Sobey SB

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Notes on Economic Growth in Canada

1. What is Economic Growth?

Economic growth is the increase of aggregate production in a given economy.

2. How can we measure Economic Growth?

Economic Growth is the increase of per capita gross domestic product (GDP) as a measure of

aggregate income. Usually, the annual rate of change in real GDP is taken as the indicator of the

annual rate of growth.

2.1. GDP as an indicator of economic growth

Gross domestic product (GDP) refers to the market value of all final goods and services

produced within a country in a given period. GDP per capita and its changes over time is often

considered an indicator of a country's standard of living and economic growth.

2.2. Measuring GDP

GDP can be determined in three ways, all of which should, in principle, give the same result.

They are the product (or output) approach, the income approach, and the expenditure approach.

The most direct of the three is the product approach, which sums the outputs of every class of

enterprise to arrive at the total. The expenditure approach works on the principle that all of the

product must be bought by somebody, therefore the value of the total product must be equal to

people's total expenditures in buying things.

The income approach works on the principle that the incomes of the productive factors

("producers," colloquially) must be equal to the value of their product, and determines GDP by

finding the sum of all producers' incomes.

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Example: the expenditure method:

GDP = Value of private consumption (C) + Value of gross investment (I) + Value of government spending (G) + Value of exports in national currency -imports

𝐺𝐷𝑃 = 𝐶 + 𝐼 + 𝐺 + 𝜀𝑋 −𝑀

Note:

"Gross" means that GDP measures production regardless of the various uses to which that

production can be put. Production can be used for immediate consumption, for investment in

new fixed assets or inventories, or for replacing depreciated fixed assets. "Domestic" means that

GDP measures production that takes place within the country's borders. In the expenditure-

method equation given above, the exports-minus-imports term is necessary in order to null out

expenditures on things not produced in the country (imports) and add in things produced but not

sold in the country (exports).

2.3. Shortcomings of GDP as an indicator of economic performance

Wealth distribution

Non-market transactions

Underground economy

Non-monetary economy

Quality improvements and inclusion of new products

3. Main factors behind Economics Growth

Economic growth is primarily driven by improvements in productivity, which involves

producing more goods and services with the same inputs of labour, capital, energy and materials.

4. Temporal Horizon for Measuring Economic Growth

The long-run path of economic growth is one of the central questions of economics; despite

some problems of measurement, an increase in GDP of a country greater than population growth

is generally taken as an increase in the standard of living of its inhabitants. Over long periods of

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time, even small rates of annual growth can have large effects through compounding (see

exponential growth).

A growth rate of 2.5% per annum will lead to a doubling of GDP within 29 years, whilst a

growth rate of 8% per annum (experienced by some Four Asian Tigers) will lead to a doubling of

GDP within 10 years. This exponential characteristic can exacerbate differences across nations.

5. Short-run versus long-run considerations

Economists draw a distinction between short-term economic stabilization and long-term economic

growth. The topic of economic growth is primarily concerned with the long run. The short-run variation

of economic growth is termed the business cycle.

6. Principal Theories of Economic Growth

6.1.Exogenous growth model (Solow–Swan growth model) 6.2.Ramsey-Cass-Koopmans model

The Ramsey model differs from the Solow model in that it explicitly models the choice of consumption at a point in time and so endogenizes the saving rate.

6.3.Endogenous growth theory

In economics, endogenous growth theory or new growth theory was developed in the 1980s as

a response to criticism of the neo-classical growth model. The endogenous growth theory holds

that policy measures can have an impact on the long-run growth rate of an economy. For

example, subsidies on research and development or education increase the growth rate in some

endogenous growth models by increasing the incentive to innovate.

In neo-classical growth models, the long-run rate of growth is exogenously determined by either

assuming a savings rate or a rate of technical progress (Solow model). However, the savings rate

and rate of technological progress remain unexplained. Endogenous growth theory tries to

overcome this shortcoming by building macroeconomic models out of microeconomic

foundations. Households are assumed to maximize utility subject to budget constraints while

firms maximize profits.

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Crucial importance is usually given to the production of new technologies and human capital.

The engine for growth can be as simple as a constant return to scale production function (the AK

model) or more complicated set ups with spillover effects (spillovers are positive externalities,

benefits that are attributed to costs from other firms), increasing numbers of goods, increasing

qualities, etc.

7. Economic Growth in Canada

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Notes on Taxation and Fiscal Policy

Instructor: Dr. Maryam Dilmaghani

1. Types of tax

1.1. Lump-sum taxes

A lump-sum tax is a tax that is a fixed amount, no matter the change in circumstance of the taxed entity. For instance, the tax-payer has to contribute $ 1000 yearly, regardless of her/his earnings, property’s value, production etc.

Lump-sum taxes do not react to the changes in those items either. Only the taxing entity (fiscal authority of government) can change them.

1.2. Proportionate taxes.

There taxes are a function of the value of the taxes item (e.g. output, added value, property, earnings).

2. Impact of tax within RBC framework

2.1. Lump-sum taxes

Lump-sum taxes are comparable to parallel shock technological shocks with starting or increasing (eliminating or reducing) a lump-sum tax is a negative (positive/progress) shock.

Hence, our previously developed General Equilibrium Model can be readily applied to these taxes.

Example: Imposing a lump-sum tax on producers, permanently. This tax is identical in impact to a parallel and permanent shock. We follow the same steps in the analysis.

2.1. Proportionate taxes

Proportionate taxes are comparable to proportionate shock technological shocks with starting or increasing (eliminating or reducing) a Proportionate taxes is a negative (positive/progress) shock.

Hence, our previously developed General Equilibrium Model can be readily applied to these taxes.

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Example: A lump-sum tax on producers, permanent

This tax is identical in impact to a proportionate and permanent negative shock. We follow the same steps in the analysis.

Recall that a parallel technological change can affect only the total output (parallel shift of

production function). For this kind of shock (𝑡ℎ𝑒 𝑓𝑖𝑔𝑢𝑟𝑒 𝑏𝑒𝑙𝑜𝑤), both MPL and MPK remain

the same.

.

Step 1: Goods Market

(i) Supply-side

(i)-1: Lump-sum tax ⤇ Output ↓⤇ All else equal, Price (P) ↑

(i)-2: MPL & MPK do not change⤇ 𝐿𝑑 & 𝐾𝑑 𝑑𝑜 𝑛𝑜𝑡 𝑠ℎ𝑖𝑓𝑡.

(ii) Demand-side

As P↑ ⤇𝑊𝑃

↓ ⤇ it generates both Income and Substitution Effect.

(ii)-1: Income Effect (IE) is negative ⤇ The agent will have to reduce both consumption

and leisure, forever. It means 𝐶𝑡 ↓ 𝑎𝑛𝑑 𝑍𝑡 ↓ (𝑳𝒕 ↑)𝒇𝒐𝒓 𝒂𝒍𝒍 𝒕, by IE.

K/L

Y/L

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(ii)-2: Intra-temporal Substitution Effect (Intra-SE)

𝑊𝑃

↓ ⤇ The opportunity cost of leisure ↓⤇ 𝐶𝑡is now more expensive relative to 𝑍𝑡⤇ 𝐶𝑡↓ and

𝑍𝑡 ↑(𝑳𝒕 ↓) in every given period, by Intra-SE.

(ii)-3: Inter-temporal Substitution Effect (Inter-SE) does NOT exist because the tax is permanent.

Recall that when the change is permanent, all the periods in future are identical, hence it does not make sense to have different patterns (a permanent change, as a rule, does not generate Inter-temporal Substitution Effect).

Labour Supply?

Hence, Total Effect on Labour Supply demands on the relative magnitude of IE (𝐿𝑡 ↑) and Intra-SE (𝐿𝑡 ↓).

If we suppose that 𝐼𝐸 > 𝐼𝑛𝑡𝑟𝑎 − 𝑆𝐸, then 𝐿𝑡 ↑ ∀𝑡 and 𝐿𝑠 shifts to the right, otherwise it shifts rightward.

Note:

Capital Supply?

It makes sense for a paramagnet change to assume IE dominates SE.

Important Note:

Step 2: Labour Market

As the change is permanent then there is no Intratemporal Substitution effect. Saving is reacting more strongly to Inter-temporal Substitution Effect, hence we can assume that it does not change hence 𝐾𝑠 remains unaffected.

Now, we just need to put supply and demand together and see what happens to the equilibrium real wage,�𝑊

𝑃�

∗, and equilibrium level of employment, 𝐿∗.

From the above, we know that MPL did not change so 𝐿𝑑 will not shift, and 𝐿𝑠 shifts to the right.

Old curves: Dash

New Curves: Solid

As we see that after this tax �𝑊𝑃

�∗

↓ and 𝐿∗ ↑. It means that Real Wage falls and the level of employment rises.

Note that Lump-sum taxes do not cause Economic Distortion is the markets (as opposed to proportionate taxes). Economic Distortion is the fall in the volume of transactions (Quantity) in

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a market (i.e. the quantity of goods sold 𝑄∗, the level of labour employed: 𝐿∗ etc) after a governmental intervention (e.g. tax or subsidy).

Step 3: Capital Market

Now, we need to put supply and demand together and see what happens to the equilibrium real wage,�𝑅

𝑃�

∗, and equilibrium level of employment, 𝐾∗.

From the above we know that as MPK did not change, 𝐾𝑑 does not shift and the shift in 𝐾𝑠 in negligible, if any since there in no Inter-temporal SE.

So, 𝑏𝑜𝑡ℎ �𝑅𝑃

�∗ and 𝐾∗ remain the same.

Again, note that Lump-sum taxes do not cause Economic Distortion is the markets (as opposed to proportionate taxes). Economic Distortion is the fall in the volume of transactions in a market after a governmental intervention (e.g. tax or subsidy).

You can try a Permanent and Proportionate (and other cases) following the same steps by noticing that its impact is identical to a Permanent and Proportionate reduction is productivity.

Labour

W/P

ECON3301 Fall 2011 SMU-Sobey SB

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Notes on Chapter 10: Monetary Policy

Instructor: Dr. Maryam Dilmaghani

1. Money Market Model

Endogenous variables: Quantity of money (in C$ for instance).

Nominal interest rate: i, in %.

To simplify, we assume that Money Supply curve is a vertical straight line (like we assumed in the beginning for Labour and Capital Supply).

The justification in this case is that the quantity of Money Supply is fixed by Monetary Policy central banks).

The Money Demand curve is assumed to be a normal downward sloping curve.

The equilibrium quantity of money and nominal interest rate is the intersection of Supply and Demand.

Quantity of Money

i

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1. Monetary Expansion & other markets

Monetary expansion is increasing Money Supply. Usually, the goal of such policy is to stimulate economy.

With a monetary expansion, Money Supply curve (𝑀𝑠), shifts rightward. The equilibrium quantity of money (𝑀∗) rises, and nominal interest rate (𝑖∗) falls.

1. Relating Money Market to other markets

To relate Money Market to other markets we must make use of No Arbitrage Principle.

NAP postulates that in free, inter-related markets (like in RBC) the rate of return on all investments must be the same in the equilibrium.

The principle relies on the assumption of rational decision making of the investors: the rational invertors will switch to the investment options that have higher return until the return in all options become equal, as follows:

Suppose investment option A (physical capital, paying R: Rental Rate) has a higher return than the investment option B (financial investment, paying nominal interest rate): MPK> 𝑖

⤇ Supply of Funds in Physical capital Market increase by investors switching to them: 𝐾𝑠 ↑ ⤇ MPK↓ and this process continues until MPK becomes equal i (nominal interest rate).

Quantity of Money

i

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So we have that at the General Equilibrium (equilibrium is all of our now 4 markets: Goods, Labour, Capital, Money):

𝑹 (𝒓𝒆𝒏𝒕𝒂𝒍 𝒓𝒂𝒕𝒆) = 𝒊

2. The impact of monetary policy

Suppose there is an expansionist monetary policy: 𝑀𝑠 ↑

2.1. In Money Market

With a monetary expansion, Money Supply curve (𝑀𝑠), shifts rightward. The equilibrium quantity of money (𝑀∗) rises, and nominal interest rate (𝑖∗) falls.

2.2. In Capital market

By virtue of No Arbitrage Principle, we have that at the equilibrium 𝑖∗ = 𝑅∗. Hence, before the monetary expansion 𝑖∗ = 𝑅∗ but with then expansion:

𝑀𝑠 ↑⤇ 𝑖∗ ↓ ⤇ Now (after expansion) 𝑅∗ > 𝑖∗ ⤇ Invertors switch to Physical Capital Market⤇𝐾𝑠 ↑⤇ 𝑅∗↓

And the process continues until 𝑖∗ = 𝑅∗ again.

Quantity of Money

i

ECON3301 Fall 2011 SMU-Sobey SB

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Figure:

At the new equilibrium in the capital market, we have: 𝑲∗ ↑ 𝒂𝒏𝒅 �𝑹𝑷

�∗

↓

Note: we assume price remain fixed for now.

2.3. In labour market

Recall that real rental the marginal productivity of labour (physical capital) is a function of the

level of capital ( labor) input: K ↑⤇ MPL ↑

(As we had in the assignment:

𝑀𝑃𝐿 = �13

� �𝐾13� 𝐿

−13 ⤇ 𝑖𝑓 𝐾 ↑ 𝑡ℎ𝑒𝑛 𝑀𝑃𝐿 ↑, 𝑡𝑟𝑦 𝐾 = 1000 𝑎𝑛𝑑 𝐾 = 8000 𝑡𝑜 𝑠𝑒𝑒.

K=1000 ⤇ MPL=�103

� 𝐿−13 𝑎𝑛𝑑 𝐼𝑓 𝐾 = 8000 𝑡ℎ𝑒𝑛 𝑀𝑃𝐿 = �80

3� 𝐿

−13 )

Hence we simply have a rightward shift of the Labour Demand Curve:

MPL↑⤇ 𝐿𝑑 𝑠ℎ𝑖𝑓𝑡 𝑟𝑖𝑔ℎ𝑡𝑤𝑎𝑟𝑑𝑠

Capital

R/P

ECON3301 Fall 2011 SMU-Sobey SB

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Figure

At the new equilibrium in the capital market, we have: 𝐿∗ ↑ 𝑎𝑛𝑑 �𝑊𝑃

�∗

↓

Note: we assume price remain fixed for now.

2.3. In Goods market: From labour and Capital market we know that:

𝐿∗ ↑ 𝑎𝑛𝑑 𝐾∗ ↑⤇ 𝑂𝑢𝑡𝑝𝑢𝑡 ↑

That is why Monetary Expansion is used for Economic Stimulus and a policy against recessions.

Note: we abstract from the impact of consumers in this market.

In the long-run, as output increases price may fall enough to compensate the change on real wage and real rental rate and even offset the impact of the policy.

This is why in the RBC framework it is said that money is neutral, in the long run.

You can try the case of contraction (fall in Money Supply) for practice!

Labour

W/P

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Notes on Chapter 11: Phillips Curve and Monetary Polic

(For Ch-10: lectures notes & sample to come)

Instructor: Dr. Maryam Dilmaghani

The Phillips curve (inflation-unemployment trade-off) for Yutopia is given by the equation below:

𝜋𝑡 = 𝑍𝑡 − 𝛼𝑢𝑡

where 𝜋𝑡 and 𝑢𝑡 denote inflation and unemployment rates (in percentage) at time t respectively; 𝑍𝑡 is a strictly positive composite variable capturing all other relevant factors such as total population of Yutopia and α is a strictly positive number, capturing how price index level reacts to labour force.

Variables (endogenous, determined by the model lie P and Q in Market Models) : 𝒖𝒕 𝒂𝒏𝒅 𝝅𝒕

Parameters (exogenous variable) 𝒁𝒕 𝒂𝒏𝒅 𝜶 (like slope and intersects, shift factors).

1. Describe Philips curve in words.

A negative relationship between inflation rate and unemployment rate so that if one increases the other falls. The magnitude of the impact of one variable upon the other is unchanged by the lever of these variables (how high they are).

2. Suppose 𝑍𝑡 = 1 and 𝛼 = 0.1. Use the chart below to depict Philips curve. Line in Red (solid)

3. Now suppose 𝑍𝑡 = 1.4 and 𝛼 = 0.1. Use the chart below to depict Philips curve. Line in Green (dashed).

4. Suppose 𝑍𝑡 = 1 and 𝛼 = 0.12. Depict Philips curve. Line in Blue (dot).

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

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Philips Curve, Monetary Policy and Economic Adjustments

The Short-run Phillips curve (inflation-unemployment trade-off) for Yutopia is given by the equation below:

𝜋𝑡 = 𝑍𝑡 − 𝛼𝑢𝑡

The Long-run Phillips curve is the blue vertical line. It means that the Inflation targeted and achieved by monetary policy will not affect the natural rate of unemployment in the long-run.

In the long run the inflation rate will be 𝜋∗ and unemployment rate 𝑢𝑁: The intersection of SR and LR Phillips curve.

In the short-run, the inflation targeted by Monterey policy and the short-run Phillips curve will determined the unemployment rate. BUT, as soon as a monetary intervention is made, SR Phillips curve starts shifting, to the right (left) for expansion (contraction). It is shown in series of figures in the next pages.

Unemployment

Inflation

LR Phillips Curve

SR Phillips Curve

𝒖𝑵

𝝅∗

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Phillips Curve and Monetary Policy

1. Monetary Expansion: To stimulate the economy 1.1.In the Short-run

𝑀𝑆 ↑: 𝑖 ↓ (𝑖𝑜𝑟𝑇 ↓) ⤇ �𝐿𝑜𝑎𝑛𝑠 ↑⤇ 𝐶 ↑:𝐸𝑥𝑐𝑒𝑠𝑠 𝐷𝑒𝑚𝑎𝑛𝑑 ⤇ 𝑃𝑟𝑖𝑐𝑒𝑠 ↑⤇ 𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 ↑𝐿𝑜𝑎𝑛𝑠 ↑⤇ 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 ↑⤇ 𝐽𝑜𝑏𝑠 ↑⤇ 𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 ↓

�

1.2. In the Long-run

In the long-run however, usually the inflation will reduce real rate of return to investments and they gradually fall (realistically not at their pre-intervention level, somewhere in between).

Mean while, the investment made through the monetary expansion increases both jobs and output and this partially neutralises Excess Demand hence inflation.

In sum, it is realistic that Monetary Policy has some impacts on Real Sectors. Not as much as monetarists believe and not at little as Real Business Cycles macroeconomists believe.

(1)

Unemployment

Inflation

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(2)

(3)

Unemployment

Inflation

Unemployment

Inflation

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(4)

More Realist Long-run Impact of Monetary Expansion & Phillips Curve Long-run Phillips curve shifts left (Solid blue) Short-run Phillips Curve does not shift all the way to the right. Hence with a higher level of Equilibrium Inflation, the natural level of unemployment will be lower.

Unemployment

Inflation

Unemployment

Inflation

LR Equilibrium

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Do the case of contraction as an exercise!

SMU: Sobey School of Business ECON3307: Fall 2011

1

Notes on Taylor Rule

Instructor: Dr. Maryam Dilmaghani

Taylor rule guides central banker in conducting monetary policy given the fundamentals of

economy (potential GDP) and target inflation rate. The rule can be written as follows:

𝒊𝒕 = 𝝅𝒕 + 𝜶𝒚 𝒐𝒖𝒕𝒑𝒖𝒕 𝒈𝒂𝒑+ 𝜶𝝅 𝒊𝒏𝒇𝒍𝒂𝒕𝒊𝒐𝒏 𝒈𝒂𝒑

(i) Description

Output gap: (𝒚𝒕 − 𝒚∗)= the difference between the current output, 𝑦𝑡, and the optimal level of output, 𝑦∗: the output that corresponds to the fundamentals of the economy (physical capital, human capital etc).

Inflation gap: (𝝅𝒕 − 𝝅∗)= the difference between the current inflation rate, 𝜋𝑡 , and the optimal inflation rate, 𝜋∗: the inflation rate that corresponds to the fundamentals of the economy (physical capital, human capital etc).

As you will see below, the coefficients of both output gap and inflation gap must be positive for the equation to have sensible prescriptions for monetary policy:

𝜶𝒚 > 𝟎 & 𝜶𝝅 > 𝟎

(ii) Application

If output gap is positive: (𝑦𝑡 − 𝑦∗) > 0 ⤇ 𝑦𝑡 > 𝑦∗ ⤇ Current output is higher than the optimal level. It is an ‘indicator of future inflation’ and ‘inflationary pressures on prices’.

The right monetary policy for central banks that are aiming at Inflation Targeting, especially pro-actives like Federal Reserve’s in the US, is to go for a Monetary contraction ( 𝑀𝑠↓, i ↑).

Taylor prescribes that the Target Interest Rate increases by 𝜶𝒚 × (𝑦𝑡 − 𝑦∗).

For instance, if output gap is 0.5% and 𝛼𝑦 = 0.5 then a Central bank using Taylor in Monetary Policy must increase the Target interest rate by 0.5 × 0.5 = 0.25%

SMU: Sobey School of Business ECON3307: Fall 2011

2

If inflation gap is positive: (𝜋𝑡 − 𝜋∗) > 0 ⤇ 𝜋𝑡 > 𝜋∗ ⤇ meaning that the inflation rate is higher than the target level, then Taylor rule postulates that Central Bank must increase the nominal interest rate to bring the inflation back to its target level:

Taylor prescribes that the Target Interest Rate increases by 𝜶𝝅 × (𝜋𝑡 − 𝜋∗).

For instance, if inflation gap is 0.5% (inflation is ½ % above its targeted level)and 𝛼𝜋 = 0.5 then a Central bank using Taylor in Monetary Policy must increase the Target interest rate by 0.5 × 0.5 = 0.25%

After the Monetary contrition ( 𝑀𝑠↓, i ↑):

𝑖𝑖 ↑ 𝑖𝑠 𝑎 𝑚𝑜𝑛𝑒𝑡𝑎𝑟𝑦 𝑐𝑜𝑛𝑡𝑟𝑎𝑐𝑡𝑖𝑜𝑛 ⤇

𝑖𝑡 𝑟𝑒𝑑𝑢𝑐𝑒𝑠 𝑙𝑜𝑎𝑛𝑠 𝑎𝑛𝑑 𝑓𝑟𝑜𝑚 𝑡ℎ𝑒𝑟𝑒 𝑒𝑐𝑜𝑛𝑜𝑚𝑖𝑐 𝑎𝑐𝑡𝑖𝑣𝑖𝑡𝑦 ⤇

𝐸𝑥𝑐𝑒𝑠𝑠 𝑠𝑢𝑝𝑝𝑙𝑦 ⤇ 𝑝𝑟𝑖𝑐𝑒𝑠 ↓ 𝑎𝑛𝑑 𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 ↓

**&**

You can try the cases of a negative output gap and inflation gap for practice.

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Notes 3

Economic General Equilibrium Theory (mainly from Wikipedia)

Note:

It goes beyond the lecture and also what I expect you. I will post another note, more focused on

equations and illustrations.

General equilibrium theory is a branch of theoretical economics. It seeks to explain the

behavior of supply, demand and prices in a whole economy with several or many interacting

markets, by seeking to prove that a set of prices exists that will result in an overall equilibrium,

hence general equilibrium, in contrast to partial equilibrium, which only analyzes single

markets. As with all models, this is an abstraction from a real economy; it is proposed as being a

useful model, both by considering equilibrium prices as long-term prices and by considering

actual prices as deviations from equilibrium.

General equilibrium theory both studies economies using the model of equilibrium pricing and

seeks to determine in which circumstances the assumptions of general equilibrium will hold. The

theory dates to the 1870s, particularly the work of French economist Léon Walras.

It is often assumed that (representative) agents are price takers, and under that assumption two

common notions of equilibrium exist.

Overview

Broadly speaking, general equilibrium tries to give an understanding of the whole economy

using a "bottom-up" approach, starting with individual markets and agents. Macroeconomics, as

developed by the Keynesian economists, focused on a "top-down" approach, where the analysis

starts with larger aggregates, the "big picture". Therefore, general equilibrium theory has

traditionally been classified as part of microeconomics.

The difference is not as clear as it used to be, since much of modern macroeconomics has

emphasized microeconomic foundations, and has constructed general equilibrium models of

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macroeconomic fluctuations. General equilibrium macroeconomic models usually have a

simplified structure that only incorporates a few markets, like a "goods market" and a "financial

market". In contrast, general equilibrium models in the microeconomic tradition typically

involve a multitude of different goods markets. They are usually complex and require computers

to help with numerical solutions.

In a market system the prices and production of all goods, including the price of money and

interest, are interrelated. A change in the price of one good, say bread, may affect another price,

such as bakers' wages. If bakers differ in tastes from others, the demand for bread might be

affected by a change in bakers' wages, with a consequent effect on the price of bread. Calculating

the equilibrium price of just one good, in theory, requires an analysis that accounts for all of the

millions of different goods that are available.

History of general equilibrium modeling

The first attempt in neoclassical economics to model prices for a whole economy was made by

Léon Walras. Walras' Elements of Pure Economics provides a succession of models, each

taking into account more aspects of a real economy (two commodities, many commodities,

production, growth, money). Some (for example, Eatwell (1989), see also Jaffe (1953)) think

Walras was unsuccessful and that the later models in this series are inconsistent.

(Not done in lecture besides about the concept of Government in Keynes & Real Business

Cycles models.)

In particular, Walras's model was a long-run model in which prices of capital goods are the same

whether they appear as inputs or outputs and in which the same rate of profits is earned in all

lines of industry. This is inconsistent with the quantities of capital goods being taken as data. But

when Walras introduced capital goods in his later models, he took their quantities as given, in

arbitrary ratios. (In contrast, Kenneth Arrow and Gerard Debreu continued to take the initial

quantities of capital goods as given, but adopted a short run model in which the prices of capital

goods vary with time and the own rate of interest varies across capital goods.)

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Walras was the first to lay down a research program much followed by 20th-century economists.

In particular, the Walrasian agenda included the investigation of when equilibria are unique and

stable.(Walras himself: Lesson 7 shows neither Uniqueness, nor Stability, nor even Existence of

an agreement is guaranteed. Immediate after closing the deal, e.g.)

Walras also proposed a dynamic process by which general equilibrium might be reached, that of

the tâtonnement or groping process.

The tatonnement process is a model for investigating stability of equilibria. Prices are announced

(perhaps by an "auctioneer"), and agents state how much of each good they would like to offer

(supply) or purchase (demand). No transactions and no production take place at disequilibrium

prices. Instead, prices are lowered for goods with positive prices and excess supply. Prices are

raised for goods with excess demand. The question for the mathematician is under what

conditions such a process will terminate in equilibrium where demand equates to supply for

goods with positive prices and demand does not exceed supply for goods with a price of zero.

Walras was not able to provide a definitive answer to this question (see Unresolved Problems in

General Equilibrium below).

In partial equilibrium analysis, the determination of the price of a good is simplified by just

looking at the price of one good, and assuming that the prices of all other goods remain constant.

The Marshallian theory of supply and demand is an example of partial equilibrium analysis.

Partial equilibrium analysis is adequate when the first-order effects of a shift in the demand

curve do not shift the supply curve. Anglo-American economists became more interested in

general equilibrium in the late 1920s and 1930s after Piero Sraffa's demonstration that

Marshallian economists cannot account for the forces thought to account for the upward-slope of

the supply curve for a consumer good.

If an industry uses little of a factor of production, a small increase in the output of that industry

will not bid the price of that factor up. To a first-order approximation, firms in the industry will

not experience decreasing costs and the industry supply curves will not slope up. If an industry

uses an appreciable amount of that factor of production, an increase in the output of that industry

will exhibit decreasing costs. But such a factor is likely to be used in substitutes for the industry's

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product, and an increased price of that factor will have effects on the supply of those substitutes.

Consequently, Sraffa argued, the first-order effects of a shift in the demand curve of the original

industry under these assumptions includes a shift in the supply curve of substitutes for that

industry's product, and consequent shifts in the original industry's supply curve. General

equilibrium is designed to investigate such interactions between markets.

Continental European economists made important advances in the 1930s. Walras' proofs of the

existence of general equilibrium often were based on the counting of equations and variables.

Such arguments are inadequate for non-linear systems of equations and do not imply that

equilibrium prices and quantities cannot be negative, a meaningless solution for his models. The

replacement of certain equations by inequalities and the use of more rigorous mathematics

improved general equilibrium modeling.

The modern conception of general equilibrium is provided by a model developed jointly by

Kenneth Arrow, Gerard Debreu and Lionel W. McKenzie in the 1950s. Gerard Debreu presents

this model in Theory of Value (1959) as an axiomatic model, following the style of mathematics

promoted by Bourbaki. In such an approach, the interpretation of the terms in the theory (e.g.,

goods, prices) are not fixed by the axioms.

Modern concept of general equilibrium in economics

Three important interpretations of the terms of the theory have been often cited. First, suppose

commodities are distinguished by the location where they are delivered. Then the Arrow-Debreu

model is a spatial model of, for example, international trade.

Second, suppose commodities are distinguished by when they are delivered. That is, suppose all

markets equilibrate at some initial instant of time. Agents in the model purchase and sell

contracts, where a contract specifies, for example, a good to be delivered and the date at which it

is to be delivered. The Arrow-Debreu model of intertemporal equilibrium contains forward

markets for all goods at all dates. No markets exist at any future dates.

Third, suppose contracts specify states of nature which affect whether a commodity is to be

delivered: "A contract for the transfer of a commodity now specifies, in addition to its physical

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properties, its location and its date, an event on the occurrence of which the transfer is

conditional. This new definition of a commodity allows one to obtain a theory of [risk] free from

any probability concept..." (Debreu, 1959)

These interpretations can be combined. So the complete Arrow-Debreu model can be said to

apply when goods are identified by when they are to be delivered, where they are to be delivered

and under what circumstances they are to be delivered, as well as their intrinsic nature. So there

would be a complete set of prices for contracts such as "1 ton of Winter red wheat, delivered on

3rd of January in Minneapolis, if there is a hurricane in Florida during December". A general

equilibrium model with complete markets of this sort seems to be a long way from describing the

workings of real economies, however its proponents argue that it is still useful as a simplified

guide as to how a real economies function.

Some of the recent work in general equilibrium has in fact explored the implications of

incomplete markets, which is to say an intertemporal economy with uncertainty, where there do

not exist sufficiently detailed contracts that would allow agents to fully allocate their

consumption and resources through time. While it has been shown that such economies will

generally still have an equilibrium, the outcome may no longer be Pareto optimal. The basic

intuition for this result is that if consumers lack adequate means to transfer their wealth from one

time period to another and the future is risky, there is nothing to necessarily tie any price ratio

down to the relevant marginal rate of substitution, which is the standard requirement for Pareto

optimality. Under some conditions the economy may still be constrained Pareto optimal,

meaning that a central authority limited to the same type and number of contracts as the

individual agents may not be able to improve upon the outcome, what is needed is the

introduction of a full set of possible contracts. Hence, one implication of the theory of

incomplete markets is that inefficiency may be a result of underdeveloped financial institutions

or credit constraints faced by some members of the public. Research still continues in this area.

ECON3301-Fall 2011 SMU-Sobey SB

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Notes on Economic Growth in Canada

1. What is Economic Growth?

Economic growth is the increase of aggregate production in a given economy.

2. How can we measure Economic Growth?

Economic Growth is the increase of per capita gross domestic product (GDP) as a measure of

aggregate income. Usually, the annual rate of change in real GDP is taken as the indicator of the

annual rate of growth.

2.1. GDP as an indicator of economic growth

Gross domestic product (GDP) refers to the market value of all final goods and services

produced within a country in a given period. GDP per capita and its changes over time is often

considered an indicator of a country's standard of living and economic growth.

2.2. Measuring GDP

GDP can be determined in three ways, all of which should, in principle, give the same result.

They are the product (or output) approach, the income approach, and the expenditure approach.

The most direct of the three is the product approach, which sums the outputs of every class of

enterprise to arrive at the total. The expenditure approach works on the principle that all of the

product must be bought by somebody, therefore the value of the total product must be equal to

people's total expenditures in buying things.

The income approach works on the principle that the incomes of the productive factors

("producers," colloquially) must be equal to the value of their product, and determines GDP by

finding the sum of all producers' incomes.

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Example: the expenditure method:

GDP = Value of private consumption (C) + Value of gross investment (I) + Value of government spending (G) + Value of exports in national currency -imports

𝐺𝐷𝑃 = 𝐶 + 𝐼 + 𝐺 + 𝜀𝑋 −𝑀

Note:

"Gross" means that GDP measures production regardless of the various uses to which that

production can be put. Production can be used for immediate consumption, for investment in

new fixed assets or inventories, or for replacing depreciated fixed assets. "Domestic" means that

GDP measures production that takes place within the country's borders. In the expenditure-

method equation given above, the exports-minus-imports term is necessary in order to null out

expenditures on things not produced in the country (imports) and add in things produced but not

sold in the country (exports).

2.3. Shortcomings of GDP as an indicator of economic performance

Wealth distribution

Non-market transactions

Underground economy

Non-monetary economy

Quality improvements and inclusion of new products

3. Main factors behind Economics Growth

Economic growth is primarily driven by improvements in productivity, which involves

producing more goods and services with the same inputs of labour, capital, energy and materials.

4. Temporal Horizon for Measuring Economic Growth

The long-run path of economic growth is one of the central questions of economics; despite

some problems of measurement, an increase in GDP of a country greater than population growth

is generally taken as an increase in the standard of living of its inhabitants. Over long periods of

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time, even small rates of annual growth can have large effects through compounding (see

exponential growth).

A growth rate of 2.5% per annum will lead to a doubling of GDP within 29 years, whilst a

growth rate of 8% per annum (experienced by some Four Asian Tigers) will lead to a doubling of

GDP within 10 years. This exponential characteristic can exacerbate differences across nations.

5. Short-run versus long-run considerations

Economists draw a distinction between short-term economic stabilization and long-term economic

growth. The topic of economic growth is primarily concerned with the long run. The short-run variation

of economic growth is termed the business cycle.

6. Principal Theories of Economic Growth

6.1.Exogenous growth model (Solow–Swan growth model) 6.2.Ramsey-Cass-Koopmans model

The Ramsey model differs from the Solow model in that it explicitly models the choice of consumption at a point in time and so endogenizes the saving rate.

6.3.Endogenous growth theory

In economics, endogenous growth theory or new growth theory was developed in the 1980s as

a response to criticism of the neo-classical growth model. The endogenous growth theory holds

that policy measures can have an impact on the long-run growth rate of an economy. For

example, subsidies on research and development or education increase the growth rate in some

endogenous growth models by increasing the incentive to innovate.

In neo-classical growth models, the long-run rate of growth is exogenously determined by either

assuming a savings rate or a rate of technical progress (Solow model). However, the savings rate

and rate of technological progress remain unexplained. Endogenous growth theory tries to

overcome this shortcoming by building macroeconomic models out of microeconomic

foundations. Households are assumed to maximize utility subject to budget constraints while

firms maximize profits.

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Crucial importance is usually given to the production of new technologies and human capital.

The engine for growth can be as simple as a constant return to scale production function (the AK

model) or more complicated set ups with spillover effects (spillovers are positive externalities,

benefits that are attributed to costs from other firms), increasing numbers of goods, increasing

qualities, etc.

7. Economic Growth in Canada

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Notes on Solow Growth Model

Dr. Maryam Dilmaghani

The notes are set to complement textbook on Solow Growth Model (Chapter 4). Chapter 5 is dropped.

Summary of Solow Growth Model

Solow Model is set to provide an understanding into the Steady State (long-run equilibrium) level of income per capita in a given economy, using simple assumptions of production function.

1. On Production Function

𝑌 = 𝐹(𝐿,𝐾) = 𝐴𝐿∝𝐾𝛽 (1)

with 0 <∝ 𝑎𝑛𝑑 𝛽 < 1

Y is output, L is labour force and K is capital investment. Cobb-Douglas version:

𝑌 = 𝐹(𝐿,𝐾) = 𝐴𝐿∝𝐾𝛽 (i)

with 0 < 𝛼𝑎𝑛𝑑 𝛽 < 1

and 𝛂+𝛽 = 1

2. Transforming production function to ‘per worker’ (with some approximation per capita):

We divide both sides of (1) by L:

𝑌𝐿 =

𝐴𝐿∝𝐾𝛽

𝐿 ⇒

Using y for income per capita (𝑌𝐿) and simplifying:

𝑦 = 𝐴𝐾𝛽 𝐿𝛼

𝐿= 𝐴𝐾𝛽𝐿𝛼−1

Since α+β=1⤇β=1-α and α=1-β so we have:

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𝑦 = 𝐴𝐾𝛽𝐿(1−𝛽)−1 = 𝐴𝐾𝛽𝐿−𝛽=𝐴.𝐾𝛽 1𝐿𝛽

= 𝐴 �𝐾𝐿�𝛽

Using k for 𝐾𝐿, meaning investment per worker (approximately investment per

capita), we get:

𝒚 = 𝑨𝒌𝜷

3. Adding other factors

(i) Saving rate, s, is the portion of income (output) per capita that us saved, hence can be invested.

(ii) Depreciation rate, δ: the portion of investment that must be replaced at each point in time so that the stock of capital does not fall.

(iii) rate of population hence labour force, growth: n

4. Deriving force of increase in output = increase in capital per worker.

5. Increase in capital per worker is possible when the Gross Investment, saving rate× 𝑜𝑢𝑡𝑝𝑢𝑡 𝑝𝑒𝑟 𝑐𝑎𝑝𝑖𝑡𝑎 (𝑠 × 𝑦), is larger than the capital per capita decline due to Depreciation and Population Growth: (δ+n)× 𝒌.

In other words:

Change in stock of capital= 𝒔 × 𝒚 − [(𝛅 + 𝐧) × 𝒌]

5. Steady state, meaning the long run equilibrium level of income per capita is achieved when there is no change in the stock of capital per capita, or:

Change in stock of capital=0⤇

𝒔 × 𝒚 = [(𝛅 + 𝐧) × 𝒌]

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6. Figures

(i) Output per capita as a function of capital per capita

(ii) Adding saving rate and gross investment (Green Line)

K/L

Y/L

K/L

Y/L

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(iii) Adding depreciation and population growth

Consumption at each point in time is Output-Gross investment= the difference between the Red and Green curves.

Net investment= change in the stock of capital is the difference between Gross Investment and Depreciation (distance between the Green curve and Back line).

At the steady state, Net investment=0, it means that the stick of capital, hence the output will remain constant forever.

K/L

Y/L

K/L

Y/LSteady State y Consumption

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(iv) Increase in saving rate: The Green curve shifts upward

For your practice:

Label this figure live the one in (iii) and discuss the impact of increase in saving rate on steady state level of output per capita, consumption and stock of capital per capita.

K/L

Y/L

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Notes 3

Economic General Equilibrium Theory (mainly from Wikipedia)

Note:

It goes beyond the lecture and also what I expect you. I will post another note, more focused on

equations and illustrations.

General equilibrium theory is a branch of theoretical economics. It seeks to explain the

behavior of supply, demand and prices in a whole economy with several or many interacting

markets, by seeking to prove that a set of prices exists that will result in an overall equilibrium,

hence general equilibrium, in contrast to partial equilibrium, which only analyzes single

markets. As with all models, this is an abstraction from a real economy; it is proposed as being a

useful model, both by considering equilibrium prices as long-term prices and by considering

actual prices as deviations from equilibrium.

General equilibrium theory both studies economies using the model of equilibrium pricing and

seeks to determine in which circumstances the assumptions of general equilibrium will hold. The

theory dates to the 1870s, particularly the work of French economist Léon Walras.

It is often assumed that (representative) agents are price takers, and under that assumption two

common notions of equilibrium exist.

Overview

Broadly speaking, general equilibrium tries to give an understanding of the whole economy

using a "bottom-up" approach, starting with individual markets and agents. Macroeconomics, as

developed by the Keynesian economists, focused on a "top-down" approach, where the analysis

starts with larger aggregates, the "big picture". Therefore, general equilibrium theory has

traditionally been classified as part of microeconomics.

The difference is not as clear as it used to be, since much of modern macroeconomics has

emphasized microeconomic foundations, and has constructed general equilibrium models of

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macroeconomic fluctuations. General equilibrium macroeconomic models usually have a

simplified structure that only incorporates a few markets, like a "goods market" and a "financial

market". In contrast, general equilibrium models in the microeconomic tradition typically

involve a multitude of different goods markets. They are usually complex and require computers

to help with numerical solutions.

In a market system the prices and production of all goods, including the price of money and

interest, are interrelated. A change in the price of one good, say bread, may affect another price,

such as bakers' wages. If bakers differ in tastes from others, the demand for bread might be

affected by a change in bakers' wages, with a consequent effect on the price of bread. Calculating

the equilibrium price of just one good, in theory, requires an analysis that accounts for all of the

millions of different goods that are available.

History of general equilibrium modeling

The first attempt in neoclassical economics to model prices for a whole economy was made by

Léon Walras. Walras' Elements of Pure Economics provides a succession of models, each

taking into account more aspects of a real economy (two commodities, many commodities,

production, growth, money). Some (for example, Eatwell (1989), see also Jaffe (1953)) think

Walras was unsuccessful and that the later models in this series are inconsistent.

(Not done in lecture besides about the concept of Government in Keynes & Real Business

Cycles models.)

In particular, Walras's model was a long-run model in which prices of capital goods are the same

whether they appear as inputs or outputs and in which the same rate of profits is earned in all

lines of industry. This is inconsistent with the quantities of capital goods being taken as data. But

when Walras introduced capital goods in his later models, he took their quantities as given, in

arbitrary ratios. (In contrast, Kenneth Arrow and Gerard Debreu continued to take the initial

quantities of capital goods as given, but adopted a short run model in which the prices of capital

goods vary with time and the own rate of interest varies across capital goods.)

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Walras was the first to lay down a research program much followed by 20th-century economists.

In particular, the Walrasian agenda included the investigation of when equilibria are unique and

stable.(Walras himself: Lesson 7 shows neither Uniqueness, nor Stability, nor even Existence of

an agreement is guaranteed. Immediate after closing the deal, e.g.)

Walras also proposed a dynamic process by which general equilibrium might be reached, that of

the tâtonnement or groping process.

The tatonnement process is a model for investigating stability of equilibria. Prices are announced

(perhaps by an "auctioneer"), and agents state how much of each good they would like to offer

(supply) or purchase (demand). No transactions and no production take place at disequilibrium

prices. Instead, prices are lowered for goods with positive prices and excess supply. Prices are

raised for goods with excess demand. The question for the mathematician is under what

conditions such a process will terminate in equilibrium where demand equates to supply for

goods with positive prices and demand does not exceed supply for goods with a price of zero.

Walras was not able to provide a definitive answer to this question (see Unresolved Problems in

General Equilibrium below).

In partial equilibrium analysis, the determination of the price of a good is simplified by just

looking at the price of one good, and assuming that the prices of all other goods remain constant.

The Marshallian theory of supply and demand is an example of partial equilibrium analysis.

Partial equilibrium analysis is adequate when the first-order effects of a shift in the demand

curve do not shift the supply curve. Anglo-American economists became more interested in

general equilibrium in the late 1920s and 1930s after Piero Sraffa's demonstration that

Marshallian economists cannot account for the forces thought to account for the upward-slope of

the supply curve for a consumer good.

If an industry uses little of a factor of production, a small increase in the output of that industry

will not bid the price of that factor up. To a first-order approximation, firms in the industry will

not experience decreasing costs and the industry supply curves will not slope up. If an industry

uses an appreciable amount of that factor of production, an increase in the output of that industry

will exhibit decreasing costs. But such a factor is likely to be used in substitutes for the industry's

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product, and an increased price of that factor will have effects on the supply of those substitutes.

Consequently, Sraffa argued, the first-order effects of a shift in the demand curve of the original

industry under these assumptions includes a shift in the supply curve of substitutes for that

industry's product, and consequent shifts in the original industry's supply curve. General

equilibrium is designed to investigate such interactions between markets.

Continental European economists made important advances in the 1930s. Walras' proofs of the

existence of general equilibrium often were based on the counting of equations and variables.

Such arguments are inadequate for non-linear systems of equations and do not imply that

equilibrium prices and quantities cannot be negative, a meaningless solution for his models. The

replacement of certain equations by inequalities and the use of more rigorous mathematics

improved general equilibrium modeling.

The modern conception of general equilibrium is provided by a model developed jointly by

Kenneth Arrow, Gerard Debreu and Lionel W. McKenzie in the 1950s. Gerard Debreu presents

this model in Theory of Value (1959) as an axiomatic model, following the style of mathematics

promoted by Bourbaki. In such an approach, the interpretation of the terms in the theory (e.g.,

goods, prices) are not fixed by the axioms.

Modern concept of general equilibrium in economics

Three important interpretations of the terms of the theory have been often cited. First, suppose

commodities are distinguished by the location where they are delivered. Then the Arrow-Debreu

model is a spatial model of, for example, international trade.

Second, suppose commodities are distinguished by when they are delivered. That is, suppose all

markets equilibrate at some initial instant of time. Agents in the model purchase and sell

contracts, where a contract specifies, for example, a good to be delivered and the date at which it

is to be delivered. The Arrow-Debreu model of intertemporal equilibrium contains forward

markets for all goods at all dates. No markets exist at any future dates.

Third, suppose contracts specify states of nature which affect whether a commodity is to be

delivered: "A contract for the transfer of a commodity now specifies, in addition to its physical

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properties, its location and its date, an event on the occurrence of which the transfer is

conditional. This new definition of a commodity allows one to obtain a theory of [risk] free from

any probability concept..." (Debreu, 1959)

These interpretations can be combined. So the complete Arrow-Debreu model can be said to

apply when goods are identified by when they are to be delivered, where they are to be delivered

and under what circumstances they are to be delivered, as well as their intrinsic nature. So there

would be a complete set of prices for contracts such as "1 ton of Winter red wheat, delivered on

3rd of January in Minneapolis, if there is a hurricane in Florida during December". A general

equilibrium model with complete markets of this sort seems to be a long way from describing the

workings of real economies, however its proponents argue that it is still useful as a simplified

guide as to how a real economies function.

Some of the recent work in general equilibrium has in fact explored the implications of

incomplete markets, which is to say an intertemporal economy with uncertainty, where there do

not exist sufficiently detailed contracts that would allow agents to fully allocate their

consumption and resources through time. While it has been shown that such economies will

generally still have an equilibrium, the outcome may no longer be Pareto optimal. The basic

intuition for this result is that if consumers lack adequate means to transfer their wealth from one

time period to another and the future is risky, there is nothing to necessarily tie any price ratio

down to the relevant marginal rate of substitution, which is the standard requirement for Pareto

optimality. Under some conditions the economy may still be constrained Pareto optimal,

meaning that a central authority limited to the same type and number of contracts as the

individual agents may not be able to improve upon the outcome, what is needed is the

introduction of a full set of possible contracts. Hence, one implication of the theory of

incomplete markets is that inefficiency may be a result of underdeveloped financial institutions

or credit constraints faced by some members of the public. Research still continues in this area.

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Chapter 7: Simple 2-period Model

(Preliminary to Basic Dynamic General Equilibrium Model)

Dr. Maryam Dilmaghani

The Model is dynamic

as it do involves time explicitly.

1. Markets involved

(i) Goods Market

(ii) Labour Market

(iii) ‘Investment’ Markets: Bonds Market (financial investment) & Rental Market (investment

physical capital) combined.

2. Endogenous variables

They are, as usual, price and quantity in each market.

(i) Goods Market: output and price of output, denoted by P.

(ii) Labour Market: employment level and wage, denoted by W.

(iii) ‘Investment’ Markets: Bonds Market (financial investment) & Rental Market (investment

physical capital): rate of return on investments.

3. Exogenous variables

(i) Subjective rate of patience (propensity to consume (or save) in period 1 compared to period 2;

i.e. how to divide the present value of life time income (𝑦1 & 𝑦2) between 𝑐1 & 𝑐2).

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(ii) real interest rate denoted by i: it is the opportunity cost of consumption is period 1 ⤇ if

price of consumption in period 2 is assumed to be 1 then the ‘price of consumption in period 1 is

(1+i).

Note that later on, we will make real interest rate Endogenous, only in this preliminary

model, it is exogenous.

(iii) Technology, i.e. parameters of production function.

(iv) Population /Labour Force, i.e. assumed Labour Supply

4. Representative agents’ budget constraint

Suppose that the representative agent receives income (from different sources) in both periods.

The income is period 1 is denoted by 𝑦1 and 𝑦2.

In period 1, income, 𝑦1, can be consumed (𝑐1) or saved (S). So we have:

𝐲𝟏 = 𝐜𝟏 + 𝐒 ⤇ 𝐒 = 𝐲𝟏 − 𝐜𝟏 (1)

In period 2, income, 𝑦2 , along the saving from period 1,

𝑆 × (1 + 𝑖):𝑎𝑠 𝑠𝑎𝑣𝑖𝑛𝑔 𝑔𝑟𝑜𝑤𝑠 𝑏𝑦 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑟𝑎𝑡𝑒, can be consumed (𝑐2). There will be no saving

as period 2 is the last period. So we have:

𝐜𝟐 = 𝐲𝟐 + 𝐒(𝟏 + 𝐢) ⤇ 𝐒 = 𝐜𝟐(𝟏+𝐢)

− 𝐲𝟐(𝟏+𝐢)

(2)

Combining (1) and (2), we get:

𝐲𝟏 − 𝐜𝟏 = 𝐜𝟐

(𝟏 + 𝐢)−

𝐲𝟐(𝟏 + 𝐢)

⤇ 𝒄𝟐 = 𝒚𝟏 × (𝟏 + 𝒊) + 𝒚𝟐 − (𝟏 + 𝒊) × 𝒄𝟏

Hence, the Inter-temporal Budget constraint, IBC, is:

𝒄𝟐 = 𝒚𝟏 × (𝟏 + 𝒊) + 𝒚𝟐 − (𝟏 + 𝒊) × 𝒄𝟏

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Example:

𝑆𝑢𝑝𝑝𝑜𝑠𝑒: 𝑦1 = 5 and 𝑦2 = 5, i=10%

Hence with no saving, the representative agent can consume 5 in period 1 and 5 in period 2.

(i) x-axis intercept

Present value of total, life-time income= 𝑦1 + 𝑦2(1+𝑖)

= 5 + 51.1

= 5 + 4.55 = 9.55

This is the maximum possible consumption in period 1 (x-axis intercept).

(ii) y-axis intercept

And, if all is saved in period 1, it grows by 10%, so we have:

Total funds in period 2=𝑦1(1 + 𝑖) + 𝑦2 = 5 × (1.1) + 5 = 10.5

***&***

Adding the choice line will show the subjective ‘discount rate’ (rate of patience: how the person compares future and present).

All life-time income consumed in period 2 through saving

The intersections with axis are extreme cases where all real life time income is spend either on

consumption in period 1 (funds equal the Present Value of income in period 2 is borrowed and

and consumed in period 1) is or it is all save for period 2 (no consumption in period 1).

0 1 2 3 4 5 6 7 8 9 10 110

2

4

6

8

10

12

C1

C2

Budget Constraint Slope is –(1+i)= -1.1

No saving and no borrowing: 𝒚𝟏 =𝒄𝟏 & 𝒚𝟐 = 𝒄𝟐

All life-time income consumed in period 1 through borrowing

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**&**

Choice and ‘Relative Price’

Supposing that the income of the decision maker is m and the prices are C1 and C2, respectively,

the equation of a budget line is:

𝑃1𝐶1 + 𝑃2𝐶2 = 𝑚

Consider the choice/ budget line figure below.

The budget line tells you about what is attainable to the decision maker (here representative

agent) given prices and his income. If all his income is spent on good 1 (C1), the decision is

characterised by the intersection of the budget constraint (line: budget line or budget constraint

means that same) with the x-axis.

Supposing that the income of the decision maker is m and the prices are C1 and C2, respectively,

we have:

𝐶1 =𝑚𝑝1

& 𝐶2 = 0

0 1 2 3 4 5 6 7 8 9 10 110

2

4

6

8

10

12

C1

C2

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Likewise, all his income is spent on good 2 (C2), the decision is characterised by the intersection

of the budget constraint (budget line: budget line or budget constraint means that same) with the

y-axis.

𝐶1 = 0 & 𝐶2 =𝑚𝑝2

The points in between are the less extreme combinations (𝑪𝟏 ≠ 𝟎 𝒂𝒏𝒅 𝑪𝟐 ≠ 𝟎).

The blue line (that I called choice-line and it is valid for Cobb-Douglass preferences)

characterises the decision makers’ preferred combination for C1 and C2, for any given budget

constraint (m and P1 and P2).

Basically, it assumes a constant share of the two goods of the decision makers’ income. In our

Basic Dynamic (Static) General Equilibrium model, it can be interpreted as ‘saving ratio.

Application

Below, there are the important points for the application of the model using the figure.

1. The slope and y-axis intercept

The slope of the budget line is the relative price of the two goods.

𝑃1𝐶1 + 𝑃2𝐶2 = 𝑚 ⤇ 𝑃2𝐶2 = 𝑚 − 𝑃1𝐶1 ⤇ 𝐶2 = 𝑚 − 𝑃2𝐶2 ⤇ 𝐶2 =𝑚𝑃2−𝑃1𝑃2

𝐶1

Given that C2 s the y-axis variable and C2 is the x-axis variable, 𝑚𝑃2

is the y-axis intercept and

𝑃1𝑃2

is the slope.

You see that the slope is the ration of Price of Good1 to Price of Good 2: 𝑃1𝑃2

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2. The choice line

The choice-line passes throughout the origin and the slope of the choice line is the ratio of

Income Spent on Good 2/Income Spent on Good 1.

For instance, if the income is divided 50-50, the slope will be 1.

3. Impact of change in prices in budget line

With the changes in prices the Budget line will rotate around the point of no-saving (in Dynamic

GE).

No-saving means when all the income of period 1 in consumed in Period 1 and all the income of

period 2 is consumed in Period 2.

Recall that the slope has been 𝑃1𝑃2

, so for instance, with any increase in P1, then 𝑃1𝑃2

↑ and the

Budget line becomes steeper. Likewise, if P2 falls, 𝑃1𝑃2

𝑖𝑛𝑐𝑟𝑒𝑠𝑒𝑠 𝑎𝑛𝑑 the budget line becomes

steeper too.

4. Impact of change in prices on choice.

Income Effect:

Income effect (IE) is the change in ‘overall’ purchasing power as a result of change in any price.

If you are a seller (producer) of the good whose price has increased, the income effect is positive for you. It is like you become richer and as a result, you can consume more of all goods you have been consuming.

If you are a buyer (consumer) of the good whose price has increased, the income effect is negative for you. It is like you become poorer and as a result, you can consume less of all goods you have been consuming. (e.g. when your rent goes up it is like you are becoming poorer).

Substitution Effect:

Substitution affect (SE), is the reallocation of funds among goods by switching to the cheaper goods, as much as possible (given the tastes and the degree of substitution for the kind of goods.

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i.e. the degree of substitution is high for markers of different color; much lower for consumption is different periods).

Application to Dynamic General Equilibrium

The only particularity of the use of this model is to us the appropriate Relative Price.

If we have two-period and the interest rate is i, then 1 unit of Good in present becomes 1+i

Good in future.

It means that the same purchasing power can buy One Unit Of C1 and (1+i) Units of C2. It

means that if 𝑃1 = 1 then 𝑃2 = 11+𝑖

(it only makes sense that P2 is smaller than P1: it means that

C2 is cheaper and it is always to happen when we discount future).

So, if 𝑃1 = 1 and 𝑃2 = 11+𝑖

then 𝑃1𝑃2

= 111+𝑖�

= 1 + 𝑖

Therefore, the slope of the Inter-temporal Budget Constraint is –(1+i) .

Recall that for the static Budget constraint, is was -1 (for it was the same good to be consumed or

saved, hence its price was the same).

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An example: 𝒊 ↑ The read line is the initial Budget Constraint. (i) If 𝒊 ↑ 𝒕𝒉𝒆𝒏 𝟏 + 𝒊 ↑ ⤇ Budget Constraint becomes Steeper (the green line). All life-time income consumed in period 2 through saving

The intersections with axis are extreme cases where all real life time income is spend either on

consumption in period 1 (funds equal the Present Value of income in period 2 is borrowed and

consumed in period 1) is or it is all save for period 2 (no consumption in period 1).

(ii) The choice

The chance in interest rate, i, is a change in Price so it generates Income Effect and Substitution

Effect.

As the increase in i, in here happens to a borrower (as his choice on the red line shows

consuming less than his income in period 1. So we have:

Income Effect is Negative ⤇ C1↓ and C2↓

Substitution Effect: Relative Price = 1+i

As the Relative Price of Good 1 (that is 1+i) then C1 falls: C1 ↓

As the Relative Price of Good 2 (that is 1/1+i) falls then C2 goes up: C2↑

0 1 2 3 4 5 6 7 8 9 10 11 12 130

2

4

6

8

10

12

C1

C2

Budget Constraint Slope is –(1+i)= -1.1

No saving and no borrowing: 𝒚𝟏 =𝒄𝟏 & 𝒚𝟐 = 𝒄𝟐

All life-time income consumed in period 1 through borrowing

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The Overall Impact is then a sure in C1 (he person will save more) and ambiguous effects of C2, it depends on the magnitude of IE and SE.

**&**

0 1 2 3 4 5 6 7 8 9 10 11 12 130

2

4

6

8

10

12

C1

C2

Budget Constraint Slope is –(1+i)= -1.1

No saving and no borrowing: 𝒚𝟏 =𝒄𝟏 & 𝒚𝟐 = 𝒄𝟐

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As an exercise, you can do the case of a Saver.

The figure will be:

As the Relative Price of Good 1 (that is 1+i) then C1 falls: C1 ↓

As the Relative Price of Good 2 (that is 1/1+i) falls then C2 goes up: C2↑

0 1 2 3 4 5 6 7 8 9 10 11 12 130

2

4

6

8

10

12

C1

C2

Budget Constraint Slope is –(1+i)= -1.1

No saving and no borrowing: 𝒚𝟏 =𝒄𝟏 & 𝒚𝟐 = 𝒄𝟐

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Chapter 7: Simple 2-period Model

(Preliminary to Basic Dynamic General Equilibrium Model)

Dr. Maryam Dilmaghani

The Model is dynamic

as it do involves time explicitly.

C1

C2

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ECON3301: Intermediate Macroeconomics

Instructor: Dr. Maryam Dilmaghani

Notes on Multi-period, Dynamic General Equilibrium (Chapter 8) The goal of this chapter is to finish the development for the RBC framework of Dynamic

General Equilibrium and use the model to explain economic fluctuations.

The basis of the model is the same as the 2-period model in chapter 7 and it makes use of a more

sophisticated version of Income and Substitution effect in drawing the predictions.

1. Application of Income and Substitution Effect to consumption decision

The representative agent’s initial budget constraint in depicted by the red-line:

𝐶1 + 𝐶2 × � 11+𝑖� = 𝑦1 + 𝑦2 × � 1

1+𝑖� ⤇ 𝐶2 = (1 + 𝑖) × 𝑦1 + 𝑦2 − 𝐶1 × (1 + 𝑖)

𝐶2 = [(1 + 𝑖) × 𝑦1 + 𝑦2] − (1 + 𝑖) × 𝐶1

The y-axis intercept is [(1 + 𝑖) × 𝑦1 + 𝑦2]. The slope is −(1 + 𝑖).

Suppose interest rate, i, goes up. Given the position of income the two periods, the green line is the new budget constraint: clockwise rotation around endowment (no saving, no borrowing) point.

C1

C2

𝒚𝟏 & 𝒚𝟐

𝑪𝟏 & 𝑪𝟐

ECON3301 Fall 2011 SMU-Sobey SB

Page 2 of 10

Answer the following questions.

(i) What can you tell about the representative agents new choice (under the green budget

constraint) given the position of 𝑪𝟏 & 𝑪𝟐 and if 𝑺𝑬 > 𝑰𝑬.

Given that the figure shows𝑦1 > 𝐶1 (& 𝑦2 < 𝐶2), this agent is a saver. For a saver the IE of an

increase in interest rate is positive. Positive IE means an increase in purchasing power and as a

result the consumption of both goods increase

The interest rate has increased. It means that the relative price of consumption in period 1,

𝐶1, has increased: the opportunity cost of 𝐶1 is higher; since through saving, it can now buy a

larger amount of consumption in the future, 𝐶2).

Therefore:

𝐼𝐸 𝑖𝑠 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒 ⤇ 𝐶1 ↑ & 𝑎𝑛𝑑 𝐶2 ↑

𝑆𝐸 𝑜𝑓 𝑖 ↑ ⤇ 𝐶1 ↓ 𝑎𝑛𝑑 𝐶2 ↑

Hence, Total Effect on 𝑪𝟐 ↑ but in 𝑪𝟏 ↓ (SINCE

𝑆𝐸 > 𝐼𝐸).

C1

C2𝑵𝒆𝒘 𝑪𝟏 & 𝑪𝟐

ECON3301 Fall 2011 SMU-Sobey SB

Page 3 of 10

(ii) What can you tell about the representative agents new choice (under the green budget constraint) given the position of 𝑪𝟏 & 𝑪𝟐 and if 𝑰𝑬 > 𝑺𝑬.

You can do it yourself as an exercise.

2. Markets involved

(i) Goods Market

(ii) Labour Market

(iii) ‘Investment’ Market: Bonds Market (financial investment) & Rental Market (investment

physical capital) combined.

3. Endogenous variables

They are, as usual, price and quantity in each market.

(i) Goods Market: output and price of output, denoted by P.

(ii) Labour Market: employment level and wage, denoted by W.

(iii) ‘Investment’ Markets: Bonds Market (financial investment) & Rental Market (investment

physical capital): rate of return on investments or Interest Rate

.

3. Exogenous variables

There are two categories of Exogenous Variables in this model:

(i) Technology (Supply-side of the Goods’ market)

It refers to the productivity of the inputs (the parameters of the production function). Typically,

two different types of technological progress are considered.

ECON3301 Fall 2011 SMU-Sobey SB

Page 4 of 10

(i)-1: The technological change can affect only the total output (parallel shift of production

function:

For a progress, we need to have B> 0, 𝑡ℎ𝑒 𝑓𝑖𝑔𝑢𝑟𝑒 𝑖𝑠 𝑏𝑒𝑙𝑜𝑤.

In this case both MPL and MPK remain the same.

Mathematics, fyi:

𝑌𝑜𝑙𝑑 = 𝐹(𝐿,𝐾) = 𝐴𝐿𝛼𝐾𝛽 ⤇ 𝑀𝑃𝐿𝑜𝑙𝑑 = 𝐴𝐾𝛽 × (𝛼) × 𝐿𝛼−1 = �𝐴𝐾𝛽 × (𝛼)� × 𝐿𝛼−1

𝑌𝑛𝑒𝑤 = 𝐹(𝐿,𝐾) + 𝐵 = �𝐴𝐿𝛼𝐾𝛽� + 𝐵 ⤇ 𝑀𝑃𝐿𝑛𝑒𝑤 = 𝐴𝐾𝛽 × (𝛼) × 𝐿𝛼−1 = �𝐴𝐾𝛽 × (𝛼)� × 𝐿𝛼−1

So, you see that: 𝑀𝑃𝐿𝑜𝑙𝑑 = 𝑀𝑃𝐿𝑛𝑒𝑤

The same happens to MPK (no change).

(i)-2: it can affect Marginal Product of Inputs (proportionate shift of production function):

Total output, 𝑌 = 𝐴𝐹(𝐾, 𝐿) ⤇ 𝑁𝑒𝑤 𝑜𝑢𝑡𝑝𝑢𝑡 𝑌𝑁𝑒𝑤 = (𝐴 × 𝜀) × 𝐹(𝐾, 𝐿)

For a progress, we need to have ε> 1, 𝑡ℎ𝑒 𝑓𝑖𝑔𝑢𝑟𝑒 𝑖𝑠 𝑏𝑒𝑙𝑜𝑤.

K/L

Y/L

ECON3301 Fall 2011 SMU-Sobey SB

Page 5 of 10

And Marginal Products (MPL & MPK)

K/L

Y/L

Labour

MPL

Capital

MPK

ECON3301 Fall 2011 SMU-Sobey SB

Page 6 of 10

Mathematics, fyi:

𝑌𝑜𝑙𝑑 = 𝐹(𝐿,𝐾) = 𝐴𝐿𝛼𝐾𝛽 ⤇ 𝑀𝑃𝐿𝑜𝑙𝑑 = 𝐴𝐾𝛽 × (𝛼) × 𝐿𝛼−1 = �𝐴𝐾𝛽 × (𝛼)� × 𝐿𝛼−1

𝑌𝑛𝑒𝑤 = 𝐹(𝐿,𝐾) × 𝜀 = �𝐴𝐿𝛼𝐾𝛽� × 𝜀 ⤇

𝑀𝑃𝐿𝑛𝑒𝑤 = 𝜀 × 𝐴𝐾𝛽 × (𝛼) × 𝐿𝛼−1 = 𝜀 × �𝐴𝐾𝛽 × (𝛼)�× 𝐿𝛼−1

So, you see that: 𝑀𝑃𝐿𝑜𝑙𝑑 < 𝑀𝑃𝐿𝑛𝑒𝑤 and it translates itself to a rightward shift.

The same happens to MPK .

(ii) Preferences (Demand-side of the Goods’ market)

(ii)-1: Subjective rate of patience

Note that 𝑙1 + 𝑧1 = 𝑇𝑜𝑡𝑎𝑙 𝑡𝑖𝑚𝑒 𝑎𝑣𝑎𝑖𝑙𝑎𝑏𝑙𝑒 𝑡𝑜 𝑡ℎ𝑒 𝑎𝑔𝑒𝑛𝑡 𝑖𝑛 𝑝𝑒𝑟𝑖𝑜𝑑 1.

(propensity to consume (or save) in period 1 compared to

period 2; i.e. how to divide the present value of life time income among 𝑐1 & 𝑐2 & 𝑐3...

(consumption in different periods) and how to allocate time for leisure (whose opportunity costs

is forgone wage) among different periods; i.e. the decision about the level of 𝑧1, 𝑧2, 𝑧3 … .

This exogenous variable (parameter of preferences) determines Inter-temporal Substitution

Effect

(ii)-2: The taste (preference) over leisure and consumption. It informs of how an agent is willing

to substitute leisure (consumption) for consumption (leisure) in the same period while achieving

the same level of satisfaction (utility).

This exogenous variable (parameter of preferences) determines Intra-temporal Substitution

Effect.

4. The duration of the exogenous changes: Permanent or Temporary

All the exogenous variables can change in a permanent or temporary manner. The impact of a

permanent change is larger than a temporary change in its magnitude. It can for instance help

assuming whether IE is larger or smaller than SE.

ECON3301 Fall 2011 SMU-Sobey SB

Page 7 of 10

Application of Multi-period Dynamic General Equilibrium Model

A. Preliminaries

The goal is to use MDGE to understand the impact of exogenous changes on endogenous

variables. The main exogenous variable considered is Technological Change.

Taking the Goods Market

(i) Producers: They are the supply-side of the Goods Market. Their objective is to maximize

their Profit. In order to maximise their profit, they choose the level of inputs the want to hire

given the productivity (affected by the abstract concept of technology) and other variables (price

–cost- of inputs and price of output).

as the benchmark, he actors in this model can be put into two

categories:

Recall that 𝐿𝑎𝑏𝑜𝑢𝑟 − 𝐷𝑒𝑚𝑎𝑛𝑑: 𝐿𝑑 = 𝑀𝑃𝐿 & 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 − 𝐷𝑒𝑚𝑎𝑛𝑑: 𝐾𝑑 = 𝑀𝑃𝐾

Technological change may affect MPL and MPK hence labour and capital demand.

(ii) Consumers: They are the demand-side of the Goods Market. Their objective is to maximize

their Utility (satisfaction). Their utility comes from Consumption and Leisure and it incorporates

the agents’ time-preference (patience) and the preferences and taste over Consumption & Leisure

(the contribution of each to their satisfaction).

In order to maximise their utility hence, they must decide how to allocate the present value (PV)

of their life-time budget (we actually assume that the representative agent lives forever,

abstracting from consideration the replacement of generations by one another). It can e

summarise as follows:

1) Given their rate of patience (subjective discount rate) as well as their income and prices

(future and current) they decide on their pattern of consumption (𝐶1,𝐶2,𝐶3, … ) and leisure

𝑍1,𝑍2,𝑍3, … ) overtime.

ECON3301 Fall 2011 SMU-Sobey SB

Page 8 of 10

This decision is affected by Income Effect (IE) as well as Inter-temporal Substitution Effect

(Inter-SE).

2) Given their taste & preference for consumption and leisure as well as their income and prices

(current & future) they decide on the pattern of consumption and leisure in every given period:

(𝐶1,𝑍1), (𝐶2,𝑍2), (𝐶3,𝑍3),... .

This decision is affected by Income Effect (IE) as well as Intra-temporal Substitution Effect

(Intra-SE).

The consumption decision determines savings hence Supply of Capital, 𝐾𝑆, and the decision of

leisure determined Labour Supply, 𝐿𝑆.

B. Application

Case 1: Proportionate and Permanent Technological Progress.

Recall that a proportionate shift of production function is characterised by an upward shift of

production function is in below:

Total output, 𝑌 = 𝐴𝐹(𝐾, 𝐿) ⤇ 𝑁𝑒𝑤 𝑜𝑢𝑡𝑝𝑢𝑡 𝑌𝑁𝑒𝑤 = (𝐴 × 𝜀) × 𝐹(𝐾, 𝐿) with ε> 1

And Marginal Products (MPL & MPK) shifts rightward.

K/L

Y/L

ECON3301 Fall 2011 SMU-Sobey SB

Page 9 of 10

Step 1: Goods Market

(i) Supply-side

(i)-1: Technological Progress ⤇ Output ↑⤇ All else equal, Price (P) ↓

(i)-2: MPL↑ & MPK ↑⤇ 𝐿𝑑 𝑠ℎ𝑖𝑓𝑡 𝑟𝑖𝑔ℎ𝑡 & 𝐾𝑑 𝑠ℎ𝑖𝑓𝑡𝑠 𝑟𝑖𝑔ℎ𝑡𝑤𝑎𝑟𝑑.

The shifts in MPL and MPK are forever

(because the technological change is permanent).

(ii) Demand-side

As P ↓⤇𝑊𝑃

↑ ⤇ it generates both Income and Substitution Effect.

(ii)-1: Income Effect (IE) is positive ⤇ The agent can have more of both consumption and

leisure, forever. It means 𝐶𝑡 ↑ (𝑆𝑡 ↓) 𝑎𝑛𝑑 𝑍𝑡 ↑ (𝐿𝑡 ↓)𝑓𝑜𝑟 𝑎𝑙𝑙 𝑡, by IE.

Note that the t subscript indicates the period of time.

(ii)-2: Intra-temporal Substitution Effect (Intra-SE)

𝑊𝑃

↑ ⤇ The opportunity cost of leisure ↑⤇ 𝐶𝑡is now cheaper relative to 𝑍𝑡⤇ 𝐶𝑡↑ (𝑆𝑡 ↓) and

𝑍𝑡 ↓ (𝐿𝑡 ↑) in every given period, by Intra-SE.

(ii)-3: Inter-temporal Substitution Effect (Inter-SE) does NOT exist.

As the change is permanent, all the periods in future are identical, hence it does not make sense to have different patterns (a permanent change, as a rule, does not generate Inter-temporal Substitution Effect).

Hence, Total Effect on Labour Demand demands on the relative magnitude of IE (𝐿𝑡 ↓) and Intra-SE (𝐿𝑡 ↑).

If we suppose that 𝐼𝐸 > 𝐼𝑛𝑡𝑟𝑎 − 𝑆𝐸, then 𝐿𝑡 ↓ and 𝐿𝑑 shifts to the left, otherwise it shifts rightward.

ECON3301 Fall 2011 SMU-Sobey SB

Page 10 of 10

Step 2: Labour Market

Now, we just need to put supply and demand together and see what happens to the equilibrium real wage,�𝑊

𝑃�∗, and equilibrium level of employment, 𝐿∗.

Old curves: Dash

New Curves: Solid

The magnitude of shifts are assumed (they can be larger or smaller). As we see that both �𝑊𝑃�∗↑

and 𝐿∗ ↑. It means that Real Wage increases and the level of employment rises.

Question:

Can a Permanent and Proportionate Technological Change cause Real Wage to fall? Explain.

Can a Permanent and Proportionate Technological Change cause Level of Employment to fall? Explain.

Labour

W/P

ECON3301 Fall 2011 SMU-Sobey SB

Page 1 of 7

ECON3301: Intermediate Macroeconomics

Instructor: Dr. Maryam Dilmaghani

Notes on Multi-period, Dynamic General Equilibrium (Chapter 8) The goal of this chapter is to finish the development for the RBC framework of Dynamic

General Equilibrium and use the model to explain economic fluctuations.

The basis of the model is the same as the 2-period model in chapter 7 and it makes use of a more

sophisticated version of Income and Substitution effect in drawing the predictions.

1. Application of Income and Substitution Effect to consumption decision

The representative agent’s initial budget constraint in depicted by the red-line:

𝐶1 + 𝐶2 × � 11+𝑖� = 𝑦1 + 𝑦2 × � 1

1+𝑖� ⤇ 𝐶2 = (1 + 𝑖) × 𝑦1 + 𝑦2 − 𝐶1 × (1 + 𝑖)

𝐶2 = [(1 + 𝑖) × 𝑦1 + 𝑦2] − (1 + 𝑖) × 𝐶1

The y-axis intercept is [(1 + 𝑖) × 𝑦1 + 𝑦2]. The slope is −(1 + 𝑖).

Suppose interest rate, i, goes up. Given the position of income the two periods, the green line is the new budget constraint: clockwise rotation around endowment (no saving, no borrowing) point.

C1

C2

𝒚𝟏 & 𝒚𝟐

𝑪𝟏 & 𝑪𝟐

ECON3301 Fall 2011 SMU-Sobey SB

Page 2 of 7

Answer the following questions.

(i) What can you tell about the representative agents new choice (under the green budget

constraint) given the position of 𝑪𝟏 & 𝑪𝟐 and if 𝑺𝑬 > 𝑰𝑬.

Given that the figure shows𝑦1 > 𝐶1 (& 𝑦2 < 𝐶2), this agent is a saver. For a saver the IE of an

increase in interest rate is positive. Positive IE means an increase in purchasing power and as a

result the consumption of both goods increase

The interest rate has increased. It means that the relative price of consumption in period 1,

𝐶1, has increased: the opportunity cost of 𝐶1 is higher; since through saving, it can now buy a

larger amount of consumption in the future, 𝐶2).

Therefore:

𝐼𝐸 𝑖𝑠 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒 ⤇ 𝐶1 ↑ & 𝑎𝑛𝑑 𝐶2 ↑

𝑆𝐸 𝑜𝑓 𝑖 ↑ ⤇ 𝐶1 ↓ 𝑎𝑛𝑑 𝐶2 ↑

Hence, Total Effect on 𝐶2 ↑ but in 𝐶1 ↓ SINCE

𝑆𝐸 > 𝐼𝐸.

C1

C2𝑵𝒆𝒘 𝑪𝟏 & 𝑪𝟐

ECON3301 Fall 2011 SMU-Sobey SB

Page 3 of 7

(ii) What can you tell about the representative agents new choice (under the green budget constraint) given the position of 𝑪𝟏 & 𝑪𝟐 and if 𝑰𝑬 > 𝑺𝑬.

You can do it yourself as an exercise.

2. Markets involved

(i) Goods Market

(ii) Labour Market

(iii) ‘Investment’ Markets: Bonds Market (financial investment) & Rental Market (investment

physical capital) combined.

3. Endogenous variables

They are, as usual, price and quantity in each market.

(i) Goods Market: output and price of output, denoted by P.

(ii) Labour Market: employment level and wage, denoted by W.

(iii) ‘Investment’ Markets: Bonds Market (financial investment) & Rental Market (investment

physical capital): rate of return on investments or Interest Rate

.

3. Exogenous variables

There are two categories of Exogenous Variables in this model:

(i) Technology (Supply-side of the Goods’ market)

It refers to the productivity of the inputs (the parameters of the production function). Typically,

two different types of technological progress are considered.

ECON3301 Fall 2011 SMU-Sobey SB

Page 4 of 7

(i)-1: The technological change can affect only the total output (parallel shift of production

function:

For a progress, we need to have B> 0, 𝑡ℎ𝑒 𝑓𝑖𝑔𝑢𝑟𝑒 𝑖𝑠 𝑏𝑒𝑙𝑜𝑤.

In this case both MPL and MPK remain the same.

Mathematics, fyi:

𝑌𝑜𝑙𝑑 = 𝐹(𝐿,𝐾) = 𝐴𝐿𝛼𝐾𝛽 ⤇ 𝑀𝑃𝐿𝑜𝑙𝑑 = 𝐴𝐾𝛽 × (𝛼) × 𝐿𝛼−1 = �𝐴𝐾𝛽 × (𝛼)� × 𝐿𝛼−1

𝑌𝑛𝑒𝑤 = 𝐹(𝐿,𝐾) + 𝐵 = �𝐴𝐿𝛼𝐾𝛽� + 𝐵 ⤇ 𝑀𝑃𝐿𝑛𝑒𝑤 = 𝐴𝐾𝛽 × (𝛼) × 𝐿𝛼−1 = �𝐴𝐾𝛽 × (𝛼)� × 𝐿𝛼−1

So, you see that: 𝑀𝑃𝐿𝑜𝑙𝑑 = 𝑀𝑃𝐿𝑛𝑒𝑤

The same happens to MPK (no change).

(i)-2: it can affect Marginal Product of Inputs (parallel shift of production function:

Total output, 𝑌 = 𝐴𝐹(𝐾, 𝐿) ⤇ 𝑁𝑒𝑤 𝑜𝑢𝑡𝑝𝑢𝑡 𝑌𝑁𝑒𝑤 = (𝐴 × 𝜀) × 𝐹(𝐾, 𝐿)

For a progress, we need to have ε> 1, 𝑡ℎ𝑒 𝑓𝑖𝑔𝑢𝑟𝑒 𝑖𝑠 𝑏𝑒𝑙𝑜𝑤.

K/L

Y/L

ECON3301 Fall 2011 SMU-Sobey SB

Page 5 of 7

And Marginal Products (MPL & MPK)

K/L

Y/L

Labour

MPL

Capital

MPK

ECON3301 Fall 2011 SMU-Sobey SB

Page 6 of 7

Mathematics, fyi:

𝑌𝑜𝑙𝑑 = 𝐹(𝐿,𝐾) = 𝐴𝐿𝛼𝐾𝛽 ⤇ 𝑀𝑃𝐿𝑜𝑙𝑑 = 𝐴𝐾𝛽 × (𝛼) × 𝐿𝛼−1 = �𝐴𝐾𝛽 × (𝛼)� × 𝐿𝛼−1

𝑌𝑛𝑒𝑤 = 𝐹(𝐿,𝐾) × 𝜀 = �𝐴𝐿𝛼𝐾𝛽� × 𝜀 ⤇

𝑀𝑃𝐿𝑛𝑒𝑤 = 𝜀 × 𝐴𝐾𝛽 × (𝛼) × 𝐿𝛼−1 = 𝜀 × �𝐴𝐾𝛽 × (𝛼)�× 𝐿𝛼−1

So, you see that: 𝑀𝑃𝐿𝑜𝑙𝑑 < 𝑀𝑃𝐿𝑛𝑒𝑤 and it translates itself to a rightward shift.

The same happens to MPK .

(ii) Preferences (Demand-side of the Goods’ market)

(ii)-1: Subjective rate of patience

Note that 𝑙1 + 𝑧1 = 𝑇𝑜𝑡𝑎𝑙 𝑡𝑖𝑚𝑒 𝑎𝑣𝑎𝑖𝑙𝑎𝑏𝑙𝑒 𝑡𝑜 𝑡ℎ𝑒 𝑎𝑔𝑒𝑛𝑡 𝑖𝑛 𝑝𝑒𝑟𝑖𝑜𝑑 1.

(propensity to consume (or save) in period 1 compared to

period 2; i.e. how to divide the present value of life time income among 𝑐1 & 𝑐2 & 𝑐3...

(consumption in different periods) and how to allocate time for leisure (whose opportunity costs

is forgone wage) among different periods; i.e. the decision about the level of 𝑧1, 𝑧2, 𝑧3 … .

This exogenous variable (parameter of preferences) determines Inter-temporal Substitution

Effect

(ii)-2: The taste (preference) over leisure and consumption. It informs of how an agent is willing

to substitute leisure (consumption) for consumption (leisure) in the same period while achieving

the same level of satisfaction (utility).

This exogenous variable (parameter of preferences) determines Intra-temporal Substitution

Effect.

ECON3301 Fall 2011 SMU-Sobey SB

Page 7 of 7

4. The duration of the exogenous changes: Permanent or Temporary

All the exogenous variables can change in a permanent or temporary manner. The impact of a

permanent change is larger than a temporary change in its magnitude. It can for instance help

assuming whether IE is larger or smaller than SE.

ECON3301 Fall 2011 SMU-Sobey SB

Page 1 of 5

ECON3301: Intermediate Macroeconomics

Instructor: Dr. Maryam Dilmaghani

Notes on Multi-period, Dynamic General Equilibrium (Chapter 9)

The goal of this chapter is to finish the development for the RBC framework of Dynamic

General Equilibrium and use the model to explain economic fluctuations in Goods Market,

Labour Market and Capital Market.

A. Review of the general points

The goal is to use MDGE to understand the impact of exogenous changes on endogenous

variables. The main exogenous variable considered is Technological Change.

Taking the Goods Market

(i) Producers: They are the supply-side of the Goods Market. Their objective is to maximize

their Profit. In order to maximise their profit, they choose the level of inputs the want to hire

given the productivity (affected by the abstract concept of technology) and other variables (price

–cost- of inputs and price of output).

as the benchmark, he actors in this model can be put into two

categories:

Recall that 𝐿𝑎𝑏𝑜𝑢𝑟 − 𝐷𝑒𝑚𝑎𝑛𝑑: 𝐿𝑑 = 𝑀𝑃𝐿 & 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 − 𝐷𝑒𝑚𝑎𝑛𝑑: 𝐾𝑑 = 𝑀𝑃𝐾

Technological change may affect MPL and MPK hence labour and capital demand.

(ii) Consumers: They are the demand-side of the Goods Market. Their objective is to maximize

their Utility (satisfaction). Their utility comes from Consumption and Leisure and it incorporates

the agents’ time-preference (patience) and the preferences and taste over Consumption & Leisure

(the contribution of each to their satisfaction).

ECON3301 Fall 2011 SMU-Sobey SB

Page 2 of 5

In order to maximise their utility hence, they must decide how to allocate the present value (PV)

of their life-time budget (we actually assume that the representative agent lives forever,

abstracting from consideration the replacement of generations by one another). It can e

summarise as follows:

1) Given their rate of patience (subjective discount rate) as well as their income and prices

(future and current) they decide on their pattern of consumption (𝐶1,𝐶2,𝐶3, … ) and leisure

𝑍1,𝑍2,𝑍3, … ) overtime.

This decision is affected by Income Effect (IE) as well as Inter-temporal Substitution Effect

(Inter-SE).

2) Given their taste & preference for consumption and leisure as well as their income and prices

(current & future) they decide on the pattern of consumption and leisure in every given period:

(𝐶1,𝑍1), (𝐶2,𝑍2), (𝐶3,𝑍3),... .

This decision is affected by Income Effect (IE) as well as Intra-temporal Substitution Effect

(Intra-SE).

The consumption decision determines savings hence Supply of Capital, 𝐾𝑆, and the decision of

leisure determined Labour Supply, 𝐿𝑆.

B. Application

Case 1: Proportionate and Permanent Technological Progress:

Note: We focus on Capital market for now.

Recall that a proportionate shift of production function is characterised by an upward shift of

production function is in below:

Total output, 𝑌 = 𝐴𝐹(𝐾, 𝐿) ⤇ 𝑁𝑒𝑤 𝑜𝑢𝑡𝑝𝑢𝑡 𝑌𝑁𝑒𝑤 = (𝐴 × 𝜀) × 𝐹(𝐾, 𝐿) with ε> 1

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And Marginal Products (MPL & MPK) shift rightward.

Step 1: Goods Market

(i) Supply-side

(i)-1: Technological Progress ⤇ Output ↑⤇ All else equal, Price (P) ↓

(i)-2: MPK ↑⤇ 𝐾𝑑 𝑠ℎ𝑖𝑓𝑡𝑠 𝑟𝑖𝑔ℎ𝑡𝑤𝑎𝑟𝑑.

The shift MPK is forever

(ii) Demand-side

(because the technological change is permanent).

As P ↓⤇𝑅𝑃

↑ ⤇ it generates both Income and Substitution Effect.

(ii)-1: Income Effect (IE) is positive ⤇ The agent can have more of both consumption and

leisure, forever. It means 𝑪𝒕 ↑ 𝒂𝒏𝒅 𝑺𝒕 ↓ 𝐛𝐲 𝐈𝐄.

𝐴𝑙𝑠𝑜: 𝑎𝑛𝑑 𝑍𝑡 ↑ (𝐿𝑡 ↓)𝑓𝑜𝑟 𝑎𝑙𝑙 𝑡 (∀𝑡).

Note that ∀𝑡 mean for all periods of time (forever).

(ii)-2: Intra-temporal Substitution Effect (Intra-SE)

K/L

Y/L

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Recall: The trade-off involved with Intra-SE is to compare the sources of utility (satisfaction) in

each period with each other, i.e. 𝐶1 𝑤𝑖𝑡ℎ 𝑍1 ,𝐶2𝑤𝑖𝑡ℎ 𝑍2 …, taking into account their

(opportunity) cost.

𝑃 ↓⤇ 𝑊𝑃

↑ ⤇ The opportunity cost of leisure ↑ ⤇ 𝐶𝑡is now cheaper relative to 𝑍𝑡⤇ 𝑪𝒕↑ and

𝑺𝒕 ↓ 𝒃𝒚 𝑰𝒏𝒕𝒓𝒂 − 𝑺𝑬.

(Also: 𝑍𝑡 ↓ (𝐿𝑡 ↑) in every given period, by Intra-SE; but here we ignore labour market).

(ii)-3: Inter-temporal Substitution Effect (Inter-SE) does NOT exist.

As the change is permanent, all the periods in future are identical, hence it does not make sense to have different patterns (a permanent change, as a rule, does not generate Inter-temporal Substitution Effect).

Hence,

Total Effect on Capital Supply is negative, meaning a shift to the left.

Step 2: Capital Market

Now, we just need to put supply and demand together and see what happens to the equilibrium real rental rate,�𝑊

𝑃�∗, and equilibrium level of physical capital, 𝐾∗.

Old curves: Dash

New Curves: Solid

The magnitude of shifts are assumed (they can be larger or smaller). As we see that both �𝑅𝑃�∗↑

and 𝐾∗ ↑. It means that Real Rental Rate increases and the level of physical capital investment rises as well.

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Questions:

Can a Permanent and Proportionate Technological Change cause Real Rental Rate �𝑅𝑃�∗ to fall?

Explain how and comment.

Can a Permanent and Proportionate Technological Change cause Level of Physical Investment (𝐾∗) to fall? Explain how and comment.

Capital

R/P

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Notes on Economic Growth in Canada

1. What is Economic Growth?

Economic growth is the increase of aggregate production in a given economy.

2. How can we measure Economic Growth?

Economic Growth is the increase of per capita gross domestic product (GDP) as a measure of

aggregate income. Usually, the annual rate of change in real GDP is taken as the indicator of the

annual rate of growth.

2.1. GDP as an indicator of economic growth

Gross domestic product (GDP) refers to the market value of all final goods and services

produced within a country in a given period. GDP per capita and its changes over time is often

considered an indicator of a country's standard of living and economic growth.

2.2. Measuring GDP

GDP can be determined in three ways, all of which should, in principle, give the same result.

They are the product (or output) approach, the income approach, and the expenditure approach.

The most direct of the three is the product approach, which sums the outputs of every class of

enterprise to arrive at the total. The expenditure approach works on the principle that all of the

product must be bought by somebody, therefore the value of the total product must be equal to

people's total expenditures in buying things.

The income approach works on the principle that the incomes of the productive factors

("producers," colloquially) must be equal to the value of their product, and determines GDP by

finding the sum of all producers' incomes.

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Example: the expenditure method:

GDP = Value of private consumption (C) + Value of gross investment (I) + Value of government spending (G) + Value of exports in national currency -imports

𝐺𝐷𝑃 = 𝐶 + 𝐼 + 𝐺 + 𝜀𝑋 −𝑀

Note:

"Gross" means that GDP measures production regardless of the various uses to which that

production can be put. Production can be used for immediate consumption, for investment in

new fixed assets or inventories, or for replacing depreciated fixed assets. "Domestic" means that

GDP measures production that takes place within the country's borders. In the expenditure-

method equation given above, the exports-minus-imports term is necessary in order to null out

expenditures on things not produced in the country (imports) and add in things produced but not

sold in the country (exports).

2.3. Shortcomings of GDP as an indicator of economic performance

Wealth distribution

Non-market transactions

Underground economy

Non-monetary economy

Quality improvements and inclusion of new products

3. Main factors behind Economics Growth

Economic growth is primarily driven by improvements in productivity, which involves

producing more goods and services with the same inputs of labour, capital, energy and materials.

4. Temporal Horizon for Measuring Economic Growth

The long-run path of economic growth is one of the central questions of economics; despite

some problems of measurement, an increase in GDP of a country greater than population growth

is generally taken as an increase in the standard of living of its inhabitants. Over long periods of

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time, even small rates of annual growth can have large effects through compounding (see

exponential growth).

A growth rate of 2.5% per annum will lead to a doubling of GDP within 29 years, whilst a

growth rate of 8% per annum (experienced by some Four Asian Tigers) will lead to a doubling of

GDP within 10 years. This exponential characteristic can exacerbate differences across nations.

5. Short-run versus long-run considerations

Economists draw a distinction between short-term economic stabilization and long-term economic

growth. The topic of economic growth is primarily concerned with the long run. The short-run variation

of economic growth is termed the business cycle.

6. Principal Theories of Economic Growth

6.1.Exogenous growth model (Solow–Swan growth model) 6.2.Ramsey-Cass-Koopmans model

The Ramsey model differs from the Solow model in that it explicitly models the choice of consumption at a point in time and so endogenizes the saving rate.

6.3.Endogenous growth theory

In economics, endogenous growth theory or new growth theory was developed in the 1980s as

a response to criticism of the neo-classical growth model. The endogenous growth theory holds

that policy measures can have an impact on the long-run growth rate of an economy. For

example, subsidies on research and development or education increase the growth rate in some

endogenous growth models by increasing the incentive to innovate.

In neo-classical growth models, the long-run rate of growth is exogenously determined by either

assuming a savings rate or a rate of technical progress (Solow model). However, the savings rate

and rate of technological progress remain unexplained. Endogenous growth theory tries to

overcome this shortcoming by building macroeconomic models out of microeconomic

foundations. Households are assumed to maximize utility subject to budget constraints while

firms maximize profits.

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Crucial importance is usually given to the production of new technologies and human capital.

The engine for growth can be as simple as a constant return to scale production function (the AK

model) or more complicated set ups with spillover effects (spillovers are positive externalities,

benefits that are attributed to costs from other firms), increasing numbers of goods, increasing

qualities, etc.

7. Economic Growth in Canada

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Notes on Taxation and Fiscal Policy

Instructor: Dr. Maryam Dilmaghani

1. Types of tax

1.1. Lump-sum taxes

A lump-sum tax is a tax that is a fixed amount, no matter the change in circumstance of the taxed entity. For instance, the tax-payer has to contribute $ 1000 yearly, regardless of her/his earnings, property’s value, production etc.

Lump-sum taxes do not react to the changes in those items either. Only the taxing entity (fiscal authority of government) can change them.

1.2. Proportionate taxes.

There taxes are a function of the value of the taxes item (e.g. output, added value, property, earnings).

2. Impact of tax within RBC framework

2.1. Lump-sum taxes

Lump-sum taxes are comparable to parallel shock technological shocks with starting or increasing (eliminating or reducing) a lump-sum tax is a negative (positive/progress) shock.

Hence, our previously developed General Equilibrium Model can be readily applied to these taxes.

Example: Imposing a lump-sum tax on producers, permanently. This tax is identical in impact to a parallel and permanent shock. We follow the same steps in the analysis.

2.1. Proportionate taxes

Proportionate taxes are comparable to proportionate shock technological shocks with starting or increasing (eliminating or reducing) a Proportionate taxes is a negative (positive/progress) shock.

Hence, our previously developed General Equilibrium Model can be readily applied to these taxes.

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Example: A lump-sum tax on producers, permanent

This tax is identical in impact to a proportionate and permanent negative shock. We follow the same steps in the analysis.

Recall that a parallel technological change can affect only the total output (parallel shift of

production function). For this kind of shock (𝑡ℎ𝑒 𝑓𝑖𝑔𝑢𝑟𝑒 𝑏𝑒𝑙𝑜𝑤), both MPL and MPK remain

the same.

.

Step 1: Goods Market

(i) Supply-side

(i)-1: Lump-sum tax ⤇ Output ↓⤇ All else equal, Price (P) ↑

(i)-2: MPL & MPK do not change⤇ 𝐿𝑑 & 𝐾𝑑 𝑑𝑜 𝑛𝑜𝑡 𝑠ℎ𝑖𝑓𝑡.

(ii) Demand-side

As P↑ ⤇𝑊𝑃

↓ ⤇ it generates both Income and Substitution Effect.

(ii)-1: Income Effect (IE) is negative ⤇ The agent will have to reduce both consumption

and leisure, forever. It means 𝐶𝑡 ↓ 𝑎𝑛𝑑 𝑍𝑡 ↓ (𝑳𝒕 ↑)𝒇𝒐𝒓 𝒂𝒍𝒍 𝒕, by IE.

K/L

Y/L

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(ii)-2: Intra-temporal Substitution Effect (Intra-SE)

𝑊𝑃

↓ ⤇ The opportunity cost of leisure ↓⤇ 𝐶𝑡is now more expensive relative to 𝑍𝑡⤇ 𝐶𝑡↓ and

𝑍𝑡 ↑(𝑳𝒕 ↓) in every given period, by Intra-SE.

(ii)-3: Inter-temporal Substitution Effect (Inter-SE) does NOT exist because the tax is permanent.

Recall that when the change is permanent, all the periods in future are identical, hence it does not make sense to have different patterns (a permanent change, as a rule, does not generate Inter-temporal Substitution Effect).

Labour Supply?

Hence, Total Effect on Labour Supply demands on the relative magnitude of IE (𝐿𝑡 ↑) and Intra-SE (𝐿𝑡 ↓).

If we suppose that 𝐼𝐸 > 𝐼𝑛𝑡𝑟𝑎 − 𝑆𝐸, then 𝐿𝑡 ↑ ∀𝑡 and 𝐿𝑠 shifts to the right, otherwise it shifts rightward.

Note:

Capital Supply?

It makes sense for a paramagnet change to assume IE dominates SE.

Important Note:

Step 2: Labour Market

As the change is permanent then there is no Intratemporal Substitution effect. Saving is reacting more strongly to Inter-temporal Substitution Effect, hence we can assume that it does not change hence 𝐾𝑠 remains unaffected.

Now, we just need to put supply and demand together and see what happens to the equilibrium real wage,�𝑊

𝑃�

∗, and equilibrium level of employment, 𝐿∗.

From the above, we know that MPL did not change so 𝐿𝑑 will not shift, and 𝐿𝑠 shifts to the right.

Old curves: Dash

New Curves: Solid

As we see that after this tax �𝑊𝑃

�∗

↓ and 𝐿∗ ↑. It means that Real Wage falls and the level of employment rises.

Note that Lump-sum taxes do not cause Economic Distortion is the markets (as opposed to proportionate taxes). Economic Distortion is the fall in the volume of transactions (Quantity) in

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a market (i.e. the quantity of goods sold 𝑄∗, the level of labour employed: 𝐿∗ etc) after a governmental intervention (e.g. tax or subsidy).

Step 3: Capital Market

Now, we need to put supply and demand together and see what happens to the equilibrium real wage,�𝑅

𝑃�

∗, and equilibrium level of employment, 𝐾∗.

From the above we know that as MPK did not change, 𝐾𝑑 does not shift and the shift in 𝐾𝑠 in negligible, if any since there in no Inter-temporal SE.

So, 𝑏𝑜𝑡ℎ �𝑅𝑃

�∗ and 𝐾∗ remain the same.

Again, note that Lump-sum taxes do not cause Economic Distortion is the markets (as opposed to proportionate taxes). Economic Distortion is the fall in the volume of transactions in a market after a governmental intervention (e.g. tax or subsidy).

You can try a Permanent and Proportionate (and other cases) following the same steps by noticing that its impact is identical to a Permanent and Proportionate reduction is productivity.

Labour

W/P

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Notes on Chapter 10: Monetary Policy

Instructor: Dr. Maryam Dilmaghani

1. Money Market Model

Endogenous variables: Quantity of money (in C$ for instance).

Nominal interest rate: i, in %.

To simplify, we assume that Money Supply curve is a vertical straight line (like we assumed in the beginning for Labour and Capital Supply).

The justification in this case is that the quantity of Money Supply is fixed by Monetary Policy central banks).

The Money Demand curve is assumed to be a normal downward sloping curve.

The equilibrium quantity of money and nominal interest rate is the intersection of Supply and Demand.

Quantity of Money

i

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1. Monetary Expansion & other markets

Monetary expansion is increasing Money Supply. Usually, the goal of such policy is to stimulate economy.

With a monetary expansion, Money Supply curve (𝑀𝑠), shifts rightward. The equilibrium quantity of money (𝑀∗) rises, and nominal interest rate (𝑖∗) falls.

1. Relating Money Market to other markets

To relate Money Market to other markets we must make use of No Arbitrage Principle.

NAP postulates that in free, inter-related markets (like in RBC) the rate of return on all investments must be the same in the equilibrium.

The principle relies on the assumption of rational decision making of the investors: the rational invertors will switch to the investment options that have higher return until the return in all options become equal, as follows:

Suppose investment option A (physical capital, paying R: Rental Rate) has a higher return than the investment option B (financial investment, paying nominal interest rate): MPK> 𝑖

⤇ Supply of Funds in Physical capital Market increase by investors switching to them: 𝐾𝑠 ↑ ⤇ MPK↓ and this process continues until MPK becomes equal i (nominal interest rate).

Quantity of Money

i

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So we have that at the General Equilibrium (equilibrium is all of our now 4 markets: Goods, Labour, Capital, Money):

𝑹 (𝒓𝒆𝒏𝒕𝒂𝒍 𝒓𝒂𝒕𝒆) = 𝒊

2. The impact of monetary policy

Suppose there is an expansionist monetary policy: 𝑀𝑠 ↑

2.1. In Money Market

With a monetary expansion, Money Supply curve (𝑀𝑠), shifts rightward. The equilibrium quantity of money (𝑀∗) rises, and nominal interest rate (𝑖∗) falls.

2.2. In Capital market

By virtue of No Arbitrage Principle, we have that at the equilibrium 𝑖∗ = 𝑅∗. Hence, before the monetary expansion 𝑖∗ = 𝑅∗ but with then expansion:

𝑀𝑠 ↑⤇ 𝑖∗ ↓ ⤇ Now (after expansion) 𝑅∗ > 𝑖∗ ⤇ Invertors switch to Physical Capital Market⤇𝐾𝑠 ↑⤇ 𝑅∗↓

And the process continues until 𝑖∗ = 𝑅∗ again.

Quantity of Money

i

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Figure:

At the new equilibrium in the capital market, we have: 𝑲∗ ↑ 𝒂𝒏𝒅 �𝑹𝑷

�∗

↓

Note: we assume price remain fixed for now.

2.3. In labour market

Recall that real rental the marginal productivity of labour (physical capital) is a function of the

level of capital ( labor) input: K ↑⤇ MPL ↑

(As we had in the assignment:

𝑀𝑃𝐿 = �13

� �𝐾13� 𝐿

−13 ⤇ 𝑖𝑓 𝐾 ↑ 𝑡ℎ𝑒𝑛 𝑀𝑃𝐿 ↑, 𝑡𝑟𝑦 𝐾 = 1000 𝑎𝑛𝑑 𝐾 = 8000 𝑡𝑜 𝑠𝑒𝑒.

K=1000 ⤇ MPL=�103

� 𝐿−13 𝑎𝑛𝑑 𝐼𝑓 𝐾 = 8000 𝑡ℎ𝑒𝑛 𝑀𝑃𝐿 = �80

3� 𝐿

−13 )

Hence we simply have a rightward shift of the Labour Demand Curve:

MPL↑⤇ 𝐿𝑑 𝑠ℎ𝑖𝑓𝑡 𝑟𝑖𝑔ℎ𝑡𝑤𝑎𝑟𝑑𝑠

Capital

R/P

ECON3301 Fall 2011 SMU-Sobey SB

Page 5 of 5

Figure

At the new equilibrium in the capital market, we have: 𝐿∗ ↑ 𝑎𝑛𝑑 �𝑊𝑃

�∗

↓

Note: we assume price remain fixed for now.

2.3. In Goods market: From labour and Capital market we know that:

𝐿∗ ↑ 𝑎𝑛𝑑 𝐾∗ ↑⤇ 𝑂𝑢𝑡𝑝𝑢𝑡 ↑

That is why Monetary Expansion is used for Economic Stimulus and a policy against recessions.

Note: we abstract from the impact of consumers in this market.

In the long-run, as output increases price may fall enough to compensate the change on real wage and real rental rate and even offset the impact of the policy.

This is why in the RBC framework it is said that money is neutral, in the long run.

You can try the case of contraction (fall in Money Supply) for practice!

Labour

W/P

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Notes on Chapter 11: Phillips Curve and Monetary Polic

(For Ch-10: lectures notes & sample to come)

Instructor: Dr. Maryam Dilmaghani

The Phillips curve (inflation-unemployment trade-off) for Yutopia is given by the equation below:

𝜋𝑡 = 𝑍𝑡 − 𝛼𝑢𝑡

where 𝜋𝑡 and 𝑢𝑡 denote inflation and unemployment rates (in percentage) at time t respectively; 𝑍𝑡 is a strictly positive composite variable capturing all other relevant factors such as total population of Yutopia and α is a strictly positive number, capturing how price index level reacts to labour force.

Variables (endogenous, determined by the model lie P and Q in Market Models) : 𝒖𝒕 𝒂𝒏𝒅 𝝅𝒕

Parameters (exogenous variable) 𝒁𝒕 𝒂𝒏𝒅 𝜶 (like slope and intersects, shift factors).

1. Describe Philips curve in words.

A negative relationship between inflation rate and unemployment rate so that if one increases the other falls. The magnitude of the impact of one variable upon the other is unchanged by the lever of these variables (how high they are).

2. Suppose 𝑍𝑡 = 1 and 𝛼 = 0.1. Use the chart below to depict Philips curve. Line in Red (solid)

3. Now suppose 𝑍𝑡 = 1.4 and 𝛼 = 0.1. Use the chart below to depict Philips curve. Line in Green (dashed).

4. Suppose 𝑍𝑡 = 1 and 𝛼 = 0.12. Depict Philips curve. Line in Blue (dot).

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

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Philips Curve, Monetary Policy and Economic Adjustments

The Short-run Phillips curve (inflation-unemployment trade-off) for Yutopia is given by the equation below:

𝜋𝑡 = 𝑍𝑡 − 𝛼𝑢𝑡

The Long-run Phillips curve is the blue vertical line. It means that the Inflation targeted and achieved by monetary policy will not affect the natural rate of unemployment in the long-run.

In the long run the inflation rate will be 𝜋∗ and unemployment rate 𝑢𝑁: The intersection of SR and LR Phillips curve.

In the short-run, the inflation targeted by Monterey policy and the short-run Phillips curve will determined the unemployment rate. BUT, as soon as a monetary intervention is made, SR Phillips curve starts shifting, to the right (left) for expansion (contraction). It is shown in series of figures in the next pages.

Unemployment

Inflation

LR Phillips Curve

SR Phillips Curve

𝒖𝑵

𝝅∗

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Phillips Curve and Monetary Policy

1. Monetary Expansion: To stimulate the economy 1.1.In the Short-run

𝑀𝑆 ↑: 𝑖 ↓ (𝑖𝑜𝑟𝑇 ↓) ⤇ �𝐿𝑜𝑎𝑛𝑠 ↑⤇ 𝐶 ↑:𝐸𝑥𝑐𝑒𝑠𝑠 𝐷𝑒𝑚𝑎𝑛𝑑 ⤇ 𝑃𝑟𝑖𝑐𝑒𝑠 ↑⤇ 𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 ↑𝐿𝑜𝑎𝑛𝑠 ↑⤇ 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 ↑⤇ 𝐽𝑜𝑏𝑠 ↑⤇ 𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 ↓

�

1.2. In the Long-run

In the long-run however, usually the inflation will reduce real rate of return to investments and they gradually fall (realistically not at their pre-intervention level, somewhere in between).

Mean while, the investment made through the monetary expansion increases both jobs and output and this partially neutralises Excess Demand hence inflation.

In sum, it is realistic that Monetary Policy has some impacts on Real Sectors. Not as much as monetarists believe and not at little as Real Business Cycles macroeconomists believe.

(1)

Unemployment

Inflation

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(2)

(3)

Unemployment

Inflation

Unemployment

Inflation

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(4)

More Realist Long-run Impact of Monetary Expansion & Phillips Curve Long-run Phillips curve shifts left (Solid blue) Short-run Phillips Curve does not shift all the way to the right. Hence with a higher level of Equilibrium Inflation, the natural level of unemployment will be lower.

Unemployment

Inflation

Unemployment

Inflation

LR Equilibrium

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Do the case of contraction as an exercise!

SMU: Sobey School of Business ECON3307: Fall 2011

1

Notes on Taylor Rule

Instructor: Dr. Maryam Dilmaghani

Taylor rule guides central banker in conducting monetary policy given the fundamentals of

economy (potential GDP) and target inflation rate. The rule can be written as follows:

𝒊𝒕 = 𝝅𝒕 + 𝜶𝒚 𝒐𝒖𝒕𝒑𝒖𝒕 𝒈𝒂𝒑+ 𝜶𝝅 𝒊𝒏𝒇𝒍𝒂𝒕𝒊𝒐𝒏 𝒈𝒂𝒑

(i) Description

Output gap: (𝒚𝒕 − 𝒚∗)= the difference between the current output, 𝑦𝑡, and the optimal level of output, 𝑦∗: the output that corresponds to the fundamentals of the economy (physical capital, human capital etc).

Inflation gap: (𝝅𝒕 − 𝝅∗)= the difference between the current inflation rate, 𝜋𝑡 , and the optimal inflation rate, 𝜋∗: the inflation rate that corresponds to the fundamentals of the economy (physical capital, human capital etc).

As you will see below, the coefficients of both output gap and inflation gap must be positive for the equation to have sensible prescriptions for monetary policy:

𝜶𝒚 > 𝟎 & 𝜶𝝅 > 𝟎

(ii) Application

If output gap is positive: (𝑦𝑡 − 𝑦∗) > 0 ⤇ 𝑦𝑡 > 𝑦∗ ⤇ Current output is higher than the optimal level. It is an ‘indicator of future inflation’ and ‘inflationary pressures on prices’.

The right monetary policy for central banks that are aiming at Inflation Targeting, especially pro-actives like Federal Reserve’s in the US, is to go for a Monetary contraction ( 𝑀𝑠↓, i ↑).

Taylor prescribes that the Target Interest Rate increases by 𝜶𝒚 × (𝑦𝑡 − 𝑦∗).

For instance, if output gap is 0.5% and 𝛼𝑦 = 0.5 then a Central bank using Taylor in Monetary Policy must increase the Target interest rate by 0.5 × 0.5 = 0.25%

SMU: Sobey School of Business ECON3307: Fall 2011

2

If inflation gap is positive: (𝜋𝑡 − 𝜋∗) > 0 ⤇ 𝜋𝑡 > 𝜋∗ ⤇ meaning that the inflation rate is higher than the target level, then Taylor rule postulates that Central Bank must increase the nominal interest rate to bring the inflation back to its target level:

Taylor prescribes that the Target Interest Rate increases by 𝜶𝝅 × (𝜋𝑡 − 𝜋∗).

For instance, if inflation gap is 0.5% (inflation is ½ % above its targeted level)and 𝛼𝜋 = 0.5 then a Central bank using Taylor in Monetary Policy must increase the Target interest rate by 0.5 × 0.5 = 0.25%

After the Monetary contrition ( 𝑀𝑠↓, i ↑):

𝑖𝑖 ↑ 𝑖𝑠 𝑎 𝑚𝑜𝑛𝑒𝑡𝑎𝑟𝑦 𝑐𝑜𝑛𝑡𝑟𝑎𝑐𝑡𝑖𝑜𝑛 ⤇

𝑖𝑡 𝑟𝑒𝑑𝑢𝑐𝑒𝑠 𝑙𝑜𝑎𝑛𝑠 𝑎𝑛𝑑 𝑓𝑟𝑜𝑚 𝑡ℎ𝑒𝑟𝑒 𝑒𝑐𝑜𝑛𝑜𝑚𝑖𝑐 𝑎𝑐𝑡𝑖𝑣𝑖𝑡𝑦 ⤇

𝐸𝑥𝑐𝑒𝑠𝑠 𝑠𝑢𝑝𝑝𝑙𝑦 ⤇ 𝑝𝑟𝑖𝑐𝑒𝑠 ↓ 𝑎𝑛𝑑 𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 ↓

**&**

You can try the cases of a negative output gap and inflation gap for practice.

ECON3301-Fall 2011 SMU-Sobey SB

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Notes 3

Economic General Equilibrium Theory (mainly from Wikipedia)

Note:

It goes beyond the lecture and also what I expect you. I will post another note, more focused on

equations and illustrations.

General equilibrium theory is a branch of theoretical economics. It seeks to explain the

behavior of supply, demand and prices in a whole economy with several or many interacting

markets, by seeking to prove that a set of prices exists that will result in an overall equilibrium,

hence general equilibrium, in contrast to partial equilibrium, which only analyzes single

markets. As with all models, this is an abstraction from a real economy; it is proposed as being a

useful model, both by considering equilibrium prices as long-term prices and by considering

actual prices as deviations from equilibrium.

General equilibrium theory both studies economies using the model of equilibrium pricing and

seeks to determine in which circumstances the assumptions of general equilibrium will hold. The

theory dates to the 1870s, particularly the work of French economist Léon Walras.

It is often assumed that (representative) agents are price takers, and under that assumption two

common notions of equilibrium exist.

Overview

Broadly speaking, general equilibrium tries to give an understanding of the whole economy

using a "bottom-up" approach, starting with individual markets and agents. Macroeconomics, as

developed by the Keynesian economists, focused on a "top-down" approach, where the analysis

starts with larger aggregates, the "big picture". Therefore, general equilibrium theory has

traditionally been classified as part of microeconomics.

The difference is not as clear as it used to be, since much of modern macroeconomics has

emphasized microeconomic foundations, and has constructed general equilibrium models of

ECON3301-Fall 2011 SMU-Sobey SB

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macroeconomic fluctuations. General equilibrium macroeconomic models usually have a

simplified structure that only incorporates a few markets, like a "goods market" and a "financial

market". In contrast, general equilibrium models in the microeconomic tradition typically

involve a multitude of different goods markets. They are usually complex and require computers

to help with numerical solutions.

In a market system the prices and production of all goods, including the price of money and

interest, are interrelated. A change in the price of one good, say bread, may affect another price,

such as bakers' wages. If bakers differ in tastes from others, the demand for bread might be

affected by a change in bakers' wages, with a consequent effect on the price of bread. Calculating

the equilibrium price of just one good, in theory, requires an analysis that accounts for all of the

millions of different goods that are available.

History of general equilibrium modeling

The first attempt in neoclassical economics to model prices for a whole economy was made by

Léon Walras. Walras' Elements of Pure Economics provides a succession of models, each

taking into account more aspects of a real economy (two commodities, many commodities,

production, growth, money). Some (for example, Eatwell (1989), see also Jaffe (1953)) think

Walras was unsuccessful and that the later models in this series are inconsistent.

(Not done in lecture besides about the concept of Government in Keynes & Real Business

Cycles models.)

In particular, Walras's model was a long-run model in which prices of capital goods are the same

whether they appear as inputs or outputs and in which the same rate of profits is earned in all

lines of industry. This is inconsistent with the quantities of capital goods being taken as data. But

when Walras introduced capital goods in his later models, he took their quantities as given, in

arbitrary ratios. (In contrast, Kenneth Arrow and Gerard Debreu continued to take the initial

quantities of capital goods as given, but adopted a short run model in which the prices of capital

goods vary with time and the own rate of interest varies across capital goods.)

ECON3301-Fall 2011 SMU-Sobey SB

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Walras was the first to lay down a research program much followed by 20th-century economists.

In particular, the Walrasian agenda included the investigation of when equilibria are unique and

stable.(Walras himself: Lesson 7 shows neither Uniqueness, nor Stability, nor even Existence of

an agreement is guaranteed. Immediate after closing the deal, e.g.)

Walras also proposed a dynamic process by which general equilibrium might be reached, that of

the tâtonnement or groping process.

The tatonnement process is a model for investigating stability of equilibria. Prices are announced

(perhaps by an "auctioneer"), and agents state how much of each good they would like to offer

(supply) or purchase (demand). No transactions and no production take place at disequilibrium

prices. Instead, prices are lowered for goods with positive prices and excess supply. Prices are

raised for goods with excess demand. The question for the mathematician is under what

conditions such a process will terminate in equilibrium where demand equates to supply for

goods with positive prices and demand does not exceed supply for goods with a price of zero.

Walras was not able to provide a definitive answer to this question (see Unresolved Problems in

General Equilibrium below).

In partial equilibrium analysis, the determination of the price of a good is simplified by just

looking at the price of one good, and assuming that the prices of all other goods remain constant.

The Marshallian theory of supply and demand is an example of partial equilibrium analysis.

Partial equilibrium analysis is adequate when the first-order effects of a shift in the demand

curve do not shift the supply curve. Anglo-American economists became more interested in

general equilibrium in the late 1920s and 1930s after Piero Sraffa's demonstration that

Marshallian economists cannot account for the forces thought to account for the upward-slope of

the supply curve for a consumer good.

If an industry uses little of a factor of production, a small increase in the output of that industry

will not bid the price of that factor up. To a first-order approximation, firms in the industry will

not experience decreasing costs and the industry supply curves will not slope up. If an industry

uses an appreciable amount of that factor of production, an increase in the output of that industry

will exhibit decreasing costs. But such a factor is likely to be used in substitutes for the industry's

ECON3301-Fall 2011 SMU-Sobey SB

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product, and an increased price of that factor will have effects on the supply of those substitutes.

Consequently, Sraffa argued, the first-order effects of a shift in the demand curve of the original

industry under these assumptions includes a shift in the supply curve of substitutes for that

industry's product, and consequent shifts in the original industry's supply curve. General

equilibrium is designed to investigate such interactions between markets.

Continental European economists made important advances in the 1930s. Walras' proofs of the

existence of general equilibrium often were based on the counting of equations and variables.

Such arguments are inadequate for non-linear systems of equations and do not imply that

equilibrium prices and quantities cannot be negative, a meaningless solution for his models. The

replacement of certain equations by inequalities and the use of more rigorous mathematics

improved general equilibrium modeling.

The modern conception of general equilibrium is provided by a model developed jointly by

Kenneth Arrow, Gerard Debreu and Lionel W. McKenzie in the 1950s. Gerard Debreu presents

this model in Theory of Value (1959) as an axiomatic model, following the style of mathematics

promoted by Bourbaki. In such an approach, the interpretation of the terms in the theory (e.g.,

goods, prices) are not fixed by the axioms.

Modern concept of general equilibrium in economics

Three important interpretations of the terms of the theory have been often cited. First, suppose

commodities are distinguished by the location where they are delivered. Then the Arrow-Debreu

model is a spatial model of, for example, international trade.

Second, suppose commodities are distinguished by when they are delivered. That is, suppose all

markets equilibrate at some initial instant of time. Agents in the model purchase and sell

contracts, where a contract specifies, for example, a good to be delivered and the date at which it

is to be delivered. The Arrow-Debreu model of intertemporal equilibrium contains forward

markets for all goods at all dates. No markets exist at any future dates.

Third, suppose contracts specify states of nature which affect whether a commodity is to be

delivered: "A contract for the transfer of a commodity now specifies, in addition to its physical

ECON3301-Fall 2011 SMU-Sobey SB

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properties, its location and its date, an event on the occurrence of which the transfer is

conditional. This new definition of a commodity allows one to obtain a theory of [risk] free from

any probability concept..." (Debreu, 1959)

These interpretations can be combined. So the complete Arrow-Debreu model can be said to

apply when goods are identified by when they are to be delivered, where they are to be delivered

and under what circumstances they are to be delivered, as well as their intrinsic nature. So there

would be a complete set of prices for contracts such as "1 ton of Winter red wheat, delivered on

3rd of January in Minneapolis, if there is a hurricane in Florida during December". A general

equilibrium model with complete markets of this sort seems to be a long way from describing the

workings of real economies, however its proponents argue that it is still useful as a simplified

guide as to how a real economies function.

Some of the recent work in general equilibrium has in fact explored the implications of

incomplete markets, which is to say an intertemporal economy with uncertainty, where there do

not exist sufficiently detailed contracts that would allow agents to fully allocate their

consumption and resources through time. While it has been shown that such economies will

generally still have an equilibrium, the outcome may no longer be Pareto optimal. The basic

intuition for this result is that if consumers lack adequate means to transfer their wealth from one

time period to another and the future is risky, there is nothing to necessarily tie any price ratio

down to the relevant marginal rate of substitution, which is the standard requirement for Pareto

optimality. Under some conditions the economy may still be constrained Pareto optimal,

meaning that a central authority limited to the same type and number of contracts as the

individual agents may not be able to improve upon the outcome, what is needed is the

introduction of a full set of possible contracts. Hence, one implication of the theory of

incomplete markets is that inefficiency may be a result of underdeveloped financial institutions

or credit constraints faced by some members of the public. Research still continues in this area.

ECON3301- Fall 2011

Intermediate Macroeconomics: Chapter 2

2 2

C h a p t e r 2 National-Income Accounting:

Gross Domestic Product and the Price Level

Gross Domestic Product

3

"Gross" means that GDP measures production regardless of the various uses to which that production can be put. Production can be used for immediate consumption, for investment in new fixed assets or inventories, or for replacing depreciated fixed assets.

"Domestic" means that GDP measures production that takes place within the country's borders. In the expenditure-method equation given in the next slides, the exports-minus-imports term is necessary in order to null out expenditures on things not produced in the country (imports) and add in things produced but not sold in the country (exports).

3

Nominal GDP

4

Nominal GDP measures the dollar (or euro, etc.) value of all the goods and services that an economy produces during a specified period, such as a year.

Flow variable - it measures the dollar amount of goods produced

per unit of time, such as a year.

Real GDP

5

Calculating Real GDP Multiply each year’s quantity of output of each good by the

price of the good in a base year. GDP in constant dollars Chain-weighted real GDP

We need to use a kind of price index to compute real

GDP.

Prices

6

Consumer Price Index (CPI) Producer Price Index (PPI)

Calculations

7

Nominal GDP/Implicit price level= real GDP

A choice must be made on the price level to use.

Calculation of GDP-1

8

GDP can be determined in three ways, all of which should, in principle, give the same result. They are the product (or output) approach, the income approach, and the expenditure approach.

The most direct of the three is the product approach, which sums the outputs of every class of enterprise to arrive at the total.

The expenditure approach works on the principle that all of the product must be bought by somebody, therefore the value of the total product must be equal to people's total expenditures in buying things.

8

Calculation of GDP-2

9

The Expenditure approach is most commonly used.

Can you think of possible practical shortcomings of the other approaches (Income, Output)?

9

GDP by Expenditure

10

Personal Consumption Expenditures Gross Private Domestic Investment Government purchases of Goods and Services Exports and Imports

Example: the expenditure method: GDP = Value of private consumption (C) + Value of gross investment (I)

+ Value of government spending (G) + Value of exports in national currency –imports

GDP as a Welfare Measure

11

GDP does not: Consider changes in income distribution

Include non-market goods.

Assign value to leisure.

Consider environmental damage.

12

13

Measuring GDP by Income

14

National Income – Income earned by factors of production.

Relationship Between GDP and National Income

15

National Income by Sector

16

National Income by Sector

17

18

19

20

Chapter 3, preliminaries

Economic Growth: Definition

21

Economic growth is the increase of aggregate production in a given economy.

Economic Growth is the increase of per capita gross domestic product (GDP) as a measure of aggregate income. Usually, the annual rate of change in real GDP is taken as the indicator of the annual rate of growth.

Canadian Growth in the past 30 years

22

GDP & Growth

23

How can we measure Economic Growth? Economic Growth is the increase of per capita gross domestic

product (GDP) as a measure of aggregate income.

Usually, the annual rate of change in real GDP is taken as the indicator of the annual rate of growth.

23

GDP & Economic Growth-1

24

Main factors behind Economics Growth

Economic growth is primarily driven by improvements in productivity, which involves producing more goods and services with the same inputs of labour, capital, energy and materials.

Human and Social capital improvements is also being more often used.

24

GDP & Economic Growth-2

25

Over long periods of time, even small rates of annual growth can have large effects through compounding. A growth rate of 2.5% per annum will lead to a doubling of GDP within 29 years, whilst a growth rate of 8% per annum (experienced by some Four Asian Tigers) will lead to a doubling of GDP within 10 years. This exponential characteristic can exacerbate differences across nations.

Short-run versus long-run considerations

Economists draw a distinction between short-term economic stabilization and long-term economic growth. The topic of economic growth is primarily concerned with the long run. The short-run variation of economic growth is termed the business cycle.

25

Canadian Growth in the past 30 years: Comments-1

26

In general positive, with a long-run average of about 2.5%

3 Recessions with growth being negative:

Oil shock of early 1980s

Gulf war of early 1990s

Recent Financial Crisis (2007)

European (Russian) Economic Crisis (the grey area): fall in growth rate but not becoming negative.

Canadian Growth in the past 30 years: Comments-2

27

The rate of growth does not seem to increase, but falls, even when one abstracts from the business cycles.

Vulnerability of Industrial Countries to Oil

Canadian economy is very much tied to the US economy.

28

GDP Growth: How good of a measure is for the economic

performance of a country?

The answer is not just economic, it also entails addressing some philosophical and moral issues....

Shortcomings of GDP as an indicator of Growth

29

Wealth distribution Non-market transactions Underground economy Environmental Quality Technological progress and quality improvements

30

31

What do you think reading this news article?

Kuznets Curve

32

A Kuznets curve is the graphical representation of Simon Kuznets's discovery that economic inequality increases over time while a country is developing, then after a certain average income is attained, inequality begins to decrease.

Inspired by Kuznets’ insight the relationship between income per capita and environmental degradation is represented by Environmental Kuznets Curve (EKC) which is an inverse U shape curve.

Simon Kuznets

Kuznets Curve: One country over time

33

Income Inequality

Income/capita

Development stage Developed stage

Kuznets Curve: All countries viewed at given time (eg 2011)

34

Income Inequality

Income/capita

Developing Countries Developed Countries