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THE ECONOMIC IN THE VERY LONG RUN
Chapter 7
Economic Growth I
October 31, 2012
2 Chapter 7: Economic Growth I. ECON204 (A01). Fall 2012
Outline
1. Stylized Facts of Economic Growth
2. Basic Solow Growth Model (CLOSED ECONOMY)
3. How a country’s standards of living depends on its
saving and population growth rates
4. Golden Rule Level of Capital
3 Chapter 7: Economic Growth I. ECON204 (A01). Fall 2012
1. Stylized Facts of Economic Growth
Objective: A model of economic growth
Economic growth of what?
Our focus: income approach – the growth rate of output (GDP) per person (per capita)
More precisely, growth of the natural rate of output in per capita or per person terms — a better measure of well-being.
4 Chapter 7: Economic Growth I. ECON204 (A01). Fall 2012
Figure: International Differences in the Standards of Living, Year 2004 (in US $)
0
5000
10000
15000
20000
25000
30000
35000
40000
45000
Nigeria Vietnam India China Mexico Russia Germany Japan Canada USA
5 Chapter 7: Economic Growth I. ECON204 (A01). Fall 2012
Stylized Facts1
1. Wide and steady income disparity across countries 2. Evidence of increasing disparity across countries
3. Almost all countries exhibit some growth As wealthy countries have grown so have poorer
countries – no absolute poverty trap.
4. Wide distribution of growth rates
1 Parente and Prescott(1993)
6 Chapter 7: Economic Growth I. ECON204 (A01). Fall 2012
Some countries have taken off, others have not — why?
(1) and (2) — cross country differences in the level of GDP per person
(3) and (4) — cross country differences in the growth rates of GDP per person.
Objective is to explain these differences.
!! We won’t be able to do everything with the Solow growth model but we make a decent start.
7 Chapter 7: Economic Growth I. ECON204 (A01). Fall 2012
Why Growth Matters?
8 Chapter 7: Economic Growth I. ECON204 (A01). Fall 2012
Economic growth raises living standards and reduces poverty….
9 Chapter 7: Economic Growth I. ECON204 (A01). Fall 2012
10 Chapter 7: Economic Growth I. ECON204 (A01). Fall 2012
2. The Solow Model
A dynamic model of output growth and capital accumulation.
Due to Robert Solow2, won Nobel Prize for contributions to
the study of economic growth
A major paradigm:
o widely used in policy making
o benchmark against which most recent growth
theories are compared
looks at the determinants of economic growth and the
standard of living in the long run
2 Solow, R. (1956), “A contribution to the Theory of Economic Growth,” Quarterly Journal of Economics
11 Chapter 7: Economic Growth I. ECON204 (A01). Fall 2012
Assumptions:
a) K is no longer fixed
- investment causes it to grow
- depreciation causes it to shrink
b) L is no longer fixed
- population growth causes it to grow
c) The consumption function is simpler
d) No G or T (only to simplify presentation; we can still do
fiscal policy experiments)
12 Chapter 7: Economic Growth I. ECON204 (A01). Fall 2012
The Supply of and Demand for Goods
Supply of Goods: the production function In aggregate terms:
Define:
Assume constant returns to scale
Let
. Then
or,
or,
13 Chapter 7: Economic Growth I. ECON204 (A01). Fall 2012
For example, if
then,
Graphically, production per worker is pictured as:
Slope of the production
function is:
and exhibits diminishing
returns
14 Chapter 7: Economic Growth I. ECON204 (A01). Fall 2012
Demand for Goods
Closed economy, no government spending so output is either consumed or invested. All variables expressed in per person terms; i.e., divided by the size of the labour force L.
Consumption per person:
Where, s is an exogenous parameter of the model
As before, the real interest rate adjusts so that AS = AD:
In other words, investment per person, i, is a constant share s of output per person:
15 Chapter 7: Economic Growth I. ECON204 (A01). Fall 2012
Growth of Capital Stock and the Steady State
Output and investment in diagram
16 Chapter 7: Economic Growth I. ECON204 (A01). Fall 2012
Investment increases the stock of capital per person, k. Depreciation (wearing out of capital) reduces the stock of k at a constant rate. Together, these are modelled as:
Solow model’s central equation
Where,
17 Chapter 7: Economic Growth I. ECON204 (A01). Fall 2012
A Steady State (SS) is defined as:
From the above, this means our steady state is described as,
or,
When this condition holds,
Where, is the steady state level of capital per person
18 Chapter 7: Economic Growth I. ECON204 (A01). Fall 2012
The Model can be represented in a single diagram combining
output and investment, and depreciation diagrams:
19 Chapter 7: Economic Growth I. ECON204 (A01). Fall 2012
At steady state, and . We get,
SS output per person
SS investment per person
SS consumption per person
Adjustment to steady state: If then ; investment exceeds depreciation; and is growing and we move toward . Output is also growing. If then ; capital per person is declining and we move toward . Output is contracting.
20 Chapter 7: Economic Growth I. ECON204 (A01). Fall 2012
The steady state represents the long-run equilibrium of the economy
21 Chapter 7: Economic Growth I. ECON204 (A01). Fall 2012
A Numerical Example
Production function:
So, output per person: Given, initial capital per person, . Solve for the SS values We know, in the SS
or,
22 Chapter 7: Economic Growth I. ECON204 (A01). Fall 2012
Plug in all values and formula, we get
That is,
So, the SS output per person,
The SS investment per person, =0.9
The SS consumption,
The SS depreciation,
Thus,
23 Chapter 7: Economic Growth I. ECON204 (A01). Fall 2012
24 Chapter 7: Economic Growth I. ECON204 (A01). Fall 2012
Savings, Growth and Steady State Output
Our simple model makes the following predictions:
• A higher saving rate, s, leads to a higher SS capital stock
per person and a higher level of SS output.
• A higher s leads to higher economic growth but only
temporarily.
Thus, the Solow model predicts that countries with higher rates
of saving and investment will have higher levels of capital and
income per worker in the long run
Note the difference between level and growth
25 Chapter 7: Economic Growth I. ECON204 (A01). Fall 2012
At A and B, output growth is zero: . From A to B due to an
increase in saving: and until the new SS is achieved.
26 Chapter 7: Economic Growth I. ECON204 (A01). Fall 2012
Golden Rule Level of Capital
What is the best steady state capital stock? As s increases, and increase. Does this imply that s = 1 is optimal? Clearly, the answer is NO. Although is as large as possible, nothing is available for consumption! An optimal level of steady state capital, :
one that provides the highest level of steady state consumption per person.
27 Chapter 7: Economic Growth I. ECON204 (A01). Fall 2012
Let be the steady state level of capital that provides this
optimal level of consumption.
In steady state,
or,
Since in steady state,
is biggest where the slope of the production
function equals the slope of the depreciation line: MPK=
28 Chapter 7: Economic Growth I. ECON204 (A01). Fall 2012
29 Chapter 7: Economic Growth I. ECON204 (A01). Fall 2012
If we are at a below then the marginal product of
capita exceeds the depreciation rate.
What this means is that if we were to increase steady state capital by one unit of capital, the gain in output (MPK) exceeds the additional required investment to maintain the capital stock, .
As a result, there is some left over for additional consumption.
Mathematically, we choose to maximize:
The solution to this problem is,
or,
30 Chapter 7: Economic Growth I. ECON204 (A01). Fall 2012
Transition to the Golden Rule SS The economy does NOT have a tendency to move toward the Golden Rule steady state. Achieving the Golden Rule requires that policymakers adjust s. This adjustment leads to a new steady state with higher consumption. If
and the s is reduced to achieve :
31 Chapter 7: Economic Growth I. ECON204 (A01). Fall 2012
32 Chapter 7: Economic Growth I. ECON204 (A01). Fall 2012
If and the s is increased to achieve
:
33 Chapter 7: Economic Growth I. ECON204 (A01). Fall 2012
Welfare Implications If we simply compare different steady states, then everyone is
better off at than they are at any other level of .
However, if we think about moving the economy from one SS to
another (by changing the s), then the welfare implications are
not so straightforward.
If and the s is reduced to achieve
:
current generation consumes more and so is better off;
future generations consume more and so are better off.
all generations are better off.
34 Chapter 7: Economic Growth I. ECON204 (A01). Fall 2012
If and the s is increased to achieve
:
current generation consumes less and so is worse off;
future generations consume more and so are better off.
Not all generations are better off.
Importantly, those who are worse off also are those that can
influence the current saving decisions. So it seems unlikely
that, if an economy is below , it will achieve it.
35 Chapter 7: Economic Growth I. ECON204 (A01). Fall 2012
Solow Growth Model with Population Growth
The model is exactly as before but we now assume that the labour force (population) is growing at a rate n.
n is a number like 0.03 or 3 percent, and is exogenous
Previously we saw, , with no population growth.
If : capital per person shrinks by rate .
Now, labour growth at rate n also causes capital per person to shrink, at a rate n. e.g. i is zero — then K is changing due to depreciation:
36 Chapter 7: Economic Growth I. ECON204 (A01). Fall 2012
or,
And, labor growth:
We know,
, and is changing:
37 Chapter 7: Economic Growth I. ECON204 (A01). Fall 2012
So, without investment,
Of course, if investment per person is not zero then it is adding
to the per person capital stock:
( + n)k = break-even investment:
the amount of investment necessary to keep k constant.
Break-even investment includes: k to replace capital as it wears out n k to equip new workers with capital
(Otherwise, k would fall as the existing capital stock would be spread more thinly over a larger population of workers.)
38 Chapter 7: Economic Growth I. ECON204 (A01). Fall 2012
Now, the steady state is:
Actual investment = break-even investment
Result: population growth lowers the SS level of capital
and output per person (for a given saving rate and depreciation rate)
39 Chapter 7: Economic Growth I. ECON204 (A01). Fall 2012
Point A: The SS level of for high population growth;
Point B: The SS level of for low population growth.
40 Chapter 7: Economic Growth I. ECON204 (A01). Fall 2012
Intuition:
A high capital stock has a high steady state replacement cost;
this gets higher with higher population growth.
In steady state:
are growing at the rate of population growth
No growth in standard of living
Golden rule is now,
Same logic as before
41 Chapter 7: Economic Growth I. ECON204 (A01). Fall 2012
Solow model predicts
Higher n lower k*. And since y = f(k) , lower k* lower y*.
Thus, the Solow model predicts that countries with higher
population growth rates will have lower levels of capital
and income per worker in the long run.
42 Chapter 7: Economic Growth I. ECON204 (A01). Fall 2012
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