macroeconomics - freeremi.bazillier.free.fr/macro_exercice_en.pdf · université d’orléans...

Université d’OrléansInstitut d’Economie d’Orléans

Licence 1, Economie-Gestion, mention Européenne

Macroeconomics

Rémi Bazillier

[email protected]

http://remi.bazillier.free.fr

Contents

1 Introduction 11.1 Stock or Flows? . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 True or false? . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 GDP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.4 GDP and wealth . . . . . . . . . . . . . . . . . . . . . . . . . 21.5 Measuring GDP . . . . . . . . . . . . . . . . . . . . . . . . . . 21.6 Nominal and real GDP . . . . . . . . . . . . . . . . . . . . . . 31.7 GDP deflator . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.8 Chain indexes . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Consumption 52.1 Keynesian consumption function . . . . . . . . . . . . . . . . 52.2 Consumption and households’ available income . . . . . . . . 62.3 Permanent income hypothesis . . . . . . . . . . . . . . . . . . 62.4 Life cycle hypothesis . . . . . . . . . . . . . . . . . . . . . . . 7

3 Investment 83.1 Demand and investment . . . . . . . . . . . . . . . . . . . . . 83.2 Investment’s decision . . . . . . . . . . . . . . . . . . . . . . . 9

4 The Goods market 104.1 The equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . 104.2 The Multiplier . . . . . . . . . . . . . . . . . . . . . . . . . . 104.3 The balanced budget multiplier . . . . . . . . . . . . . . . . . 114.4 Automatic stabilizers . . . . . . . . . . . . . . . . . . . . . . . 12

5 Financial markets 135.1 Demand for money . . . . . . . . . . . . . . . . . . . . . . . . 135.2 Bond prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145.3 The interest rate . . . . . . . . . . . . . . . . . . . . . . . . . 14

ii

6 The IS-LM model 156.1 The IS curve . . . . . . . . . . . . . . . . . . . . . . . . . . . 156.2 The LM curve . . . . . . . . . . . . . . . . . . . . . . . . . . . 166.3 The IS-LM model . . . . . . . . . . . . . . . . . . . . . . . . . 166.4 The IS-LM model . . . . . . . . . . . . . . . . . . . . . . . . . 17

Chapter 1

Introduction

1.1 Stock or Flows?

• The wealth of an individual

• Number of unemployed

• Trade deficit

• Level of investments

• Public debt

• Number of workers who have lost their job

• Level of capital in the economy

***

The following exercises are taken from: Blanchard (2011), “Macroeco-nomics, fifth edition”, eds. Pearson.

1.2 True or false?

• The share of labor income in GDP is much larger than the share ofcapital income

• French GDP was 29 times higher in 1999 than it was in 1960

• When the unemployment rate is high, the participation rate is alsolikely to be high

1

• The rate of unemployment tends to fall during expansions and riseduring recessions

• If Japanese CPI is currently at 108 and American CPI is at 104, theninflation rate is higher in Japan than in the US

• The inflation rate measured using the CPI is a better index of inflationthan the one computed using GDP deflator

1.3 GDP

Suppose that GDP is measured by summing final value of all goods andservices produced. Determine the effect of the following transactions.

1. A consumer buys e100 worth of fish from a fisherman. Fishes areconsumed at home.

2. A seafoo restaurant buys e100 worth of fish from a fisherman.

3. Air France buys a new plane from Airbus for e200 billions.

4. The Greek national airline buys a plane from Airbus for e200 billions.

5. Air France sells a plane to Gerard Depardieu for e100 billions.

1.4 GDP and wealth

Instead of cooking for your dinner, you work one hour more, earn 12 e andbuy your dinner 10 e.

1. Does the measured GDP increase? If yes, how much is the increase?

2. How much should increase the “true” GDP?

1.5 Measuring GDP

1. A silver mining company pays its workers e200 000, invests in a newmachine-tool for 50000 and mines 75 kg of gold. The silver is then soldto a jewelry manufacturer for e300 000.

2. The jewelry manufacturer pays its employees e250 000 buys e300000of silver, and makes silver necklaces directly sold to consumers for e1million.

3. A third firm pays its employees for e30000, buys for e10000 of rawmaterials and sells a machine-tool to the silver mining company fore50000

4. The last firm sells for e10000 of raw materials to the firm specializedin raw material.

• Calculate the GDP using the production approach.

• Calculate the added-value for each step of production. Calculate theGDP using the added-value approach.

• Give levels of wages and profit. Calculate the GDP using the incomeapproach.

1.6 Nominal and real GDP

The economy can be summarized by the following table.

Year 2009 2009 2010 2010Quantity Price Quantity Price

Cars 10 2000 12 3000Oranges 1000 1 1000 1Computers 4 1000 6 500

1. What is nominal GDP in 2009 and 2010? What is the growth rate ofthe nominal GDP?

2. Using 2009 as the reference year, what is the real GDP in 2009 and2010?

3. Same question using 2010 as the reference year.

4. True or False? The real growth rate changes with the reference year.

1.7 GDP deflator

You will use data from the previous example.

1. Suppose that we use 2009 prices as a basis to calculate real GDP in2009 and 2010. Calculate the GDP deflator for 2009 and 2010, and theinflation rate 2009-2010.

2. Suppose that we use 2010 prices as a basis to calculate real GDP in2009 and 2010. Calculate the GDP deflator for 2009 and 2010, and theinflation rate 2009-2010.

3. Why are the two inflation rate different? Which one is true? Justifyyour answer.

1.8 Chain indexes

As shown in exercises 1.6 and 1.7, the choice of the reference year has aninfluence on some results. To avoid this problem, chain indexes can be used.The reference year is always the previous year.

1. Using data from exercise 1.6, calculate the real GDP using the previousyear as the reference year.

2. What is the growth rate of GDP?

3. What is the GDP deflator? What is the inflation rate calculated usingthis method?

Chapter 2

Consumption

2.1 Keynesian consumption function

In a country, the general consumption function is given by the followingequation:

C = 0.7Y + 3 (2.1)

with C the level of consumption and Y the national income.

1. How does Keynes define the saving? Determine the saving function.

2. Draw on the same graph the consumption line and the saving line (forY between 0 and 30). Find the breaking point (the level of incomecharacterized by C = S). What does the value 3 represent?

3. Give the average propensity to consume (APC) and the marginal propen-sity to consume (MPC). How do these propensities move when Y rises?Show them on the previous graph for Y = 1, Y = 10, Y = 30

4. When income rises, how does the spread between national income andglobal consumption move?

5. What does mean a consumption function determined by the followingequation?

C = 0.7Y − 3 (2.2)

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2.2 Consumption and households’ available income

In a country, the consumption function is given by the following equation:

C = CO + cYd (2.3)

Where Yd is the households’ available income.

1. Give the relation between aggregated consumption and national incomewhen the State puts in place a lump-sum system of taxes (T0)

2. Same question if the State puts in place a lump-sum tax (T0) and aflat-rate tax tY (with 0 < t < 1 the tax rate).

3. Same question if the State puts in place a lump-sum tax, a flat-ratetax and redistributes social transfers, proportional to the level of in-come (θY , with θ the transfer rate), and redistributes also a lump-sumtransfer (Tr0).

4. For each system of taxes and transfers defined in the previous questions,give the effect on the average and marginal propensities to consume.

2.3 Permanent income hypothesis

Here is the income level observed in a country during 10 years.

Year 0 1 2 3 4 5 6 7 8 910 11Y 10000 11000 13000 12000 9000 10000 12000 13000 10000 8000

1. The permanent income Y P is given by the income average of the cur-rent year and the three previous years. Calculate this permanent in-come for years 4 to 10 .

2. Calculate the transitory income Y T for the same years.

3. The consumption is a function of the permanent income: Ct = 0.9Y Pt .

What is the marginal propensity to consume the permanent income?And the average propensity to consume the permanent income? Cal-culate the consumption for years 4 to 10.

4. Calculate the average propensity to consume the current income. Com-ment its evolution. Why this evolution is contrary to the Keynesianassumptions?

2.4 Life cycle hypothesis

Mr. X starts his professional life at 20 years old, without any initial capital.He earns e36000 yearly until he retires at 65 years old. His life expectancyis 80 years old. We suppose that his saving is not remunerated and there isno pension system.

1. If he spends his income constantly all over his life, what is his annualconsumption? Calculate his average propensity to consume during hisactive years, his level of annual saving and the available capital whenhe retires.

2. How does his saving and consumption behavior change if the pensionage is post-pone to 70 years-old?

3. What is the level of consumption for Ms. Y who earns the same wagebut whose life expectancy is 85 years-old. Comment.

4. We now suppose that Mr. X receives e300000 of inheritance and doesnot want to give inheritance to his children after his death. Calcu-late consumption and saving levels and compare them with the onesobtained in the first question. Comment.

Chapter 3

Investment

3.1 Demand and investment

We suppose that the demand of consumption goods is given by the followingtable:

Year 0 1 2 3 4 5 6 7 8 9 10 11Demand 1000 1000 1100 1500 1600 1500 1000 700 700 900 1000 1000

In year 0, the production capacity usage rate is 100%. Fixed capitalis e4000. The capital coefficient (the ratio of capital/demand) is constantover time. Equipments goods are not depreciated over time. Production isimmediatly adjusted to the demand at each period.

1. Calculate the capital coefficient. What hypothesis should be made inorder to ensure that this coefficient keeps constant over time?

2. Calculate the investment for each period. How do firms can make“negative investments”? at the firm level? at the sector level? at thenational level?

3. On the same graph, draw the curve of demand and investment. Com-ment.

4. What would be the consequences of a stronger mechanization of theproduction process?

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3.2 Investment’s decision

You should analyze two projects of investments.

Project A Project BLife expectancy 5 years 2 yearsAnticipated income (per year) 100 200Initial cost 400 350

Firms can borrow or make financial investment at a 5% interest rate.

1. Calculate the net present value of both projects.

2. Calculate the internal rate of return of project B.

3. Which project should be chosen? Why?

4. Let’s now suppose that the cost of borrowing increases. The interestrate is 10%. The remuneration of financial investments is unchanged(5%). Give the net present value of both projects (1) if the firm financesit through internal financing, (2) if the firm has to borrow. Comment.

Chapter 4

The Goods market

The following exercises are taken from: Blanchard (2011), “Macroeconomics,fifth edition”, eds. Pearson.

4.1 The equilibrium

The economy has the following characteristics:

C = 160 + 0.6Yd (4.1)I = 150 (4.2)G = 150 (4.3)T = 100 (4.4)

1. Find the equilibrium GDP Y

2. Find the disposable income Yd

3. Find the consumption C

4. Assume that G is now equal to 110. Solve for equilibrium output.Compute total demand. Is it equal to production? Explain.

5. Is the sum of private and public saving equal investment? explain.

4.2 The Multiplier


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C = C0 + cYd (4.5)

I = I (4.6)

G = G (4.7)

T = T (4.8)

1. Give the analytical value of Y

2. What is the government spendings multiplier?

3. What is the tax multiplier?

4. The government has two policy options to boost growth: increasinggovernment spendings or decreasing taxes. Which policies would bemore efficient in this case? Why?

4.3 The balanced budget multiplier

For both political and macroeconomic reasons, governments are often reluc-tant to run budget deficits. Here we examine whether policies changes in Gand T that maintain a balanced budget are macroeconomically neutral.


C = C0 + cYd (4.9)

I = I (4.10)

G = G (4.11)

T = T (4.12)

1. Give the level of Y at the equilibrium (same that for the last exercice)

2. Suppose that G and T increase by ine unit each. What is the change inequilibrium GDP? Are balanced budget changes in G and T macroe-conomically neutral?

3. How does the specific value of the propensity to consume affect youranswer? Why?

4.4 Automatic stabilizers

So far, we have assumed that the policy variables G and T are independentof the level of income. In the real World, however, it is not the case. Taxestypically depend on the level of income and so tend to be higher when incomeis higher. Here, we examine how this automatic responses of taxes can helpreduce the impact of changes in autonomous spending on output.


C = C0 + cYd (4.13)T = t0 + tY (4.14)

G = G (4.15)

I = I (4.16)

0 < t < 1

1. Solve for equilibrium output

2. What is the multiplier? Does the economy respond more to changesin autonomous spending when t is 0 or when t is positive. Explain.

3. Why is fiscal policy in this case called an automatic stabilizer.

Chapter 5

Financial markets

The following exercises are taken from: Blanchard (2011), “Macroeconomics,fifth edition”, eds. Pearson.

5.1 Demand for money

Suppose that a person’s yearly income is $60000. Also suppose that thisperson’s money demand function is given by:

Md = $Y (0.35− i) (5.1)

1. What is this person’s demand for money when the interest rate is 5%?10%?

2. Explain how the interest rate affects money demand.

3. Suppose that the interest rate is 10%. In percentage terms, what hap-pens to this person’s demand for money if her yearly income is reducedby 50%?

4. Suppose that the interest rate is 5%. In percentage terms, what hap-pens to this person’s demand for money if her yearly income is reducedby 50%?

5. Summarize the effect of income on money demand. In percentageterms, how does this effect depend on the interest rate?

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5.2 Bond prices

Consider a bond that promises to pay $100 in one year.

1. What is the interest rate on the bond if its price today is $75? $85?$95?

2. What is the relation between the price of the bond and the interestrate?

3. If the interest rate is 8%, what is the price of a bond today?

5.3 The interest rate

Suppose that money demand is given by:

Md = $Y (0.25− i) (5.2)

where $Y is 100. Also suppose that the money of supply M s is $20.

1. What is the equilibrium interest rate?

2. If the central banks wants to increase i by 10 percentage points (e.g.from 2% to 12%), at what level should it set the supply of money?

Chapter 6

The IS-LM model

6.1 The IS curve


C = 0.8Yd + 200 (6.1)I = 300− 4000i (6.2)

G = 100 (6.3)

1. Build the IS curve. Find the equilibrium output if i = 4%

2. What does happen if the marginal propensity to consume becomes 0.7?

3. What does happen if I = 300?

4. What does happen if I = 5000i?

5. What does happen if I = 400− 4000i?

6. The government decides to increase public spendings. G is now equalto 150. What is the equilibrium output if i = 4%?

7. The government decides to put in place taxes. T is now equal to 50.Find the new formulation of IS and the equilibrium output for i = 4%

8. Same question for T = 50

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6.2 The LM curve

The financial markets have the following characteristics:

Md = 0.6Y + 600− 12000i (6.4)Ms = 1300 (6.5)

For i ≥ 1%.

Remark: for i<1%, we are in a liquidity trap.

1. Show graphically the demand for money for Y = 1500.

2. Build and comment the LM curve.

3. What does happen if Md = 0.8Y + 600− 12000i?

4. What does happen if Ms = 1500? How can we call such a policy?

5. What does happen if Md = 0.6Y + 600− 10000i

6.3 The IS-LM model

The economy of GROLAND has the following characteristics:

C = 0.3Yd + 140 (6.6)I = 500− 2000i (6.7)

Md = 0.4Y + 700− 10000i (i > 0.5%) (6.8)Ms = 900 (6.9)

1. Build IS and LM

2. Find the equilibrium output Y ∗ and the equilibrium interest rate i∗

3. The government of GROLAND decides to put in place public spend-ings. G is now equal to 100. How does this decision affect the equilib-rium?

4. What does happen if the marginal propensity to consume becomesequal to 0.2?

5. What does happen if firms change their investment behavior? The newinvestment function is: I = 500− 2500i.

6. What does happen if the function of demand for money changes? It isnow equal to Md = 0.4Y + 700− 11000i.

7. We suppose that the employment level (N) is defined by the followingfunction: Y = 3

√N . If the active population in Groland is 16000,

what is the full employment level of output YFE?

8. If the government wants to reach this level through fiscal policy. Whatshould be the level of public spendings?

9. Let’s now suppose that the government decides that G = 230. Whatshould be the level of money supplied by the central bank in order toreach full employment?

6.4 The IS-LM model

A country has the following characteristics:

C = 0.8Yd + 50 (6.10)I = 100− 2000i (6.11)

Ms = 1100 (6.12)Md = 0.2Y + 1050− 8000i (6.13)

Part 1

1. Find the equilibrium output (Y ∗) and interest rate (i∗).

2. Show graphically the IS and LM curves.

3. What does happen if the central bank lowers the money supply? (Ms =1080)?

4. Let’s now suppose that the demand for money takes the following form:

Md = 0.2Y + 1050 (6.14)

• Find the equilibrium output and the interest rate if the moneysupply is equal to 1100.• Find the equilibrium output and the interest rate if the money

supply is equal to 1080.

• Compare both equilibrium.


Md = 0.2Y + 1050− 8500i (6.15)

• Find the equilibrium output and the interest rate if the moneysupply is equal to 1100.



6. Same question is the investment function is:

I = 100− 500i (6.16)

7. Give the analytical value of the monetary policy multiplier. Commentby analyzing your previous results.

Part 2 We now consider the effects of government spendings. We nowhave:

G = 500 (6.17)

1. Find the equilibrium output and the interest rate.

2. What does happen if the Government decides to increase public spend-ings? (G = 550)

3. Show graphically the IS and LM curves?


Md = 0.2Y + 1050 (6.18)

• Find the equilibrium output and the interest rate if G = 500.




Md = 0.2Y + 1050− 6000i (6.19)




6. Same question is the investment function is independent from the in-terest rate:

I = 100 (6.20)

7. We still suppose that the investment function is I = 100.




8. Give the analytical value of the budget multiplier. Comment by ana-lyzing your previous results.

6.5 The IS-LM model (II)

This exercise is from: Blanchard (2011), “Macroeconomics, fifth edition”,eds. Pearson.

Consider first the goods market model with constant investment function(as seen in Chapter 4). Consumption is given by:

C = c0 + c1(Y − T ) (6.21)

I, T, and G are given.

1. Solve for equilibrium output. What is the value of the multiplier.

2. Let’s now suppose that investment depend on both sales and the in-terest rate:

I = b0 + b1Y − b2i (6.22)

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