Download Macroeconomics - Rémi Bazillier

Université d’Orléans
Institut d’Economie d’Orléans
Licence 1, Economie-Gestion, mention Européenne
Macroeconomics
Rémi Bazillier
[email protected]
http://remi.bazillier.free.fr
Contents
1 Introduction
1.1 Stock or Flows? . . . .
1.2 True or false? . . . . .
1.3 GDP . . . . . . . . . .
1.4 GDP and wealth . . .
1.5 Measuring GDP . . . .
1.6 Nominal and real GDP
1.7 GDP deflator . . . . .
1.8 Chain indexes . . . . .
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1
1
1
2
2
2
3
3
4
2 Consumption
2.1 Keynesian consumption function . . . . . . . .
2.2 Consumption and households’ available income
2.3 Permanent income hypothesis . . . . . . . . . .
2.4 Life cycle hypothesis . . . . . . . . . . . . . . .
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5
5
6
6
7
3 Investment
3.1 Demand and investment . . . . . . . . . . . . . . . . . . . . .
3.2 Investment’s decision . . . . . . . . . . . . . . . . . . . . . . .
8
8
9
4 The
4.1
4.2
4.3
4.4
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Goods market
The equilibrium . . . . . . . . .
The Multiplier . . . . . . . . .
The balanced budget multiplier
Automatic stabilizers . . . . . .
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10
10
10
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12
5 Financial markets
13
5.1 Demand for money . . . . . . . . . . . . . . . . . . . . . . . . 13
5.2 Bond prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
5.3 The interest rate . . . . . . . . . . . . . . . . . . . . . . . . . 14
ii
6 The
6.1
6.2
6.3
6.4
IS-LM model
The IS curve . .
The LM curve . .
The IS-LM model
The IS-LM model
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15
15
16
16
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), “Macroeconomics, fifth edition”, eds. Pearson.
1.2
True or false?
• The share of labor income in GDP is much larger than the share of
capital income
• French GDP was 29 times higher in 1999 than it was in 1960
• When the unemployment rate is high, the participation rate is also
likely to be high
1
• The rate of unemployment tends to fall during expansions and rise
during recessions
• If Japanese CPI is currently at 108 and American CPI is at 104, then
inflation rate is higher in Japan than in the US
• The inflation rate measured using the CPI is a better index of inflation
than the one computed using GDP deflator
1.3
GDP
Suppose that GDP is measured by summing final value of all goods and
services produced. Determine the effect of the following transactions.
1. A consumer buys e100 worth of fish from a fisherman. Fishes are
consumed 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 and
buy 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 new
machine-tool for 50000 and mines 75 kg of gold. The silver is then sold
to a jewelry manufacturer for e300 000.
2. The jewelry manufacturer pays its employees e250 000 buys e300000
of silver, and makes silver necklaces directly sold to consumers for e1
million.
3. A third firm pays its employees for e30000, buys for e10000 of raw
materials and sells a machine-tool to the silver mining company for
e50000
4. The last firm sells for e10000 of raw materials to the firm specialized
in raw material.
• Calculate the GDP using the production approach.
• Calculate the added-value for each step of production. Calculate the
GDP using the added-value approach.
• Give levels of wages and profit. Calculate the GDP using the income
approach.
1.6
Nominal and real GDP
The economy can be summarized by the following table.
Year
Cars
Oranges
Computers
2009
Quantity
10
1000
4
2009
Price
2000
1
1000
2010
Quantity
12
1000
6
2010
Price
3000
1
500
1. What is nominal GDP in 2009 and 2010? What is the growth rate of
the nominal GDP?
2. Using 2009 as the reference year, what is the real GDP in 2009 and
2010?
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 in
2009 and 2010. Calculate the GDP deflator for 2009 and 2010, and the
inflation rate 2009-2010.
2. Suppose that we use 2010 prices as a basis to calculate real GDP in
2009 and 2010. Calculate the GDP deflator for 2009 and 2010, and the
inflation rate 2009-2010.
3. Why are the two inflation rate different? Which one is true? Justify
your answer.
1.8
Chain indexes
As shown in exercises 1.6 and 1.7, the choice of the reference year has an
influence 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 previous
year as the reference year.
2. What is the growth rate of GDP?
3. What is the GDP deflator? What is the inflation rate calculated using
this method?
Chapter 2
Consumption
2.1
Keynesian consumption function
In a country, the general consumption function is given by the following
equation:
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 (for
Y between 0 and 30). Find the breaking point (the level of income
characterized by C = S). What does the value 3 represent?
3. Give the average propensity to consume (APC) and the marginal propensity 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 and
global consumption move?
5. What does mean a consumption function determined by the following
equation?
C = 0.7Y − 3
5
(2.2)
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 income
when 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 a
flat-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-rate
tax and redistributes social transfers, proportional to the level of income (θY , with θ the transfer rate), and redistributes also a lump-sum
transfer (T r0 ).
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
10
Y
0
11
10000
1
2
3
4
5
6
7
8
9
11000
13000
12000
9000
10000
12000
13000
10000
8000
1. The permanent income Y P is given by the income average of the current year and the three previous years. Calculate this permanent income 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 = 0.9YtP .
What is the marginal propensity to consume the permanent income?
And the average propensity to consume the permanent income? Calculate the consumption for years 4 to 10.
4. Calculate the average propensity to consume the current income. Comment its evolution. Why this evolution is contrary to the Keynesian
assumptions?
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 expectancy
is 80 years old. We suppose that his saving is not remunerated and there is
no pension system.
1. If he spends his income constantly all over his life, what is his annual
consumption? Calculate his average propensity to consume during his
active years, his level of annual saving and the available capital when
he retires.
2. How does his saving and consumption behavior change if the pension
age is post-pone to 70 years-old?
3. What is the level of consumption for Ms. Y who earns the same wage
but whose life expectancy is 85 years-old. Comment.
4. We now suppose that Mr. X receives e300000 of inheritance and does
not want to give inheritance to his children after his death. Calculate consumption and saving levels and compare them with the ones
obtained 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 following
table:
Year
Demand
0
1000
1
1000
2
1100
3
1500
4
1600
5
1500
6
1000
7
700
8
700
9
900
In year 0, the production capacity usage rate is 100%. Fixed capital
is e4000. The capital coefficient (the ratio of capital/demand) is constant
over time. Equipments goods are not depreciated over time. Production is
immediatly adjusted to the demand at each period.
1. Calculate the capital coefficient. What hypothesis should be made in
order 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 the
national level?
3. On the same graph, draw the curve of demand and investment. Comment.
4. What would be the consequences of a stronger mechanization of the
production process?
8
10
1000
11
1000
3.2
Investment’s decision
You should analyze two projects of investments.
Life expectancy
Anticipated income (per year)
Initial cost
Project A
5 years
100
400
Project B
2 years
200
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 interest
rate is 10%. The remuneration of financial investments is unchanged
(5%). Give the net present value of both projects (1) if the firm finances
it 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
The economy has the following characteristics:
10
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: increasing
government spendings or decreasing taxes. Which policies would be
more efficient in this case? Why?
4.3
The balanced budget multiplier
For both political and macroeconomic reasons, governments are often reluctant to run budget deficits. Here we examine whether policies changes in G
and T that maintain a balanced budget are macroeconomically neutral.
The economy has the following characteristics:
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 in
equilibrium GDP? Are balanced budget changes in G and T macroeconomically neutral?
3. How does the specific value of the propensity to consume affect your
answer? Why?
4.4
Automatic stabilizers
So far, we have assumed that the policy variables G and T are independent
of the level of income. In the real World, however, it is not the case. Taxes
typically depend on the level of income and so tend to be higher when income
is higher. Here, we examine how this automatic responses of taxes can help
reduce the impact of changes in autonomous spending on output.
The economy has the following characteristics:
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 changes
in 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 this
person’s money demand function is given by:
M d = $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 happens to this person’s demand for money if her yearly income is reduced
by 50%?
4. Suppose that the interest rate is 5%. In percentage terms, what happens to this person’s demand for money if her yearly income is reduced
by 50%?
5. Summarize the effect of income on money demand. In percentage
terms, how does this effect depend on the interest rate?
13
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 interest
rate?
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:
M d = $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
The economy has the following characteristics:
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 equal
to 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
15
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 spendings. G is now equal to 100. How does this decision affect the equilibrium?
4. What does happen if the marginal propensity to consume becomes
equal to 0.2?
5. What does happen if firms change their investment behavior? The new
investment function is: I = 500 − 2500i.
6. What does happen if the function of demand for money changes? It is
now equal to Md = 0.4Y + 700 − 11000i.
7. We suppose that √
the employment level (N ) is defined by the following
function: Y = 3 N . If the active population in Groland is 16000,
what is the full employment level of output YF E ?
8. If the government wants to reach this level through fiscal policy. What
should be the level of public spendings?
9. Let’s now suppose that the government decides that G = 230. What
should be the level of money supplied by the central bank in order to
reach 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 money
supply is equal to 1100.
• Find the equilibrium output and the interest rate if the money
supply is equal to 1080.
• Compare both equilibrium.
5. Let’s now suppose that the demand for money takes the following form:
Md = 0.2Y + 1050 − 8500i
(6.15)
• Find the equilibrium output and the interest rate if the money
supply is equal to 1100.
• Find the equilibrium output and the interest rate if the money
supply is equal to 1080.
• Compare both equilibrium.
6. Same question is the investment function is:
I = 100 − 500i
(6.16)
7. Give the analytical value of the monetary policy multiplier. Comment
by analyzing your previous results.
Part 2 We now consider the effects of government spendings. We now
have:
G = 500
(6.17)
1. Find the equilibrium output and the interest rate.
2. What does happen if the Government decides to increase public spendings? (G = 550)
3. Show graphically the IS and LM curves?
4. Let’s now suppose that the demand for money takes the following form:
Md = 0.2Y + 1050
(6.18)
• Find the equilibrium output and the interest rate if G = 500.
• Find the equilibrium output and the interest rate if G = 550.
• Compare both equilibrium.
5. Let’s now suppose that the demand for money takes the following form:
Md = 0.2Y + 1050 − 6000i
(6.19)
• Find the equilibrium output and the interest rate if G = 500.
• Find the equilibrium output and the interest rate if G = 550.
• Compare both equilibrium.
6. Same question is the investment function is independent from the interest rate:
I = 100
(6.20)
7. We still suppose that the investment function is I = 100.
• Find the equilibrium output and the interest rate if the money
supply is equal to 1100.
• Find the equilibrium output and the interest rate if the money
supply is equal to 1080.
• Compare both equilibrium.
8. Give the analytical value of the budget multiplier. Comment by analyzing 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 interest rate:
I = b0 + b1 Y − b2 i
(6.22)