Download Department of Economics, University of Toronto

Department of Economics, University of Toronto
Halina Kalita von dem Hagen
ECO 208Y: MACROECONOMIC THEORY
PROBLEM SET #3
PART I:
1. An economy is known to have the following relationships:
aggregate production function:
labour supply:
aggregate demand curve:
Y = 128 N0.5
NS = (W/Pe)2
AD = (M+G)/P
a. Derive the labour demand curve.
b. Determine the long-run levels of employment and of the real wage.
c. Find the classical aggregate supply curve.
d. If the money supply M = 1500, the government spending G = 548, and people form
expectations rationally, what is the expected price level in this economy?
e. Given your answer to (d) above, find the New Classical aggregate supply curve (EAS) curve
for this economy.
f. Assuming that nominal wage contracts were signed when the economy was in the long-run
equilibrium, determine the level of contractual nominal wages.
g. Given your answer to (f) above, derive the New Keynesian AS curve.
h. Assume the government undertakes a very ambitious fiscal policy expansion so that the
government spending G unexpectedly rises to 5412 (i.e. new G = 5412). Determine the level of
prices, nominal and real wages, output and employment in the short-run assuming:
i.
New Classical framework
ii.
New Keynesian framework.
i. Given the monetary shock described in (h), calculate the long-run equilibrium levels of output
and prices.
2. An economy is known to have the following relationships:
aggregate production function:
labour supply:
aggregate demand curve:
Y = N0.5
Ns = (32*W/Pe)2
AD = 10/P
a. Derive the labour demand curve.
b. Determine employment and the real wage in a classical equilibrium.
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c. Find the classical aggregate supply curve.
d. Find the level of prices and the level of nominal wages consistent with the classical
equilibrium.
e. Find the New Classical expectations augmented aggregate supply curve.
f. Assume that the economy was initially both in the long-run and in the short-run equilibrium.
As a result of an unexpected expansionary monetary policy, the aggregate demand is now defined
by:
AD = 20/P
Determine both the short-run and the long-run equilibrium level of income and prices.
3. A New Keynesian economy is characterized by the following:
aggregate production function: Y = ln(N)
labour supply curve:
NS = (2.72)2(W/Pe)
aggregate demand curve:
AD = 2G + (1/2)(M/P)
(a) Derive the labour demand curve. Find the long-run aggregate supply curve.
(b) Find the actual price level if the government spending is (1/4) and the money supply is 4.
(c) Determine the nominal wage signed in the labour contracts.
(d) Given your answers to (b) and (c) above, find the New Keynesian aggregate supply curve
(NK AS).
4.
Let the production function given by: Y = 5N - 0.5 (N)2
Let the labour supply be given by:
NS = 4W/Pe
Let the aggregate demand be given by: AD = M/P + G
a.
Derive the labour demand curve.
b.
Compute the real wage and the employment level in the classical equilibrium.
c.
Find the classical aggregate supply curve.
d.
Assume rational expectations. The classical aggregate supply curve is known to
economic agents. If the money supply M=16 and the government spending G=11, what is the
expected price level in this economy?
e.
Given your answer to (d) above, find the New Classical aggregate supply curve (EAS)
for this economy.
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f.
Assuming that nominal wage contracts were signed when the economy was in the longrun equilibrium, determine the level of contractual nominal wages.
g.
Given your answer to (f) above, derive the New Keynesian AS curve.
h.
Consider the New Classical economy. The government reduces its spending from G=11
to G=3, and this change is well known to everybody. Calculate the new level of income,
employment, real wages, nominal wages, and prices in this economy.
5. Assume a constant level of output (i.e. y=0). Suppose that in the New Classical economy the
growth rate of money decreases unexpectedly and that expectations are given by:
expected inflation = last-period growth of money supply m(-1)
i.e. expectations are based on last period's money growth.
a.
Analyze the first-round effects of the decreased rate of monetary growth on
output, real wage rate, real interest rate, consumption and investment.
b.
Analyze the long-run effects of the shock on output, inflation, real and
nominal interest rates, and the level of real money supply.
PART II:
Evaluate the following statements. Carefully explain your reasoning:
1. The Bank of Canada could assure a low nominal interest rate - but to do so, it would have to
start in what seems like the opposite direction, by engaging in a deflationary policy.
2. Inflation can be viewed as a tax on real money holdings.
3. A once-and-for-all decrease in government expenditures leads to a once-and-for-all decrease
in the price level.
4. In the long-run, the choice of the rate of monetary growth is completely irrelevant.
PART III:
ANSWER ALL QUESTIONS. Mark the best answer to each question.
1.
In the Classical economy, the money supply has been growing at 16% per year. Today
monetary authorities commit themselves to reduce the growth rate of the money supply to 8% per
year. As a result of the policy change,
(a)
(b)
(c)
(d)
both the price level and the inflation rate increase
both the price level and the inflation rate fall
the price level increases and the inflation rate falls
the price level decreases and the inflation rate increases
2.
In two economies A and B, the money supply grows at the same rate. Both economies
enjoy the same rate of growth of output. The income-elasticity of demand for real money
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balances is the same in both countries. If money in economy A starts circulating faster so that
the velocity in A increases at the rate of 2% per year, then, compared to B,
(a)
(b)
(c)
(d)
A has both a higher inflation rate and a higher nominal interest rate
A has a lower inflation rate and a higher nominal interest rate
A has a higher inflation rate and a lower nominal interest rate
A has both a lower inflation rate and a lower nominal interest rate
3.
Assume the New Classical economy in which markets are initially in equilibrium. If both
firms and suppliers of labour correctly expect an increase of 10% in the relevant prices,
employment will:
(a)
(b)
(c)
(d)
4.
much
In Russia the price level has been rising very rapidly over the past years--in some cases as
as 50 percent per month. This is most likely caused by
(a)
(b)
(c)
(d)
5.
wage controls
de-indexation of tax brackets in the tax system
long-term fixed nominal commitments
the payment of interest at close to market rates on all assets that are used as money
If the inflation rate increased by ten percent and the change was known to all people, the
immediate reaction would be:
(a)
(b)
(c)
(d)
7.
an increase in the demand for money in excess of the growth of money supply
an expansion of the money supply in excess of the growth of output
stagnant investment spending
a combination of all three of the above circumstances
Which of the following reduces the welfare costs of inflation:
(a)
(b)
(c)
(d)
6.
fall
increase
stay the same
any of the above
a decrease in desired real money holdings
an increase in the real value of money holdings
hoarding of goods in expectation of further increases in the inflation rate
none of the above
In a closed economy with flexible prices (classical economy), both output and the
quantity of money have been constant. Suddenly, the growth rate of output becomes 5
percent per year. As a result,
(a)
(b)
(c)
(d)
the price level instantaneously rises
the inflation rate rises
both a and b
neither a nor b
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