Homeworks and answers will be posted here.
Each Tuesday evening, a new homework assignment will be posted here, and it
will be due in the Econ 311 box in the Economics Department Office by the
following Teusday. The first homework will be posted here January 4.

First homework: questions 2, 3 and 4 at end
of Chapter 3. Due January 11.

Answers to homework #1.

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Homework #2, due January 18.

1. Consider the model in question 2, page 62.
Suppose G rises permanently from 150 to 160.

(a) derive what happens to equilibrium
income.

(b) describe the transition from the old
equilibrium to the new equilibrium in detail. To do this, you will need some
additional assumptions about disequilibrium dynamics in the goods market.
Suppose each day is divided into a morning and an afternoon. The production of
goods by factories occurs in the morning and sales occur in the afternoon.
Suppose firms set production in the morning equal to the previous day’s sales.
For example, if production was 1000 in the previous period and there was
unplanned inventory decumulation in the amount 10, then we can infer that sales
in the previous afternoon were 1010. Under our assumption about disequilibrium
dynamics, production in the current morning would be 1010.

Suppose that the economy was in the old
equilibrium in day 0. Record the values in day 0 of: total income, household
saving, the government deficit, production, sales, unanticipated inventory accumulation,
consumption and investment. Do the same for period 1, 2, and 3. You should
report these results in a table.

2. Consider our Keynesian Cross model with
the planned investment equation replaced by I (planned) = I(bar) – b*i.

Suppose money demand is M/P=a0*Y – a1*i.
Suppose the supply of M/P is an exogenously given number, say MM. Derive a
formula for equilibrium output in the IS-LM model.

3. Do question 4, page 85 in the textbook. Do
question 2, with 0.35 replaced by 0.50 in the money demand equation.

Answers to homework
#2.

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Homework #3, due January 25.

1. Questions 5, 7, 8 at the end of chapter 5.

2. Consider the model in question 4, end of
chapter 5. (i) Compute the equilibrium level of consumption, saving, output,
investment and the interest rate for the model. Now compute the equilibrium
values of these variables when taxes are cut from 200 to 150. (ii) Repeat (i),
except do so for the version of the model without the investment accelerator,
i.e., the version in which the coefficient on Y in the investment equation is
zero. (iii) Compare the magnitude of the increase in equilibrium output between
(i) and (ii). Provide the intuition for the difference in the results. In which
case does the cut of taxes generate less crowding out? Give intuition for your
answer.

Answers to homework #3.

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Homework #4, due February 2

Questions 1, 6, 7, page 131 in the book.

Answers to homework #4.

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Homework #5, due February 9, answers.

1. Questions 6 and 7, page 159 in the book.

2. Using the AS-AD model, show the effects of
an increase in I(bar): (i) begin by drawing the AD-AS model in medium run
equilibrium, before the shock to I(bar); (ii) show how the increase in I(bar)
moves the AD curve (make your argument taking into account the fact that the AD
curve is constructed from the IS-LM diagram); (iii) point out the short run and
medium run equilibria; (iv) describe in detail what happens to the interest
rate, investment, consumption, employment, unemployment and output as you move
from the old medium run equilibrium to the short run equilibrium, to the new
medium run equilibrium (illustrate your argument by using the various graphs
that go into constructing the AD and AS curves); (v) how does the size of the
multiplier effect in the short run compare with the multiplier in the Keynesian
Cross model and the multiplier in the IS-LM model? Why are the multipliers
different? What is the multiplier in medium run in the AD-AS model? (vi) what
happens to the composition of spending, between investment, consumption and
government spending, differ across the old and the new medium run equilibria?

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Homework #6, due Thursday, February 17. Answers.

Using the AS-AD model,

1. Consider a rise in labor productivity: (i)
explain in detail how this shifts the AS curve, but does not change the natural
rate of unemployment. (ii) Work out the implications in the short run and the
medium run, for the interest rate, C, P, I, employment and unemployment of the
rise in labor productivity. Establish your results using graphs, and then provide
intuition. (iii) Why might globalization produce a rise in the economy’s labor
productivity?

2. Suppose that the size of the labor force
increases. What happens to the natural rate of unemployment in the medium run?
What happens to the natural rate of output?

3. Suppose there is a rise in the quality of
unemployment insurance. Explain why this increases the natural rate of
unemployment. What is the impact on output, interest rates, the price level,
investment, consumption in the short run and the medium run. Establish your
results using graphs, and also provide the intuition.

4. Explain why globalization may lead to a
fall in the natural rate of unemployment in the medium run. Work out the
implications, in the short and medium run, for interest rates, the price level,
the unemployment rate and consumption, of increased globalization. Make your
argument using graphs, and then provide the economic intuition.

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Homework #7, due Thursday, February 24. Answers

1. Suppose there is a decrease in the money
supply.

(a) Work through the short run impact of this
change on output, employment, the price level, the interest rate and
unemployment. What happens in the medium run? How much does the expected price
level move in the medium run? First show what is going on in the AD-AS and the
IS-LM diagrams. Then, provide a journalistic discussion.

(b) Reconsider the experiment in (a). This
time, suppose that when the money supply falls, the expected price level falls
at the same time, by the amount it changed in the medium run in (a). Redo the
analysis in (a).

(c) What can you infer from your analysis in
(a) and (b) about the importance of slow adjustment in expectations for the
transmission of money supply changes to economic variables?

2. Consider an economy that begins in medium
run equilibrium, and is then hit by two shocks: there is a drop in government
spending, and a substantial improvement in the quality of the unemployment
insurance system. Suppose the initial medium run price level is above the level
that is consistent with the Gold Standard. In addition to the above two shocks,
the government wants to manipulate the money supply to restore the Gold
Standard.

(a) In the AD-AS diagram, illustrate what the
G and unemployment system shocks do to the AD and AS curves. Where are the
short run and medium run equilibria in the absence of a monetary policy
response?

(b) Suppose the monetary authorities simply
want to reach the Gold standard in the medium run. How much do they need to
move the AD curve to accomplish this? Explain why this requires a decrease in
the money supply.

(c) Suppose the monetary authorities want to
reach the Gold Standard in the short run. Show how much they need to move the
AS curve to accomplish this. Which generates a greater recession, (b) or (c)?
What does the monetary authority need to do to the money supply as the economy
moves to its medium run equilibrium, if it wants to remain on the Gold Standard
all the time?

3. Suppose you observe P and Y going in the
opposite direction, but no change in the real wage, W/P. What is the shock
driving the economy? Explain using graphs.

4. Suppose that in 3 you instead observe W/P
rising. How does this change what you infer about the source of the shocks? Use
graphs.

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Homework #8, Due March 3.

1.
Suppose there is
a rise in Pe, the expected price level.

a.
Explain, in full
detail (i.e., describe the movements of all the endogenous variables, and
motivate your conclusions using graphs), where the economy goes in the short
run and where it goes in the medium run.

b.
Discuss the
dilemma faced by a central bank, which sees the rise in Pe (it sees the strong
wage demands) and correctly understands that the scenario in (a) will unfold if
it does nothing (i.e., if the central bank chooses ‘non-accommodation’).
Describe in detail the ‘accommodation scenario’, the one in which the central
bank uses its control of the money supply to prevent any rise in unemployment.
Discuss the advantages and disadvantages of accommodation versus
non-accommodation.

c.
Suppose the
central bank is known to be inclined towards increasing the money supply in the
event that it observes unemployment rising. What does this do to the likelihood
that Pe may rise sometime in the future?

d.
Use your analysis
in the previous parts of this question to explain why it is that the European
Central Bank was made independent of national or euro area-wide government
organizations (hint: independence means they will be less subject to political
pressure to keep unemployment low), and was given a mandate to place a very
high priority on achieving low inflation. Does it not seem to be a waste, to
give up the possibility to use monetary policy to help stabilize the economy?

2.
Up to now, we
modeled an increase in productivity as showing up only in the equation relating
unemployment to output: *u=1-Y/(aL)*, where the production
function is given by *Y=aN*. This gave
rise to the following AS curve: *P=(1+ µ
)F(1-Y/(aL),z)*. Now, we’ll take a slightly more sophisticated approach, one
that does not change the AS curve, but which does change its parts. Let the
productivity parameter, a, enter the price equation like this: *P=(1+µ)W/a. *To understand why
this is, recall that *P* is the price
for one good. Under our theory this is equated to a markup over the marginal
labor cost of labor in producing the good. W measures the marginal cost of one
hour of labor. So, if *a*=1 then the marginal labor cost of one good is *W*. But, if *a *jumps to, say, 2,
then the marginal labor cost of one good is *W/2*,
because it now takes the worker only 1/2 hour to make the good, at a labor cost
of *W/2*. Now consider the bargaining
equation. I suppose that *a* shows up in this expression as follows: *W=aP ^{e}F(u,z)*. The idea behind
this is that when a rises, the amount produced by a given worker goes up. The
nature of the bargaining is that what the worker gets for his/her labors goes
up in the same proportion as

a.
Suppose *a* goes up. Explain carefully why the
natural rate of unemployment does not change, but the natural rate of output
does. Also, explain why the real wage, *W/P*,
rises. These are sensible properties for our model to have, since over long
periods of time a does rise, while *W/P*
and output both rise too, but unemployment does not rise.

b.
Suppose *a*
goes up. Explain in detail what happens as the economy moves to the short run
equilibrium. Then, explain how it moves to the medium run equilibrium.