**14.02 Principles of
Macroeconomics**

**Problem Set 4**

**Posted: Wednesday, March 14,
2001**

**Due: Wednesday, March 21,
2001**

Please
remember to write your TA’s name and section time on the front page or your
problem set.

Part 1: True/False Questions: Decide whether each statement is true or false and justify your answer with a short argument. (5 points each, 25 points total)

1. An increase in productivity shifts the Aggregate Supply curve to
the right.

2. According to the AD-AS model, tax cuts should lead to an increase
in the price level.

3. Total wealth is the sum of financial wealth and housing wealth.

4. Lowering the retirement age increases total wealth because the
present value of financial wealth increases while housing wealth and human
wealth remain unchanged.

5. For a given change in annual income, consumption should increase
more the more permanent people believe the change to be.

Part 2: IS-LM (5 points each, 40 points total)

Consider
an economy characterized by the following equations:

C=200+(3/4)(Y-T)

I=50+(1/20)Y+100(6-i)

G=200

T=(1/10)Y

Md=Y/i

M=400

P =
1

where
C is consumption, Y is income, T is taxes, I is investment, i is the interest
rate, G is government expenditures, Md is money demand, M is the money supply,
and P is the price level.

1. State the equilibrium condition for the goods market. Solve for national income as a function of
the interest rate. What is the value of
the multiplier?

2. Solve for equilibrium in financial markets. Briefly explain why money demand is
increasing in income and decreasing in the interest rate.

3. Find the equilibrium values of the interest rate, income, and
government deficit.

4. Plot the IS and LM curves (recall that income should be on the
horizontal axis). Be sure to label the
curves and their intersection.

Now
assume that consumers become nervous about the future causing autonomous
consumption to drop below 200.

5. What is the impact on the equilibrium values of income, the
interest rate, and the government deficit?
Please give a brief explanation of your reasoning.

6. Is the fall in income greater than, less than, or equal to the
drop in autonomous spending times the multiplier? Why?

7. What are three possible policy actions that could be taken to
offset the effect of the drop in consumer confidence on income?

8. What are the pros and cons of each possibility?

Part 3: Consumption (5 points each, 35 points total)

Note:
This is Question 5 from the problems at the end of Chapter 16 in the text,
except for part (h).

Suppose that every consumer is born with
zero financial wealth and lives for three periods: youth, middle age, and
retirement age. Consumers work in the
first two periods and retire in the last one.
Their income is $5 in the first period, $25 in the second, and $0 in the
last one. Inflation and expected
inflation are zero, and the real interest rate is also zero.

a. What is the present discounted value of future labor income at
the beginning of life? What is the
highest sustainable level of consumption such that consumption is equal in all
three periods?

b. For each age group, what is the amount of saving that allows
consumers to maintain the constant level of consumption you found in (a)?
(Hint: Saving can be a negative number, if the consumer needs to borrow in order
to maintain a certain level of consumption.)

c. Suppose there are N people born each period. What is total saving? (Hint: Compute the
total amount saved by the generations that save and subtract the total amount
dissaved by the generations that dissave.)
Explain.

d. What is total financial wealth in the economy? (Hint: Compute the
financial wealth of people at the beginning of the first period of life, of the
second period of life, of the third period of life. Remember that people can be in debt, so financial wealth can be
negative. Add them up.)

Suppose
now that restrictions on borrowing do not allow young consumers to borrow. At each age group, consumers once again
compute their total wealth and then determine their desired level of
consumption as the highest level that allows their consumption to be equal in
all three periods. However, if that is
greater than their income plus their financial wealth, then they are
constrained to consuming exactly their income plus their financial wealth.

e. Derive consumption in each period of life. Explain the difference
from your answer to (a).

f. Drive total saving.
Explain the difference, if any, from your answer to (c).

g. Derive total financial wealth.
Explain the difference from your answer to (d).

No
Credit: “Financial liberalization may be good for people, but it is bad for
overall capital accumulation.” Please
take a moment to reflect on this statement given your answers to (a) through
(g).