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).