14.02 Principles of Macroeconomics
Problem Set 4 – AD-AS, IS-LM, and Consumption
Posted: Wednesday, March 14, 2001
Due: Wednesday, March 21, 2001
Part I: True orFalse
1. True. First note that productivity affects the labor market, so changes in productivity will affect the AS curve, not the AD curve. With higher productivity, at every price workers will be able to produce more so output will be higher. (It might help your intuition to begin by thinking of the long-run vertical aggregate supply curve. Since this was covered quickly in most sections you also might want to refer to Chapter 6 in the text for further explanation.)
2. True. Tax cuts are associated with the goods market (T), so begin by thinking of how the AD curve will shift in response to a cut in taxes: the IS curve shifts right yielding higher equilibrium output for a given price level. Thus the AD curve shifts right causing prices to increase.
3. False. Total wealth also includes human wealth.
4. False. Human wealth will decrease due to lost years of wage earnings.
5. True. This is a central result of the Permanent Income Theory (see Chapter 16).
Part 2: IS-LM
1. Equilibrium in the goods market: Y=C+I+G. Substitution yields Y=1050+29/40Y-100i so Y=(40/11)[1050-i] (it may look messy now, but leave it as a fraction and have faith). The multiplier is 40/11 or about 3.6.
2. Equilibrium in financial markets: Md=M or Y/i=400. Money demand is increasing in income because you need money to perform transactions and the nominal value of transactions in the economy is increasing in income. The interest rate is the opportunity cost of holding money so money demand falls with higher interest rates.
3. Substituting i=Y/400 in the goods market equilibrium yields Y=(40/11)1050-(10/11)Y so Y=(40/21)1050=2000 (you might find it easier to solve for i first). Then i=Y/400=5 and G-T=200-200=0.
4. Two straight lines: the IS slopes down, the LM slopes up.
5. A drop in autonomous consumption shifts the IS curve to the left yielding lower equilibrium income and interest rate. Since taxes are a fraction of income, T falls, but G remains constant so the government moves from a balanced budget into deficit.
6. The fall in income is less than the drop is autonomous spending times the multiplier. Income would fall by that much if the interest rate remained constant, but the interest rate falls. This stimulates investment partially offsetting the fall in income.
7. The government could increase spending or cut the tax rate, or the central bank could increase the money supply.
8. There are many possible answers. Here are a few suggestions. Monetary Policy Pros: The policy decision can be made quickly and should work relatively quickly. Monetary Policy Cons: This is more difficult. Some possibilities: the stimulation will work primarily through investment (and perhaps you think there's already enough investment), interest rates may already be near zero (cf. Japan), you may not want the Fed moving interest rates too frequently, and most central banks are fairly independent of the rest of the government, so there is little democratic control of their policies and decisions. Fiscal Policy Pros: This time the pros are more difficult. Tax cuts can help consumers more directly, there are more possible actions to take than with monetary policy (i.e. there are many ways to increase spending or cut taxes, but the Fed only controls a few interest rates), and the policy can be targeted to help specific groups. Fiscal Policy Cons: The budget deficit will worsen and it may take time to decide on and implement the policy.
Part 3: Consumption
a. Expected present discounted value of future labor income = $30 (note that since interest rates are zero this is just the sum). Optimal consumption is $10 in all three periods.
b. Savings: young: -5; middle age: 15; old: -10
c. Total savings: -5N + 15N - 10N = 0 (This should be intuitive since each generation is the same size.)
d. 0 - 5N + 10N = 5N Note that these are the values at the beginning of each period.
e. Optimal consumption: young: 5; middle age: 12.5; old: 12.5. Individuals cannot borrow against future income when young, but still want to smooth consumption between middle age and retirement.
f. Total Savings: 0 + 12.5N - 12.5N = 0
g. 0 + 0 + 12.5N = 12.5N
No Credit: True. By allowing people to have more even consumption, financial liberalization may lead to less overall accumulation of capital.