ANALYTICAL PROBLEMS
1. Why is some state and local spending paid for by grants in aid from the Federal government instead of entirely through taxes levied by states and localities on residents? What are the advantages and disadvantages of a system of grants in aid?
2.
Both transfer programs and taxes affect incentives. Consider a program designed to help the poor that promises each aid recipient a minimum income of $10,000. That is, if the recipient earns less than $10,000, the program supplements his income by enough to bring him up to $10,000.Explain why this program would adversely affect incentives for low-wage recipients. (Hint: Show that this program is equivalent to giving the recipient $10,000 and then taxing his labor income at a high marginal rate.) Describe a transfer program that contains better incentives. Would that program have any disadvantages? If so, what would they be?
3. a Use the fact that the nominal deficit equals the
nominal primary deficit plus nominal interest payments on government debt to rewrite Equation Show the values of seignorage for inflation rates of 0, 0.02, 0.04, 0.06,..., 0.30.
b. What inflation rate maximizes seignorage?
c. What is the maximum amount of seignorage revenue?
d. Repeat Parts (α)-(c) for Y = 1000 and r = 0.08.
9. Consider an economy in which the money supply consists of both currency and deposits. The growth rate of the monetary base, the growth rate of the money supply, inflation, and expected inflation all are constant at 10% per year. Output and the real interest rate are constant. Monetary data for this economy as of January 1, 2019, are as follows:
Currency held by nonbank public $200
Bank reserves $50
Monetary base $250
Deposits $600
Money supply $800
a. What is the nominal value of seignorage over the year? (Hint: How much monetary base is created during the year?)
b.
Suppose that deposits and bank reserves pay no interest, and that banks lend deposits not held as reserves at the market rate of interest. Who pays the inflation tax (measured in nominal terms), and how much do they pay? (Hint: The inflation tax paid by banks in this example is negative.)c. Suppose that deposits pay a market rate of interest. Who pays the inflation tax, and how much do they pay?
(15.4) showing the change in the debt-GDP ratio as a function of the ratio of the primary deficit to GDP, the ratio of debt to GDP, and the difference between the growth rate of nominal GDP and the nominal interest rate.
b. Show that, if the primary deficit is zero, the change in the debt-GDP ratio equals the product of (1) the debt-GDP ratio and (2) the excess of the real interest rate over the growth rate of real GDP.
4. A constitutional amendment has been proposed that would force Congress to balance the budget each year (that is, outlays must equal revenues in each year). Discuss some advantages and disadvantages of such an amendment. How would a balanced-budget amendment affect the following, if in the absence of such an amendment the Federal government would run a large deficit?
a. The use of automatic stabilizers.
b. The ability of Congress to “smooth" taxes over time.
c. The ability of Congress to make capital investments.
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