NUMERICAL PROBLEMS

1. The following budget data are for a country having both a central government and provincial governments:

Central purchases of goods and services 200

Provincial purchases of goods and services 150

Central transfer payments 100

Provincial transfer payments 50

Grants in aid (central to provincial) 100

Central tax receipts 450

Provincial tax receipts 100

Interest received from private sector by 10

central government

Interest received from private sector by 10

provincial governments

Total central government debt 1000

Total provincial government debt 0

Central government debt held by provincial 200

governments

Nominal interest rate 10%

Calculate the overall and primary deficits for the central government, the provincial governments, and the combined governments.

2. At the beginning of year one, there is no government debt outstanding. The government runs a $100 billion deficit in year one. Interest at a nominal rate of 10% must be paid starting in year two. Assume nominal GDP in year one is $2 trillion, and the nominal growth rate of GDP is 4%. Assume the government balances its pri­mary budget in the future and the interest rate and growth rate do not change.

a. What will be the government deficit in years two, three, four, and five?

b. What will be the value of government bonds out­standing at the end of the fifth year?

c. What will be the debt-GDP ratio at the end of year five? ^[305]

4. Suppose that the income tax law exempts income of less than $8000 from the tax, taxes income between $8000 and $20,000 at a 25% rate, and taxes income greater than $20,000 at a 30% rate.

a. Find the average tax rate and the marginal tax rate for someone earning $16,000 and for someone earning $30,000.

b. The tax law is changed so that income of less than $6000 is untaxed, income from $6000 to $20,000 is taxed at 20%, and income of more than $20,000 continues to be taxed at 30%.

c. How will the tax law change in part (b) affect the labor supply of the person initially earning $16,000? How will it affect the labor supply of the person initially earning $30,000?

5. Suppose that all workers value their leisure at 90 goods per day. The production function relating output per day, Y, to the number of people working per day, N, is

Y = 250N - 0.5N².

Corresponding to this production function, the mar­ginal product of labor is

MPN = 250 - N.

a. Assume that there are no taxes. What are the equi­librium values of the real wage, employment, N, and output, Y? (Hint: In equilibrium the real wage will equal both the marginal product of labor and the value of a day's leisure to workers.)

b. A 25% tax is levied on wage income. What are the equilibrium values of the real wage, employment, and output? In terms of lost output, what is the distortion cost of this tax?

c. Suppose that the tax on wages rises to 50%. What are the equilibrium values of the real wage, employment, and output? In terms of lost output, what is the distortion cost of this higher tax rate? Compare the distortion caused by a 50% tax rate with that caused by a 25% tax rate. Is the distortion caused by a 50% tax rate twice as large, more than twice as large, or less than twice as large as that caused by a 25% tax rate? How does your answer relate to the idea of tax smoothing?

6. Find the largest nominal deficit that the government can run without raising the debt-GDP ratio, under each of the following sets of assumptions:

a. Nominal GDP growth is 10% and outstanding nominal debt is 1000.

b. Real GDP is 5000 and remains constant, nominal GDP is initially 10,000, inflation is 5%, and the debt-GDP ratio is 0.6.

7. In this problem you are asked to analyze the ques­tion: By issuing new bonds and using the proceeds to pay the principal and interest on its old bonds, can government avoid ever repaying its debts?

a. Suppose that nominal GDP is $1 billion and the government has $100 million of bonds outstand­ing.

b. Repeat part (a) for nominal GDP growth of 8% per year and a nominal interest rate on government bonds of 7% per year.

8. Real money demand in an all-currency economy with fixed real output and real interest rate, and constant inflation rate and money growth rate is

L = 0.2Y - 500i,

where Y is real income and i is the nominal interest rate. In equilibrium, real money demand, L, equals real money supply, M/P. Suppose that Y is 1000 and the real interest rate, r, is 0.04.

a. Draw a graph with real seignorage revenue on the vertical axis and inflation on the horizontal axis.

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