# Intermediate Macroeconomics

1. A consumer lives three periods, called the learning period, the working period, and the retirement period. Her income is 200 during the learning period, 800 during the working period, and 200 again during the retirement period. The consumer's initial assets are 300. The real interest rate is zero. The consumer desires perfectly smooth consumption over her lifetime.

a. What are consumption and saving in each period, assuming no borrowing constraints? What happens if the consumer faces a borrowing constraint that prevents her from borrowing?
b. Assume that the consumer's initial wealth is zero instead of 300. Repeat part (a). Does being borrowing-constrained mean that consumption is lower in all three periods of the consumer's life than it would be if no borrowing constraints applied?

2. Here are some balance of payments data (without pluses and minuses):

Exports of goods, 100
Imports of goods, 125
Service exports, 90
Service imports, 80
Income payments to foreigners, 150
Increase in home country's ownership of assets abroad, 160
Increase in foreign ownership of assets in home country, 200
Increase in home reserve assets, 30
Increase in foreign reserve assets, 35

Assuming that unilateral transfers equal zero, find net exports, the current account balance, the capital and financial account balance, the official settlements balance, and the statistical discrepancy.

3. In a small open economy, output (gross domestic product) is \$25 billion, government purchases are \$6 billion, and net factor payments from abroad are zero. Desired consumption and desired investment are related to the world real interest rate in the following manner:

World Real Interest Rate Desired Consumption Desired Investment
5% \$12 billion \$3 billion
4% \$13 billion \$4 billion
3% \$14 billion \$5 billion
2% \$15 billion \$6 billion

For each value of the world real interest rate, find national saving, foreign lending, and absorption. Calculate net exports as the difference between output and absorption. What is the relationship between net exports and foreign lending?

4. In a small open economy,

Desired national saving, S^d = \$10 billion + (\$100 billion)r^w
Desired investment, I^d = \$15 billion - (\$100 billion)r^w
Output, Y = \$50 billion
Government purchases, G = \$10 billion;
World real interest rate, r^w = 0.03

a. Find the economy's national saving, investment, current account surplus, net exports, desired consumption, and absorption.
b. Owing to a technological innovation that increase future productivity, the country's desired investment rises by \$2 billion at each level of the world real interest rate. Repeat part (a) with this new information.

5. Consider two large open economies, the home economy and the foreign economy. In the home country the following relationships hold:

Desired consumption, C^d = 320 + 0.4(Y - T) - 200r^w
Desired investment, I^d = 150 - 200r^w
Output, Y = 1000
Taxes, T = 200
Government Purchases, G = 275

In the foreign country the following relationships hold:

Desired consumption, C^dFor = 480 + 0.4(YFor - Tfor) - 3000r^w
Desired investment, I^dFor = 225 - 300r^w
Output, YFor = 1500
Taxes, TFor = 300
Government purchases, GFor = 300

a. What is the equilibrium interest rate in the international capital market? What are the equilibrium values of consumption, national saving, investment, and the current account balance in each country?
b. Suppose that in the home country government purchases increase by 50 to 325. Taxes also increase by 50 to keep the deficit from growing. What is the new equilibrium interest rate in the international capital market? What are the new equilibrium values of consumption, national saving, investment, and the current account balance in each country?

6. Consider a world with only two countries, which are designated the home country (H) and the foreign country (F). Output equal sits full-employment level in each country. You are given the following information about each country:

Home Country
Consumption: CH = 100 + 0.5YH - 500r
Investment: IH = 300 -500r
Government Purchases: GH = 155
Full-employment Output: YH = 1000

Foreign Country
Consumption: CF = 225 + 0.7YF - 600r
Investment: IF = 250 - 200r
Government Purchases: GF = 190
Full-employment Output: YF = 1200

a. Write national saving in the home country and in the foreign country as functions of the world real interest rate r.
b. What is the equilibrium value of the world real interest rate?
c. What are the equilibrium values of consumption, national saving, investment, the current account balance, and absorption in each country?

7. A small island nation is endowed with indestructible coconut trees. These trees live forever and no new tress can be planted. Every year \$1 million worth of coconuts fall off the trees and can be eaten locally or exported to other countries. In past years the island national ran current account surpluses and capital and financial account deficits, acquiring foreign bonds. It now owns \$500,000 of foreign bonds. The interest rate on these bonds is 5% per year. The residents of the island nation consume \$1,025,000 per year. What are the values of investment, national saving, the current account balance, the capital, and financial account balance, net exports, GDP, and GNP in this country?

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