Homework Assignment #2 ECO 3203, Fall 2020

Homework Assignment #2 ECO 3203, Fall 2020

Instructions: Answer each of the following questions. Show your work wherever possible, and justify your responses wherever appropriate. Due: Friday, October 23rd at the beginning of class. 1. According to classical macroeconomic theory, money supply shocks are “neutral.” a. Explain what this means. Hint: see 5.7 of the textbook. b. Based on that theory, how would a 5% increase in a nation’s money supply affect its real

wage rate (W/P), all else equal (up, down, or no change, and by how much)? c. According to the quantity theory of money, how would a 5% increase in the money supply

affect the price of goods and services (P), all else equal (up, down, or no change, and by how much)?

d. To be consistent with both theories, what would have to happen to the nominal wage rate (W)? Explain.

2. Suppose that in the U.S., the income velocity of money (V) is constant. Suppose, too, that every year, real GDP grows by 2.5 percent (%∆Y/year = 0.025) and the supply of money grows by 10 percent (%∆M/year = 0.10). a. According to the Quantity Theory of Money, what would be the growth rate of nominal GDP

= P×Y? Hint: %∆(X×Y)  %∆X + %∆Y. b. In that case, what would be the inflation rate (i.e. %∆P/year)? c. If the central bank wants the inflation rate to be 0%, what money supply growth rate (i.e. -

%∆M per year) should it set? 3. Use the classical model of a closed economy (chapter 3) and the quantity theory of money (chapter 5, section 1) to predict how each of the following shocks would affect real aggregate income (Y), the real interest rate (r), and the price of goods and services (P) in a closed economy in the long run, all else equal. For each shock, be sure to clearly state a prediction for all three variables (up, down, or no change) and illustrate your predictions with supply/demand diagrams for the goods market and the loanable funds market. a. A decrease in supply of capital (KS down). b. An increase in the income velocity of money (V up).

4. Consider the following model of a closed economy:

 𝑌 = 𝐴𝐾1/2𝐿1/2  𝑌𝑑 = 𝐶 + 𝐼 + 𝐺  𝑌 = 𝑌𝑑  𝐶 = 250 + 0.7(𝑌 − 𝑇)  𝐼 = 2000 − 20,000𝑟  𝐴 = 25; 𝐾 = 144; 𝐿 = 100

 𝐺 = 600; 𝑇 = 500

 𝑀 = 1500; 𝑉 = 8 a. What values of aggregate income (Y) and national saving (S) result from full employment of

labor and capital? b. What must the interest rate (r) be in order to establish long run equilibrium in the market

for loanable funds? c. According to the quantity theory of money, what is the equilibrium price of goods (P) for

this economy? d. If the money supply increases by 20% (from 1500 to 1800), what will the new equilibrium

price of goods be, all else equal? 5. Consider the following model of a small, open economy:

 𝑌 = 4000  𝑌𝑑 = 𝐶 + 𝐼 + 𝐺 + 𝑁𝑋  𝑌 = 𝑌𝑑  𝐶 = 400 + 0.8(𝑌 − 𝑇)  𝐼 = 800 − 5000𝑟  𝑁𝑋 = 800 − 400𝜀  𝐺 = 300  𝑇 = 1000

a. Assuming that the world’s real interest rate is 8% (rw* = .08), what will national saving (S)

and investment (I) be for this economy?

b. What are the equilibrium values of net exports (NX) and the real exchange rate ()? c. What are the equilibrium values of net exports and the real exchange rate if the world’s real

interest falls to 6%, all else equal? d. What are the equilibrium values of net exports and the real exchange rate if the world’s real

interest rate is 8%, but domestic government purchases (G) are reduced to 100, all else equal?

6. Define the terms “net exports” and “net capital outflow”. How are the two variables related in an open economy with clearing markets? 7. Use the textbook’s model of a small, open economy with perfectly mobile capital to predict how each of the following shocks will affect a nation’s national saving (S), investment (I), trade

balance (NX), and real exchange rate (), all else equal. For each shock, be sure to clearly state a prediction for all four variables and illustrate your predictions with the relevant supply/demand diagrams. a. The domestic supply of capital increases (KS up) b. Domestic government purchases are reduced (G down) c. Forecasts of a recession cause an exogenous decrease in autonomous investment (i0 down) d. A decrease in the world’s supply of loanable funds, pushes world interest rates up (rw* up) 8. Suppose that last year, the nominal exchange rate between the Japanese yen and the British pound was ¥150.0 per £1.0, one unit of Japanese output cost ¥1300, and one unit of British output cost £8.0. a. What was the real exchange rate between the U.K. and Japan last year, expressed as the

cost of British output (i.e. – the quantity of Japanese output that exchanges for 1 unit of British output)? In which country were goods more expensive last year?

b. Suppose that between last year and this year the British pound appreciated by 20% against the Japanese yen (a 20% increase in the number of yen required to buy 1 pound). If the price of goods in the U.K and Japan are unchanged from last year, what is this year’s new real exchange rate? In which country are goods more expensive this year?

c. Now suppose, instead, that between last year and this year, the pound appreciated by 20% against the yen and Japan experienced a 30% inflation rate (a 30% increase in the number of yen required to purchase one unit of Japanese output). All else equal, what is this year’s real exchange rate in that case? In which country are goods more expensive this year?

9. Describe the difference between a nation’s real exchange rate with another country and its nominal exchange rate. 10. In Mankiw’s model of a small open economy, domestic interest rates are set by the world’s market for loanable funds, rather than by domestic saving and investment. a. What are the two simplifying assumptions in the model that disconnect domestic interest

rates from domestic saving and investment? b. What is determined by domestic saving and investment in the model?

11. Suppose that apples were the only good produced in the United States and Mexico. In Mexico, apples sell for 12 pesos apiece. In the Unites states, apples sell for $0.50 apiece. a. According to the theory of Purchasing Power Parity, what is the equilibrium nominal

exchange rate between the U.S. dollar and the Mexican peso? What would the real exchange rate between the U.S. and Mexico in that case?

b. Suppose the price of apples rises at a rate of 3% per year in the U.S., but at a rate of 12% per year in Mexico. According to PPP, by how much should we expect the nominal U.S dollar/Mexican peso exchange rate to change in the course of 1 year (up, or down, and by what %)?

c. Starting at the exchange rate you calculated in (a), and assuming the rates of inflation remain the same as in (b), what nominal exchange rate would you expect in 3 years?

12. What is “arbitrage” (in goods)? Why don’t arbitrage opportunities last? 13. Suppose the Federal Reserve increases the U.S. money supply in an effort to prevent the U.S. economy from slipping further into recession. a. According to the Quantity Theory of Money, what will the increased money supply do to the

price of goods in the United States in the long run, all else equal? b. According the theory of PPP, what will happen to the exchange value of the U.S. dollar as a

result, all else equal? In particular, would you expect the dollar to appreciate or depreciate against foreign currencies?

c. According to PPP, what will happen to the real cost paid by foreigners for U.S. products? 14. According to the Keynesian Cross model of income, how would each of the following shocks affect a nation’s real aggregate income (Y) in the short run, all else equal? For each shock, be sure to clearly state a predicted direction of change for income, illustrate your prediction with a Keynesian Cross Diagram, and explain your predictions intuitively in words. a. Government purchases decline b. Congress cuts household income taxes c. Autonomous consumption increases d. Total factor productivity increases 15. According to the Keynesian model of income determination, what determines a nation’s real aggregate income? According to the classical model of income determination, what determines a nation’s real aggregate income? Why do the models give different answers to the question, and can they both be right?

16. Consider a closed economy with demand for goods as follows:

 𝑌𝑑 = 𝐶 + 𝐼 + 𝐺  𝐶 = 200 + 0.80(𝑌 − 𝑇)  𝐼 = 600  𝐺 = 1000  𝑇 = 1000

a. What is “autonomous expenditure” for this economy? b. Graph this economy’s (planned) aggregate expenditure function. Be sure to give the

coordinates of at least 2 distinct points in your graph. c. According to the Keynesian Cross model of income determination, what would be the short

run equilibrium value of real aggregate income (Y) for this economy? d. If government purchases (G) were to increase to 1,200, what would the new short run

equilibrium value of income be? 17. Consider a closed economy with the following expenditure function:

 𝑌𝑑 = 𝐶 + 𝐼 + 𝐺  𝐶 = 400 + 0.75(𝑌 − 𝑇)  𝐼 = 1200  𝐺 = 800  𝑇 = 1000

a. What is autonomous expenditure (E0) for this economy? b. According to the Keynesian Cross model of income determination, what would be the short

run equilibrium value of real aggregate income (Y*) for this economy? c. All else equal, what would be the short run equilibrium value of income if government

purchases (G) increased by 100 (i.e. - from 800 to 900)? d. What is the government purchases multiplier (i.e. ∆𝑌∗ ∆𝐺⁄ ) for this economy? e. All else equal, what would be the short run equilibrium value of income if government

purchases remained at 800, but taxes (T ) are cut by 100 (i.e - from 1000 to 900)? f. What is the tax multiplier (i.e. ∆𝑌∗ ∆𝑇⁄ ) for this economy? g. According to the Keynesian Cross model, which is more effective at raising aggregate

income in the short run, tax cuts or government spending? Why?