### Assignment #2

Assignment #2

CHAPTER 4 & 5: THE MONETARY SYSTEM & INFLATION 1.

Suppose a country has a money demand function ( M / P )d ? kY , where k > 0 is a constant parameter. The money supply (M) grows by 12% per year, and real

income (Y) grows by 4% per year. a. What is the average inflation rate? (Hint: express the quantity equation in percentagechange form) b. How would inflation be

different if real income growth were higher? Explain. c. How do you interpret the parameter k? What is its relationship to the velocity of money? d. Suppose instead

of a constant money demand function, the velocity of money in this economy was growing steadily due to a financial innovation. How would that affect the

inflation rate? Explain. 2. Suppose that the money demand function takes the form ( M / P) d ? Y / (5i ) . a. If output grows at rate g, at what rate will the demand for

real balances grow (assuming constant nominal interest rate)? b. Use the quantity equation and the money demand function to derive an expression of the velocity

of money in terms of the nominal interest rate, i. c. If inflation and nominal interest rates are constant, at what rate, if any, will velocity grow? 3. In each of the

following scenarios, explain and categorize the cost of inflation. a. Because inflation has risen, the L.L. Bean Company decides to issue a new catalog quarterly

rather than annually. b. Grandma buys an annuity for $100,000 from an insurance company, which promises to pay her $10,000 a year for the rest of her life. After

buying it, she was surprised that high inflation triples the price level over the next few years. c. Maria lives in an economy with hyperinflation. Each day after being

paid, she runs to the store as quickly as possible so she can spend her money before it loses value. d. Warren lives in an economy with an inflation rate of 10% per

year. Over the past year, he earned a return of $50,000 on his million dollar portfolio of stocks and bonds. Because his tax rate is 20%, he paid $10,000 to the

government.

4. Define the terms “real variable” and “nominal variable.” Give examples of each. What does monetary neutrality mean? What is the classical dichotomy?

CHAPTER 7: UNEMPLOYMENT 1. Describe the difference between frictional and structural unemployment. What causes each type of unemployment? 2. Consider an

economy with the following Cobb-Douglas production function: Y ? K 1/3 L2/3 . The economy has 12,000 units of capital and a labor force of 12,000 workers.

a. Derive the equation describing labor demand in this economy as a function of the real wage and the capital stock. (hint: use the equilibrium condition W/P=MPL

and solve for labor demand, L, after obtaining an expression for the marginal product of labor b. If the real wage can adjust to equilibrate labor supply and labor

demand, what is the equilibrium real wage? In this equilibrium, what are employment, output, and the total amount earned by workers? c. Now suppose that

Congress, concerned about the welfare of the working class, passes a law requiring firms to pay workers a real wage of one unit of output. How does this wage

compare to the equilibrium wage? d. Congress cannot dictate how many workers firms hire at the mandated wage. Given this fact, what are the effects of this law?

Specifically, what happens to total employment, output, and the total amount earned by workers? e. Will Congress succeed in its goal of helping the working class?

Explain.

3. Researchers at Purdue have collected data on the number of undergraduate Purdue students either involved in a relationship or uninvolved. Among involved

students, 10% experience a breakup of their relationship each month. Among uninvolved students, 5% enter into a relationship every month. Illustrate the flow of

students between the two states (involved and uninvolved) using a diagram. What is the steady-state fraction of residents who are uninvolved?

CHAPTER 8: ECONOMIC GROWTH 1. Country A and country B both have the production function Y ? F ( K , L) ? K 1/2 L1/2 . a. Does this production function have

constant returns to scale? Explain. b. What is the per-worker production function y ? f ( k ) ? c. Assume that neither country experiences population growth nor

technological progress and that 5% of capital depreciates each year. Assume further that country A saves 10% of output each year and country B saves 20% of

output each year. Using your answer from part (b) and the steady-state condition that investment equals depreciation, find the

steady-state level of capital per worker for each country. Then find the steady-state levels of income per worker and consumption per worker. d. Suppose that both

countries start off with a capital stock per worker of 2. What are the levels of income per worker and consumption per worker? Remembering that the change in the

capital stock is investment minus depreciation, use a calculator or spreadsheet to show how the capital stock per worker will evolve over time in both countries.

For each year 1 to 3, calculate income per worker and consumption per worker. How many years will it be before the consumption in country B is higher than the

consumption in country A? Country A Year k 1 2 2 3

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