Question

Homework Assignment #1 ECO 3203, Spring 2020

Instructions: Answer each of the following questions. Show your work wherever possible, and justify your responses wherever appropriate.

Due: Friday, January 31st at the beginning of class


1. What is meant by the “marginal product of labor”? What typically happens to a firm’s marginal product of labor as it increases labor employment, all else equal? Why is that? What typically happens to a firm’s marginal product of labor as it increases capital employment, all else equal? Why is that?


2. Consider the following production functions:

 Y = AK1/2L1/2  Y = AK + 3L

a. Fixing total factor productivity (A) at 2 and labor employment (L) at 16 units, what is the marginal product of capital when capital employment (K) is 25, 35, and 45 for each production function? Do these production functions exhibit diminishing returns to capital employment? Explain. b. Are labor and capital complements under these production functions? Explain. c. Is either production function a “Cobb-Douglas” function? Explain.


3. Describe the difference between what the “nominal” wage rate and the “real” wage rate measure. How is a nominal wage rate converted into its real equivalent?


4. Consider a perfectly competitive, profit-maximizing firm facing the following marginal product of labor function and prices:

 MPL = 0.5A(K/L)1/2  W = 40  R = 60  P = 8  K = 4

a. What is the real wage rate paid by this firm?
b. If total factor productivity (A) is 20, how much labor (L) would this firm want to employ? c. If the price of output (P) rises from $8/unit to $10/unit, what will the new real wage rate be? All else equal, how much labor would the firm want to employ at that wage rate? d. Assuming that total factor productivity is 20, graph this firm’s labor demand function (quantity of labor demanded graphed against the real wage paid for labor) for values of the real wage between 4 and 40. Be sure to plot at least 3 distinct points.


5. Describe the difference between the “endogenous” and the “exogenous” variables of an economic model. In the classical model of a closed economy (Mankiw, chapter 3), which variables are endogenous and which are exogenous? List at least 4 variables in each category.


6. Use the classical model of factor markets (Mankiw, chapter 3) to predict how each of the following shocks should affect a nation’s real wages (W/P) and real rental price of capital (R/P). Be sure in each case to clearly state your predicted direction of change (up, down, or no change) for both variables and to depict your predictions with supply/demand diagrams for both the labor and capital markets.

a. The supply of capital (KS) decreases b. Technological innovation increases total factor productivity (A) c. Government purchases (G) are increased


7. How do macroeconomists typically define the difference between the “short run” and the “long run”? Is the classical model of a closed economy (Mankiw, chapter 3) considered a short run model or a long run model? Why?


8. Use the classical model of a closed economy to predict how each of the following shocks should affect a nation’s real aggregate income (Y), national saving (S), investment (I), and interest rate (r). Be sure in each case to clearly state your predicted direction of change (up, down, or no change) for all four variables and illustrate your predictions for S, I and r with a supply/demand diagram for the loanable funds market.

a. The supply of capital (KS) decreases b. Technological innovation increases total factor productivity (A) c. Government purchases (G) are increased d. Autonomous investment (i0) decreases

9. According to the classical model of a closed economy, what determines the size of a nation’s real aggregate income? Based on that theory, what kind of public policies could be used to increase a nation’s income? Give at least two specific examples.


10. Consider the following model of a closed economy:

 YS = AK1/2L1/2  Yd = C + I + G  C = 300 + 0.70(Y – T)  I = 2000 – 10,000r  W/P = MPL  R/P = MPK  KS = 100  LS = 225  A = 30  G = 1,000  T = 1,500

a. What are the market-clearing values of the real wage (W/P) and real rental price of capital (R/P) for this economy? b. Assuming that both factor markets clear, labor market and capital market clear, what will real aggregate income (Y) and national saving (S) be for this economy? c. What must the real interest rate (r) be in order to establish equilibrium in the market for loanable funds? d. What would the new equilibrium values of W/P, R/P, Y, S and r be if the capital supply (KS) increased from 100 to 144, all else equal? e. What would the new equilibrium values of W/P, R/P, Y, S and r be if taxes (T) decreased from 1,500 to 1000, all else equal? Assume that KS = 100.


11. What is “autonomous consumption”? Describe two shocks that would increase a nation’s autonomous consumption. According to the classical model, how would national saving (S) and investment (I) be affected (up, down, or no change) by those shocks? How would the aggregate demand for goods (Yd) be affected (up, down, or no change)? Explain.


12. What is “crowding out,” and why does it happen when government purchases are increased? Would an exogenous increase in autonomous consumption also cause crowding out? Explain.

13. Consider a nation with a marginal propensity to consume of 0.75.

a. What will its marginal propensity to save be? b. What would happen to its consumption (give the direction and size of the effect) if taxes (T) were to increase by 100, assuming that real aggregate income is unaffected? What would happen to private saving? To public saving? To national saving? c. Suppose, instead, that government purchases (G) increase by 100 while taxes remain unchanged. Assuming that aggregate income is unaffected, what would happen to consumption? What would happen to private saving? To public saving? To national saving?


14. Suppose you deposit $200 into a bank for 1 year. At the time of your deposit, goods cost $2.50 apiece. A year later, you withdraw your deposit with interest, which totals $215. At that time, the price of goods has fallen to $2.40 apiece.

a. What was the “real” value of your $200 at the time of your deposit? b. What nominal interest rate did your bank pay you for your deposit? c. What was the rate of inflation over the year that your money was sitting in the bank? d. What real interest rate did you earn on your deposit?

Answer 1

Marginal product of labour refers to the change in total product when an additional unit of labour is employed in the production process.

When we keep on adding more and more units of labour in the production of a commodity, the marginal product labour starts falling after reaching an ideal ratio. MP of labour will rise initially but once the ideal combination of labour with other factors of production is reached, any furthur addition of labour (with other things remaining constant), will lead to fall in marginal product of labour with every additional unit. This is because of the following reasons:

1. Lack of substitutability between the factors of production.

2. Lack of divisibility of factors of production.

3. Existence of ideal ration between the factors of production after which one of the factor will become overworked if we keep on employing more of the other factor on it. This will also cause the wear and tear of the fixed factor of production.

If the firm keeps on adding more capital, then the ideal ratio between labour and capital will keep on changing. Due to this, more and more of labour will lead to increasing marginal product of labour till the ideal ratio is reached. Now if the addition of more capital at this point will improve the ideal ratio furthur, then the diminishing returns to labour will get postponed. However, if the addition of more calital will not improve the ideal ratio, this will set in the diminishing returns to labour.