Answer each of the following questions. Show your work wherever possible, and justify your responses wherever appropriate.
1. Consider the following production functions:
- Y = 10K1/2L1/2
- Y = 2K + 3L
a. Fixing labor employment (L) at 16 units, what is the marginal product of capital when capital employment 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” functions? Explain.
2. Describe the difference between a “real” wage rate and a “nominal” wage rate. How is a nominal wage rate converted into its real equivalent?
3. Consider a perfectly competitive, profit-maximizing firm facing the following marginal product of labor function and prices:
- MPL = 0.5A(K/L)1/2
- MPK = 0.5A(L/K)1/2
- W = 40
- R = 60
- P = 8
- K = 4
a. Does this firm’s production function exhibit diminishing returns to labor employment? Are labor and capital complements for this firm? Explain.
b. What is the real wage rate paid by this firm?
c. If total factor productivity (A) is 20, how much labor (L) would this firm want to employ?
d. 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?
e. 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.
f. Now suppose that total factor productivity rises to 30. Re-graph the firm’s labor demand function for values of the real wage between 4 and 40. Again, be sure to plot at least 3 distinct points.
4. Describe the difference between the “endogenous” and the “exogenous” variables of an economic model. In the version of the classical model presented in class, which variables are endogenous and which are exogenous?
5. Consider the following model of a closed economy:
- Y S = AK1/2L 1/2
- C = 200 + 0.75(Y – T
- I = 1200 - 10,000r
- K S = 100
- L S = 225
- A = 24
- G = 1000
- T = 800
a. What must the real wage (W/P) and real rental price of capital (R/P) be to establish equilibrium in the labor and capital markets?
b. What values of aggregate income (Y) and national saving (S) result from full employment of labor and capital?
c. What must the interest rate (r) be in order to establish long run equilibrium in the market for loanable funds?
d. What are the long run equilibrium values of W/P, R/P, Y, S and r if the labor supply (LS) increases from 225 to 625, all else equal?
e. What are the long run equilibrium values of W/P, R/P, Y, S and r if government purchases
(G) Decrease from 1000 to 200, all else equal? Assume that L = 225.
6. 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? Explain. What typically happens to a firm’s marginal product of labor as it increases capital employment, all else equal? Explain.
7. Use the classical model of a closed economy to predict the impact of each of the following shocks on the real wage rate (W/P), the real rental price of capital (R/P), real aggregate income (Y), and the real interest rate (r), all else equal. In each case, be sure to (1) clearly state the predicted direction of change for all four variables, (2) depict the impact of the shock with the relevant diagrams, and (3) explain your predictions intuitively in words.
a. A natural disaster reduces the economy’s stock of capital (K decreases).
b. Immigration reform increases the size of the labor force (L increases).
c. Autonomous consumption increases (c0 increases).
d. Congress reduces government purchases (G decreases).
8. According to classical macroeconomic theory, what determines the size of a nation’s aggregate income? Based on that theory, what sorts of public policies could be used to expand aggregate income? Give at least two specific examples.
9. Consider an economy with the following consumption function:
a. What is the marginal propensity to consume for this economy? What is the marginal propensity to save for this economy?
b. What would happen to consumption (magnitude and direction of change) if income taxes (T) were to increase by 100, assuming that aggregate income is unaffected? What would happen to private saving? To public saving? To national saving?
c. What would happen to consumption if autonomous consumption (c0) were to increase by 100, assuming that aggregate income is unaffected? What would happen to private saving? To public saving? To national saving?
d. What would happen to consumption if income government purchases (G) were to increase by 100, assuming that aggregate income is unaffected? What would happen to private saving? To public saving? To national saving?
10. How do macroeconomists typically define the “long run”? Why are the predictions of the classical model normally thought to be only valid in the long run?