# Assignment

Instructions: Answer each of the following questions. Show your work whereverpossible, and justify your responses wherever appropriate.Due: Friday, February 3rd at the beginning of class 1. What is meant by the “marginal product of labor”? What typically happens to a firm’smarginal 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 capitalemployment, all else equal? Why is that? 2. Consider the following production functions: = ( 0.5 )(0.5 ) = + a. Fixing total factor productivity (A) at 10 and capital employment (K) at 4 units, whatis the marginal product of labor associated with labor employment of 25, 35, and 45for each production function? Do these production functions exhibit diminishingreturns to labor employment? Explain.b. Are labor and capital complements under these production functions? Explain.c. Is either production function a “Cobb-Douglas” function? Explain. 3. Consider a perfectly competitive, profit-maximizing firm facing the following marginalproduct of labor function and prices: = 0.5(/)1/2 = 40 = 60 = 10 a. What is the real wage rate paid by this firm?b. If total factor productivity (A) is 50 and the firm is employing 16 units of capital (K =16), how much labor (L) would the firm demand?c. If the nominal wage (W) rises from $40 to $200, what will the new real wage ratebe? All else equal, how much labor would the firm want to employ at the new realwage rate? d. Assuming that A = 50 and K = 16, graph this firm’s labor demand function (quantityof labor demanded graphed against the real wage paid for labor) for values of thereal wage between 4 and 20. Be sure to plot at least 3 distinct points. 4. Describe the difference between a nation’s “real” wage rate and its “nominal” wagerate. According to the model presented in chapter 3 of the text, what variablesdetermine a nation’s real wage rate? Describe two distinct shocks which, according tothat model, would raise real wage rates. 5. Use the classical model of factor markets to predict how each of the following shocksshould affect real wages (W/P) and the real rental price of capital (R/P). Be sure in eachcase to clearly state your predicted direction of change (up, down, or no change) forboth variables and depict your predictions with supply/demand diagrams for both thelabor and capital markets.a. The size of the capital stock shrinks (KS decreases)b. Technological innovation increases total factor productivity (A increases)c. Inflation causes all prices (R, W, and P) to double. 6. Describe the difference between the “endogenous” and the “exogenous” variables ofan economic model. In the version of the classical model presented in class, whichvariables are endogenous and which are exogenous? List at least 5 variables in eachcategory. 7. How do macroeconomists typically define the “long run”? Why are the predictions ofthe classical model normally thought to be only valid in the long run? 8. Use the classical model to predict how each of the following shocks should affect realaggregate income (Y), national saving (S), investment (I), and the interest rate (r). Besure in each case to clearly state your predicted direction of change (up, down, or nochange) for all four variables and illustrate your predictions for S, I and r with asupply/demand diagram for the loanable funds market.a.b.c.d. The size of the labor force shrinks (LS decreases)The economy’s supply of capital expands (K increases)Congress passes a budget that restricts government purchases (G decreases)Forecasts of a recession cause an exogenous decrease in autonomous investment (i0decreases)