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Production
where Q is units of output, K is machine hours, and L is labor hours. Suppose that the amount of K available to the firm is fixed at 100 machine hours. a. What is the firm’s total product of labor equation? Graph the total product of labor equation for values L = 0 to L = 200. b. What is the firm’s marginal product of labor equation? Graph the marginal product of labor equation for values L = 0 to L = 200. c. What is the firm’s average product of labor equation? Graph the average product of labor equation for values L = 0 to L = 200. 5.5 Suppose that a firm’s short-run production function has been estimated as Q = 2L + 0.4L2 - 0.002L3 where Q is units of output and L is labor hours. a. Graph the production function for values L = 0 to L = 200. b. What is the firm’s marginal product of labor equation? Graph the marginal product of labor equation for values L = 0 to L = 200. c. What is the firm’s average product of labor equation? Graph the average product of labor equation for values L = 0 to L = 200. 5.6 Lothian Company has estimated the following production function for its product lembas Q = 10 K 0.3 L0.7 where Q represents units of output, K units of capital, and L units of labor. What is the coefficient of output elasticity? What are the returns to scale? 5.7 The average product of labor is given by the equation APL = 600 + 200L - L2 a. What is the equation for the total product of labor (TPL)? b. What is the equation for the marginal product of labor (MPL)? c. At what level of labor usage is APL = MPL?
SELECTED READINGS Brennan, M. J., and T. M. Carrol. Preface to Quantitative Economics & Econometrics, 4th ed. Cincinnati, OH: South-Western Publishing, 1987. Cobb, C. W., and P. H. Douglas. “A Theory of Production.” American Economic Review March (1928), pp. 139–165. Douglas, P. H. “Are There Laws of Production?” American Economic Review, March (1948), pp. 1–41. ———. “The Cobb–Douglas Production Function Once Again: Its History, Its Testing, and Some New Empirical Values.” Journal of Political Economy, October (1984), pp. 903–915.
