Selected Readings

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. 5.5Suppose that a firm’s short-run production function has been estimated as

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. 5.6Lothian Company has estimated the following production function for its product lembas

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? 5.7The average product of labor is given by the equation

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?

Q L L L = + -2 04 00022 3 . .

Q K L = 10 03 07 . .

AP L L L = + 600 200 2

SELECTED READINGS

Brennan,M.J.,and T.M.Carrol. PrefacetoQuantitativeEconomics&Econometrics,4th ed.

Cincinnati,OH:South-Western Publishing,1987. Cobb,C.W.,and P.H.Douglas.“A Theory of Production.” AmericanEconomicReview March (1928),pp.139–165. Douglas,P.H.“Are There Laws of Production?” AmericanEconomicReview,March (1948), pp.1–41. ———.“The Cobb–Douglas Production Function Once Again:Its History,Its Testing,and

Some New Empirical Values.” JournalofPoliticalEconomy,October (1984),pp.903–915.

Glass,J.C. AnIntroductiontoMathematicalMethodsinEconomics. New York:McGraw-Hill, 1980. Henderson,J.M.,and R.E.Quandt. MicroeconomicTheory:AMathematicalApproach,3rd ed.New York:McGraw-Hill,1980. Maxwell,W.D.Production Theory and Cost Curves. AppliedEconomics,1,August (1969),pp. 211–224. Silberberg,E. TheStructureofEconomics:AMathematicalApproach,2nd ed.New York:

McGraw-Hill,1990. Walters,A.A.Production and Cost Functions:An Econometric Survey. Econometrica,January (1963),pp.1–66.

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