Managerial Economics 12th Edition by Christopher Thomas,Charles Maurice

Exercise 3

For the short-run production function in exercise 1, let the wage be $20.
a. Derive AVC ( Q ).
b. When 160 units are produced, _________ units of labor are employed, and the average product is _________. Average variable cost is $_________.
c. Derive SMC ( Q ).
d. Using the marginal product ( MP ) function derived in part c , the marginal product is _________ when 160 units are produced. SMC is $ _________. Verify that SMC (Q) evaluated at Q = 4 is identical to calculating SMC by using the ratio w/MP.
Exercise 1 for Reference:
Consider the production function Q = 20 K 1/2 L 1/2. The firm operates in the short run with 16 units of capital.
a. The firm's short-run production function is Q = _______.
b. The average product of labor function is AP = _______.
c. The marginal product of labor function is MP = _______.
d. Show that marginal product diminishes for all levels of labor usage.