Consider the production function Q= 20K 1/2 L 1/2 The firm operates in the short

Question

Consider the production function Q= 20K1/2L1/2 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.

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.

Explanation / Answer

Given Q=20k1/2L1/2

THe general cobb Douglas is given by

Q=AL^K^

hence =1/2 and =1/2

MP=TP/L

AP=TP/L

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