Consider the production function Q = 20K1/2L1/2. The firm operates in the short run with 16 units of capital.
a. Derive the firm's short run production function, Q(L).
b. Derive the frirm's average product of labor, AP(L).
c. Derive the firm's marginal product of labor, MP(L).
d. Let the wage rate be $20. Derive the AVC(Q).
e. Let the wage rate be $20. Derive the SMC(Q).
f. If the firm produces 160 units, determine the units of labor that are employed, the average product of labor, the marginal product of labor, the average varibale cost, and the marginal cost of producing 160 units of output.
g. If fixed cost is equal to $400, derive the TC(Q)