Consider the following short-run production function (where L = variable input, Q = output):
Suppose that output can be sold for $10 per unit. Also assume that the firm can obtain as much of the variable input (L) as it needs at $20 per unit.
a. Determine the marginal revenue product function.
b. Determine the marginal factor cost function.
c. Determine the optimal value of L, given that the objective is to maximize profits.