Consider the following short-run production function (where L=variable input, Q=output):
Q= 10L - 0.5L^2
Suppose the output can be sold for $10 per unit. Also, assume the firm can obtain as much of the variable input (L) as it needs at $20 per unit. Determine the following:
a. the marginal revenue product function.
b. the marginal factor cost function.
c. the optimal value of L, given that the objective is to maximize profits.