Question #49858

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

Expert's answer

Q=10L-0.5L^2. P = $10 per unit, Pl = $20 per unit.

A. Marginal revenue product function is:

MRP = MR*MP = 10*Q' = 100 - 10L

B. Marginal factor cost function MC = Q' = 10 - L

C. The optimal value of L, given the objective is to maximize profits, is when MRP = 0, so 100 - 10L = 0, L = 10, so 10 workers should be hired to maximize profits.

A. Marginal revenue product function is:

MRP = MR*MP = 10*Q' = 100 - 10L

B. Marginal factor cost function MC = Q' = 10 - L

C. The optimal value of L, given the objective is to maximize profits, is when MRP = 0, so 100 - 10L = 0, L = 10, so 10 workers should be hired to maximize profits.

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