# Answer to Question #49858 in Microeconomics for Alexandria

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

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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