Firm X produces output $x$ and Firm Y produces output $y$ using capital, K, and labor, L, as inputs. Firm X has marginal rate of technical substitution MRTS^x_K,L = K_x/L_x, while firm Y has marginal rate of technical substitution MRTS^y_K,L = 9K_y/L_y. Which of the following allocations satisfies input efficiency? A) Firm X has 5 units of K and 3 units of L, and Firm Y has 3 units of K and 1 unit of L. B) Firm X has 5 units of K and 5 units of L, and Firm Y has 1 unit of K and 9 units of L. C) Firm X has 9 units of K and 1 units of L, and Firm Y has 5 units of K and 5 units of L. D) Firm X has 5 units of K and 5 units of L, and Firm Y has 1 unit of K and 3 units of L.

Question

Quizplus · Accepted Answer

For input efficiency, MRTS should be equal for both firms. In option B, MRTS^x_K,L = 5/5 = 1 and MRTS^y_K,L = 9/9 = 1, satisfying the condition.

Firm X Produces Output xxx And Firm Y Produces Output yyy Using Capital, K, and Labor, L, as Inputs

Firm X Produces Output $x$ And Firm Y Produces Output $y$ Using Capital, K, and Labor, L, as Inputs