An industry consists of two firms producing identical goods. The market demand for the combined output of both firms is (Q_A + Q_B) = 500 !0.5P. The total cost function of each firm is TC_i = 250 + 50Q_i, where i = A,B. Firm A's best-response function is: A) Q_A = 250 !0.5Q_B. B) Q_A = 250 !0.25Q_B. C) Q_A = 50 !0.5Q_B. D) Q_A = 100 !0.5Q_B. E) Q_A = 100 !0.25Q_B."

Question

Quizplus · Accepted Answer

The correct answer is A because the best-response function for Firm A is Q_A = 250 - 0.5Q_B. This can be derived by maximizing Firm A's profit function, which is given by:π_A = P(Q_A + Q_B) - TC_A= (500 - 0.5Q_A - 0.5Q_B)(Q_A) - (250 + 50Q_A)= 500Q_A - 0.5Q_A^2 - 0.5Q_AQ_B - 250 - 50Q_A= 250Q_A - 0.5Q_A^2 - 0.5Q_AQ_BTaking the derivative of this profit function with respect to Q_A and setting it equal to zero, we get:dπ_A/dQ_A = 250 - Q_A - 0.5Q_B = 0Q_A = 250 - 0.5Q_B

An Industry Consists of Two Firms Producing Identical Goods