Question

Firm A and Firm B compete in the sale of a product with market inverse demand given by P(0) = 160-Q, where Q is market output, and Q = qA + qB (8a-Firm A's output, qB-Firm B's output). Firm A's Total Cost function is given by TCA(qA) 10qA and Firm B's is given by Find the value of Q when Firms A and B Cournot compete to maximize profits (i.e when they simultaneously determine profit maximizing output). At what price will Firms A and B sell their output? Suppose that Firm A's total cost function were to change to TG4(qa) 109a + 50. (so, a fixed cost of 50 has been added). Which of the following statements would then be TRUE? This will decrease Firm A's equilibrium level of output. b. a. This will increase Firm B's equilibrium level of output. This will not affect either firm's equilibrium level of output d. c. This will increase the price at which output is sold in this market. Suppose that Firm A's total cost function were to change to TCA(qA) 20qA. (so, Firm A's marginal cost has increased from 10/unit to 20un. Which of the following statements would then be TRUE? a. b. c. d. This will decrease both Firm A's and Firm B's equilibrium levels of output. This will decrease Firm A's equilibrium level of output, but increase Firm B's. This will increase Firm A's equilibrium level of output, but decrease Firm B's. This will increase both Firm A's and Firm B's equilibrium levels of output.

Answer 1

Demand: P(Q) = 160 - Q Q = q_A + q_B cost TC_A (q_A) = 10 q_A TC_B (q_B) = 10 q_B For cannot we will maximize the profit of each firm and obtain the best response function Profit Firm A pi_A = [160 - q_A - q_B] q_A -10 q_A partial differential pi_A/partial differential q_A = 160 - 2q_A - q_B - 10 = 0 150 - q_B = 2q_A [75 - 1/2 q_B = q_A] Firm B pi_B = [160 - q_A - q_B] - 10 q_B FOC: partial differential pi_B/partial differential q_B = 160 - q_A - 2q_B - 10 = 0 150 - q_A = 2 q_B 75 - 1/2 q_A = q_B put eq (2) in (1) 75 - 1/2 [75 - 1/2 q_A] = q_A 75/2 = 3/4 q_A = > q_A = 50 q_B = 50 so frim A and B will produce 50 units each. \r\n Price = 160 - 100 = $ 60 Firm A and B will sell at $ 60 The correct option is (c) because each firm choose output where MR_i