In: Economics
Two profit maximizing oligopolists produce electricity. They set their productions levels,y1 and y2, simultaneously.p(y) = 10−y, where y=y1+y2. Assume the cost curve for firm 1 and firm 2 are C(y1) = 2y1 and C(y2) = 2y2 respectively. Marginal cost for each firm is constant at 2.
Suppose firm 1 and firm 2 decide their output simultaneously.
1. Write down each firm’s profit maximization problem.
2. Determine each firm’s best response function (i.e BR1(y2) and BR2(y1)) and plot it on a graph.
3. Determine the optimal (equilibrium ) levels of production y^Co_1 and y^Co_2.
4. Determine the Consumer Surplus, Producer Surplus and Dead weight loss.
Answer summary:
(1) π1 = 8y1 - y12 - y1y2 and
π2 = 8y2 - y22 - y1y2
(2) BR1(y2) : y1 = 4 - (y2/2) and
BR2(y1) : y2 = 4 - (y1/2)
(3) y^Co_1 = 2.67 and y^Co_2 = 2.67
(4) C.S. = 14.2578
P.S. = 24.8844
D.W.L. = 10.8578
Please refer to following two images for full answer: