Question

Two firms with a constant MC and no fixed cost compete in a Cournot fashion. Firm A's MC=20 and Firm B's MC=40.

Market demand is given by x=180-p. The government imposes a per unit tax of ?=10 which the producer pays. What is market price?

Answer 1

MC = 20 MC₂ = 40 x=180-p = p = 180-X tax ; t = 10 - 160 - x + lo P = 190-X Profit function P= 190 - x, ~ X2 ^, = P,X, - MC, X, t = (190-x, x2) x,- 20x, t = 1908, -X2 - X₂ X, -20x, A = 170 x - x2-x2x, dxi NL d^. 170 - 2x, - X2 3 x 4 x = 10 – 2. Similarly for from 2 , P = 190-X, - X2 Az = (190 - X, -X₂)X₂ - 40X2 A2 = 190x2 - X, ₂-1² -40x2 dzi 150 X - X, X₂ - X ² day = 150-X,- QX2 1 100 = X,+ 2%, L d X2

IX, & X2 = 170 X, + 2x2 = 100 x 2 2x + x2 = 1 to 2x, & 4X₂ i 3n - 3X2 = - 130 X 2 = 130 2x, & 130 - 170 8x = 120 - 130 2x, = 540-130 => 380- 2%, -51X, = 19.00 P = 190-X, - X2 = 190 -190 - 130 = 570 - 190-130 570 - 320 1P2 200 den