Question

Name: Consider the market for a good where the demand curve facing a firm who has considerable market power is given by P = 80 -0.05Q, the marginal revenue curve is given by MR = 80 -0.1Q, and the firm's marginal cost curve is given by MC = 17 + 0.020. a. If the firm behaves like a competitive firm, find equilibrium price and quantity. Graphically identify and calculate consumer and producer surplus. b. If the firm behaves like a monopolist, find equilibrium price and quantity. Graphically identify and calculate consumer and producer surplus, and deadweight loss.

Answer 1

(a) p= 80 -0.050 Mc = 17+0.020 P = MC 80 -0.050 = 17 + 0.020 80-17 = 0.02Q +0.050 63 = 0.070 Q: goo P = 80 -0.05x qoo P = 80- 45 p=35 Thus equilibrium price 35 and quantity goo P мс 35 P=ARED 900 5600 ps = 135 - 13) (900) = { x 18X900 = 8100 cs = ļ (80 - 35)(900) = x 45 x 900 = 20250

(6) monopoly MR = mc 80 - 0.10 = 17 +0.028 80-17 = 0.020+ 0.10 63 = 0.120 Az 525 P= 800.05x525. = 80 - 26.25 = 53.75 Thus, mono po ust equilibrium price and quantity are Pm = 53.75 8 - Om = 525 respectively. -

-MC Pm 53.75 € Pc 35 27.5 MR 525 800 900 1600 am ac es= 180-53.757 (525) = ** 26.25% 595 = 6890.625 PS = (53.75 - 27.5) (525) + 1 (27.5-172 (525) | = 13781.25 + 2756-25 16537.5 DWL = {( 53. 75 – 27.5) ( 900-525) = I x 26.25 X 375 = 4921.875