Question

6. There is a market characterized by a linear demand function given by Q = 18 - 2P. In this market there are two identical firms each with a linear cost function C(q) = 49 (a) Assume the equilibrium in this market is determined by a leader-follower dynamic where firms one enters first i.e. sets its quantify first), and firm two enters second. Find the quantities produced by each firm, and the market price. (b) Find the profits for each firm in (a) and the consumer surplus (c) Now assume that instead of following a leader-follower game, both firms make their production decisions simultaneously (they both chose quantities to be produced at the same time). Find the quantities produced by each firm and the market price. (d) Find the profits for each firm in (c) and the consumer surplus (e) What would consumers prefer (a) or (c)? And what would each firm prefer?

Answer 1

Leader output ( = (2-2) 8 = 18-2P ap = 18-ą P = 18 - 28 = gta = (9-4) 2x0.5 MC = 4 = 5 = 5 Follower = output (a-c) 4b p= g-0-5 (7:5) =g- 3.75 = 5.29 = (5) = 12: 5 1 Leader = 5.25X 5 - 4X5 = $16.25 t Follower = 2.5X 5:25 - 4x2.5 = $3.12 525 C8 = GABXH - 0.569-5.25) (7:5) - [14006 75 c) Рамс p= - 9-0.5X10 9-5 9-12 B = 4 0.58=5 140 Cournot output = ( 2 ) Competitive output -10 - 3x10 = 20 = [666] P = 9-v. 5 (666) 3 - E 9 3.33 = 5.67

r = 5.67X 6.66 - 4x567 = 15.08 Each from s = 17.54] cs = 65x (9-6-66) (5.67). = 0.58 2 3 4 x 5.67 = 16.63] c) Consumer surplus is larger in case of (a). Thus, Consumer would go with a