Oligopoly Strategy

MGEC612 Week3: Strategy II, Strategies in Oligopolies II, Bidding and Selling in Auctions

< Strategies in Oligopolies II> Question 1 Consider the market for flights between Philadelphia and Chicago. Assume there are two airlines that fly this route: Southwest (S) and U.S. Airways (U). For various reasons, flights on these two airlines are close, but not perfect substitutes, so each airline faces a demand curve that depends on its ticket price and that of its competitor, as follows: qS = 24 – 2pS + 2pU and qU = 24 – 2pU +2pS. These firms compete by setting prices simultaneously. Both firms have marginal costs equal to $4/passenger. Compute the equilibrium prices, profits, and quantities. ∏S=(24 – 2pS + 2pU)(pS-4) ∂∏S/∂pS=24-4pS+2pU+8=0 4pS=32+2pU pS=8+pU/2 Because firms are symmetric, U.S. Airways’ best response function will be pU=8+pS/2. ∏U=(24 – 2pU + 2pS)(pU-4) ∂∏U/∂pU=24-4pU+2pS+8=0 4pU=32+2pS pU=8+pS/2. Now solve the system of equations: pS=8+ (8+ps/2)/2 pS=8+4+pS/4 3pS/4=12 pS=pU=16 qS=qU=24. Their profits are identical: each is ∏=(24)(16-4)=$288.

Question 2 For decades, Gat’s Steaks and Peno’s Steaks have been selling cheesesteaks at a certain intersection in South Philly. Both firms are famous and, hence, have market power. Every day early in the morning

each firm places an order for bread rolls which determines the quantity of cheesesteaks each firm can supply to the market that day. (You cannot have cheesesteaks without fresh bread rolls!) The total cost functions for each firm are given by: TCG = 1QG + 0.25QG2 TCp= 6Qp

The firms are across the road from each other so they face the same market demand curve: QM = 40 – 4P ; QM = QG + QP. Quantities can be non-integers. The scale of each unit Q is 1000 cheesesteaks (don’t convert your answers for scale). Peno decides to get up extra early in the morning to make his order for bread rolls. Peno is going to have the delivery truck unload all his bread rolls out in the open so Gat is able to count...