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Suppose the airline industry consists of only two firms: Firm1=American and Firm2 =Texas Air Corp. Let the two firms have identical cost functions: tci(xi) = 40xi. Assume the demand curve for the industry is given by P = 100 – X where X = x1+x2, and that each firm expects the other to behave as a Cournot competitor.

a. American: (A = (100 – xA – xT)xA – 40xA ( FOC: 100 – 2xA – xT – 40 = 0.

So American’s reaction function is xA = 30 – (1/2)xT.

Texas Air: (T = (100 – xA – xT)xT – 40xT ( FOC: 100 – 2xT – xA – 40 = 0.

So Texas Air’s reaction function is xT = 30 – (1/2)xA.

Solving simultaneously yields: xACN = 20 = xTCN; pCN = 60; (ACN = 400 = (TCN.

b. American’s reaction function is still xA = 30 – (1/2)xT.

Texas Air: (T = (100 – xA – xT)xT – 25xT ( FOC: 100 – 2xT – xA – 25 = 0.

So Texas Air’s reaction function is xT = 37.5 – (1/2)xA.

Solving simultaneously yields: xTCN = 30; xACN = 15; pCN = 55.

Texas Air’s profits with the lower costs are (TCN = (55)30 – (25)30 = 900.

With the higher costs, Texas Air’s profits are 400 [see (a)]. So the most Texas Air would be willing to invest to lower its marginal cost would be $500.

c. See answers to b – basically the same question.

1. Suppose Tops and Wegmans are the only two big grocery stores in a small town. They open their grocery store from 8 a.m. to midnight and have revenues of $4 million/year and costs of $2.5 million/year each. Now Tops and Wegmans are individually considering extending their operating hours to 24 hours/day. If one store extends its hours and its rival store doesn't, the store extending its hours will increase its revenues by 40% and its costs by 50%, while its rival store will lose 20% of its revenues and 20% of its costs. If they both extend their hours, both will see revenues increase by 10% and costs increase by 20%.

a. The payoff matrix is illustrated in Table (a). The first entry in each cell denotes Tops' payoff and the second entry denotes Wegmans' payoff. The Nash noncooperative equilibrium is illustrated in the table. Tops and Wegmans will both open 24 hours a day and each will receive $1.4 million in profit. The light green entries (light gray) are Tops' best responses against each of Wegmans' decisions. The purple entries (dark gray) are Wegmans' best responses against each of Tops' decisions. Notice that opening 24 hours a day is a best response for Tops to either of Wegmans' decisions. The same is true for Wegmans: staying open all day is a best response for Wegmans to either of Tops' decisions. Therefore, staying open all day is a dominant strategy for both firms.

b. The joint profit is maximized when one of the store opens 24 hours a day and the other store opens 16 hours a day. They will earn 3.05 million per year in total.

c. The payoff matrix incorporating Wegmans's proposed payments to Tops is illustrated in Table (c). In this situation, there is no dominant strategy for Tops. However, the Nash equilibrium is that Wegmans opens 24 hours a day and Tops does not. In the new Nash equilibrium, Tops will get $1.52 million each year. Since Tops earns more profit if it accepts the offer (as compared to its equilibrium profits in the previous part), Tops will accept Wegmans's offer.

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2. Suppose that Nick and Bill are the only two farmers supplying eggs to Ithaca. The market demand for eggs is Q = 50 - 2P, where Q is dozens/week and P is $/dozen. Consumers will buy eggs from the producer who offers a lower price for eggs. The cost of producing 1 dozen of eggs is $5 for both Nick and Bill.

a. The demand function can be rewritten as P = 25 - Q/2, ( MR = 25 - Q. Since Nick and Bill each have the same constant marginal cost, we simply have MC = $5. Setting MR = MC we have 25 - Q = 5, giving Q = 20 dozen. So the price is set at P = 25 - 20/2 = $15/dozen. Also, each farmer supplies Q/2 = 20/2 = 10 dozen. Bill's profits are ($15 - $5)*10 = $100. Nick's profits are ($15 - $5)*10 = $100.

b. Bill now charges ($15 - $1) = $14/dozen while Nick still charges $15/dozen. Since Bill's price is lower, he will get all the customers. So at P = 14, Q = 50 - 2(14) = 22 dozen. Bill's profit is therefore ($14 - $5)*22 = $198.

c. Nick will undercut Bill and offer lower prices. If no further agreement is made the two of them may undercut each other's prices until the price of eggs go down to $5 (which is their marginal cost). At that point both of them will make zero economic profit.

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Econ 313 - Wissink – Spring 2006

PS#7 – XtraQ

ANSWERS

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