Question

2. It was late on Saturday afternoon. As Barney's men pulled up the net for the last time that day he couldn't believe his eyes: there were bluefish in the net. He had accidentally stumbled upon an area populated by bluefish. Barney knew that as soon as he started bringing in bluefish, Fred would find out. There being no sense in keeping the word to himself, he told Fred over their traditional drink at Greta's. Fred popped a cheese ball in his mouth and settled back to consider the news. "Bluefish, you say. What if you specialize in hauling in blues and I'll stick to the cod? That should give us a little market power." Barney thought about Fred's suggestion. It seemed fair. But with two types of fish in the market, what would happen to prices? Fred and Barney went over to the Nantucket Bait Shop and Fishing Museum that an old fish auctioneer, Leon Walrus, now ran. Walrus had some old copies of the Nantucket Fisherman's Daily, a local trade paper. The copies were from ten years before, when blues were locally available, before they seemingly disappeared from the area. The newspaper carried a story about a study of the demand for different fish by an economist at the local university. Focusing on cod and blue, the following (inverse) demand functions had been estimated: P = 16 -.019. -.0054, P = 16 -.019. -.0059, where the b subscript refers to bluefish and the c subscript refers to cod. Assume that Fred fishes for cod (so P = P, and q. = 9) and Barney fishes for bluefish (so P = P, and q. = 9), and that they choose their catch sizes simultaneously and non-cooperatively (i.e., they act as Cournot duopolists). Assume there is a constant marginal and average cost per pound of either fish of $4. (a) What is Fred's profit as a function of his output and Barney's output qo? What is Fred's best response function? (b) What is Barney's profit as a function of his output qs and Fred's output x? What is Barney's best response function? (c) What are the Cournot-Nash equilibrium output levels qCN and qCN, (d) What are the equilibrium prices for cod and bluefish P.CN and P, CN (e) What are the equilibrium profits tp and Tg , for Fred and Barney, respectively?

Answer 1

- a) FRED's boft fu (ITA) Te = Pre qf - Megt TE = (16-0.0195 - 0:00593) IF - uq - Tip = 1296 0.19 -0.0059696 OTTA = 12 -0.296 -0.00598 = 0. 21 0.298 2 12-0.00596 12 -0.0059B 0.2 BiR of freed: 1 q- 60=0.02596 ] 896 2212 1999999999999999 (5) BARNEY's profit fh(TB) - TB2 PB² qB - Mega =(16-0.019 -0.0059 E) QB - 49 TIR = 1298 -0.0193 -00059790 = 12 -0.0296-0.0059 = a qoi 12 -0.00594 B. R of Barneys: 23 = 60 -0.025961 (c) Houndt WE : solve the BR fusinaltaneously 95=60 - 0.025/60-0.025967 a = 60 - 1.5 + 0.000625 qe "0.9994 = 58.5 9 ECN=58.535) 2.02

GCN = 60 - 0.025 q. CN = 60 – 0.025 58.35 G N258.547 (d) PCCN a 16- 0.019 GN - 0.0059 N. - 16 -0.01*58.535 - 0.00545854 I PCCN = 15.12 PB C N 2 16-0.01 09 CN - 0.005qca = 16-0.01 58.535 - 0.005 58.54 TPCN= 15:12] ( TE PICNOLCN - Mchq CN = (15012-4) 58.535 TN - 651.02 TEN PBCNqCN - AUCQCN (15.12-4) 58.54 ID 650.98