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  ECO303: Economics of Market Structure andCompetition (ECO & IT) Assignment 3 Due: Tuesday, October 29, 2012 1. Consider a market with inverse demand curve given by  P   = 100 − Q , where Q  is the aggregate output. There are 4 firms in this market. The first 3have constant an identical production cost of 20 per unit. The 4th firm hasconstant cost of (20 +  γ  ) per unit. a)  Find the Cournot equilibrium. Be sure to identify the values for  γ   forwhich all firms cover their production cost. b)  Assume that firm 1 and firm 4 merge. Can this merger be profitable if  γ >  0 (firm 4 is a high-cost firm)? What happens to the profits of thenon-merged firms? c)  Now suppose that in addition to the variable costs, the firms also haveto incur a fixed cost  F  . When 2 firms merge together, the fixed costfor the merged firm is  bF   where 1 ≤ b ≤ 2. Derive a condition on  b,F  and  γ   such that a merger between firm 1 and 4 would be profitable.2. D1 and D2 are two firms engaged in price competition in the cola marketwith differentiated products. The inverse demand curves are given by  p 1  = 25 − q  1 − q  2  p 2  = 25 − q  2 − q  1 Both companies need sugar syrup as an ingredient. The syrup market isserved by two firms U1 and U2 both with identical unit cost of 5. The syrupmade by either firm is identical. a)  Confirm that competition between U1 and U2 leads to syrup priced at5. b)  What is the resulting equilibrium for D1 and D2 (prices, quantities,profits). c)  Now suppose U1 and D1 merge together. Find the profit for the threepost-merger companies. d)  Do U2 and D2 have any incentive to merge together?3. Consider an entry game with capacity choice. There are two firms, anincumbent, and a potential entrant. The inverse demand curve is given by P  ( Q ) = 56 − 2 Q , where  Q  is aggregate output. The incumbent first choosescapacity  k  which is observed by the potential entrant. If the entrant decides1  to enter, then the firms engage in quantity competition. Costs for the firmsare 18 per unit of capacity, 2 per unit of production, and  F   in fixed costs.Find the equilibrium.4.  Learning by doing:  A monopolist produces in two time periods. Inversedemand in each time period is given by  P   = 40 − 2 q  . The monopolist’s perunit production cost is 6 in period 1 and 6 − θq  1  in period 2. a)  Find the monopolist’s optimal choice of output in time period. b)  Redo the above when the monopolist knows that a rival firm will enterthe market in the second period with production cost 6 per unit.5.  Reading assignment:  Read this article. Writedown the 3 most interesting things you picked up from here (from an eco-nomics perspective).2
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