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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:  http://bit.ly/PBIdx5  Read this article. Writedown the 3 most interesting things you picked up from here (from an eco-nomics perspective).2

Jul 23, 2017

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