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Unformatted text preview: Problem Set 4: Cournot Model, Product Differentiation, Vertical Integration Question 1 : Consider a Cournot duopoly that sells a homogeneous product. Market demand given by: P ( Q ) = 100 Q , where Q denotes aggregate output. There are two firms, each with cost functions: c ( q ) = 10 q . (i) Define the game being played. (ii) Determine the best response functions. (iii) Determine firm outputs, aggregate output, and market price under the CournotNash equilibrium. (iv) Calculate the deadweight loss. How does it compare to the deadweight loss of a monopolized market? (v) Who is better off with Cournot competition? Consumers? Producers? Society? (vi) Suppose the Cournot competitors could sit down at a table and discuss a pricesetting agreement. What is the best price they should agree on? Where is the difficulty in maintaining this agreement? (vii) Suppose there is a credit crisis that locks up firm 2’s capital flows. His cost function becomes c 2 = 40 q . Firm 1 keeps costs down because it is family owned and operated. His cost function remains the same. Calculate the new CournotNash equilibrium. What is the effect on social welfare? How is the effect borne by the different sectors of the economy (consumers, firm 1 and firm 2). Question 2 : Consider an Nfirm Cournot oligopoly that sells pencils. Let demand be given by: P ( Q ) = A Q , marginal cost given by c . For this question follow the lecture notes. (i) Determine the function that gives consumer surplus as a function of N , the number of firms. (Assume the firms are in Cournot equilibrium.) (ii) Do consumers prefer fewer or more Cournot competitors? (iii) If there was no fixed cost to production, how many firms would enter? (iv) With parameters A = 10, b = 1, c = 2, f = 1, fill in Church Table 8.3 for N = 6 and N = 7 firms....
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 Spring '11
 Galunic
 Economics, Deadweight Loss, Supply And Demand, Cabral, socially optimal locations

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