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ec3313_aut2010_takehome_with_cover

# ec3313_aut2010_takehome_with_cover - EC3313 Industrial...

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EC3313: Autumn 2010 Maris Goldmanis Take-Home Test 1. Homogeneous Cournot with Multiple Firms This problem consists of multiple parts, which vary considerably in difficulty. Do not get dis- couraged if you get stuck at some point. Intermediate answers to several parts are given in the text; you can use these in the latter parts even if you could not derive the previous answers yourself. Suppose that in a market there are N firms, all of which have the same constant-returns- to-scale technology with marginal cost c 0, so that C i ( q i ) = cq i for all i. The market demand is given by P ( Q ) = A - BQ, where Q = N i q i is the aggregate market output. Assume that A > c and B > 0. The firms compete in a Cournot game. (a) Warm-up exercise: three firms First, consider the case when there are three firms, N = 3. In addition, assume that the marginal cost is c = 0 and that A = 1 and B = 2. i. Find the Cournot equilibrium. What are the quantities, prices, and profits in this equilibrium? ii. Suppose that two of the three firms merge. Solve for the new Cournot equilib- rium. Show that the joint profit of the two merging firms actually decreases as a result of the merger. iii. What if all three firms merge? Does the joint profit of the merging firms increase or decrease as a result of this merger? (b) The general case: N 2 firms Now, let us solve for the Cournot equilibrium when there is an arbitrary number of firms ( N 2). We will also let A , B , and c take arbitrary values (with A > c 0 and B > 0). This is slightly harder, so let us work it out step-by-step.
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ec3313_aut2010_takehome_with_cover - EC3313 Industrial...

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