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ec3313_aut2010_takehome_with_cover - EC3313 Industrial...

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EC3313: Industrial Economics Maris Goldmanis Autumn Take-Home Test (Non-Assessed) Due: Thursday, January 13, 2011 Instructions to candidates: This is a take-home test. It is due Thursday, January 13, 2011. You may consult class notes, textbooks, the web and other resources; however, you may NOT consult with others , in the class or outside. Should you have any questions about the instructions to this exam, feel free to e-mail the instructor. However, hints to help you answer the questions will not be given. You must attempt to answer all questions. Please write up your detailed derivations neatly. No credit will be given for answers without proper derivations. You may either write your derivations by hand and then scan these pages to a pdf file, or type the derivations up using L A T E X or a word processor (such as MS Word). Attach a cover page that gives short answers (without derivations) to all questions. These answers must be typed (L A T E X or word processor). Submit your complete answers (including both the cover sheet and the derivations) using TURNITIN. The TURNITIN details for this class are as follows: Course: EC3313 Class ID: 222063 Password: EC331310 Fill in the boxes in the Department’s standard non-assessed coursework submission form (last page of this exam) and submit the form to the drop-box in Horton H209. Good Luck and Happy Holidays!
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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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