Week #4-5

Principles of Macroeconomics (with Xtra!)

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1 TEXTBOOK PROBLEMS 3 rd Edition Chapter 6 1, 3, 5, 6, 9-11 2 nd Edition Chapter 7 Extra Oligopoly Study Notes/Questions Q1. Suppose we have two firms (N=2) with identical costs (technologies) and who produce the same (homogeneous) product as Cournot Duopolists. Further imagine that the market demand curve for their product is P = 100 - Q and that their marginal cost is constant at $40 per unit of output. Recall that Q = q 1 + q 2 is total output from both firms. PART A - Cournot Solution Lets look at firm 1's optimal plans. Firm 1 wants to chose their own output to maximize their own level of profit GIVEN the level of output that they believe that firm 2 will produce. i.e. MAX Profit 1 GIVEN q 2 q 1 Profit 1 = (P)q 1 - (MC)q 1 = ( 100 - (q 1 + q 2 ) )q 1 - 40q 1 = 100q 1 - q 1 2 - q 1 q 2 - 40q 1 first derivative WRT q 1 = 60 - 2q 1 - q 2 = 0 q 1 * = (½)( 60 - q 2 ) Firm 1's Reaction Function Symmetry implies that firm 2's optimal problem looks the same as firm 1's, all we have to do is interchange ALL subscripted 1's and 2's. This means that firm 2's solution also looks the same with the same sort of notation switch. Ultimately this implies that each firms profits are equal and so are their levels of output in equilibrium. Symmetry means q 1 * = q 2 * , therefore q 1 * = 30 - (½)q 2 * = 30 - (½)q 1 * (3/2)q 1 * = 30, so that q 1 * = 60/3 = 20 = q 2 * & Q * = q 1 * + q 2 * = 40 . P * = 100 - Q * = 60 Profit 1 * = (P * )q 1 * - (AC)q 1 * = ( P * - AC )Y 1 * = ( 60 - 40 )20 = 20(20) = $400 = Profit 2 *
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2 So in this Cournot Duopoly Equilibrium 40 units of output are made, 20 by each identical firm, and sold at the price of $60 per unit which earns each firm a profit of $400. PART B - Cartel or Monopoly Solution Now suppose that you are running one of these two firms and having taken ECM C40 you know that if you really wanted to maximize your profits you can earn even more profits than in the Cournot Duopoly case if you were a Monopolist. So you decide to convince the owner of firm 2 that this is the case.
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Week #4-5 - Competitors & Competition: Market Structure...

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