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Review 1

Review 1 - Midterm Review Econ 210C UCSB Strategic...

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Unformatted text preview: Midterm Review Econ 210C UCSB April 28, 2011 Strategic Decisions Strategic decisions are those in which each agent, in deciding what actions to take, must consider how others might respond to that action. Because the number of firms in an oligopoly market is small, each firm must act strategically. Each firm knows that its profit depends not only on how much it produces but also on how much the other firms produce. Econ 210C UCSB Paper Basic Models of Imperfect Competition Monopoly The monopolist chooses price and quantity so as to solve max p [ pD ( p )- C ( D ( p ))] or max Q [ P ( Q ) Q- C ( Q )] . Conditions for positive optimal solutions: (i) P ( · ) ≤ 0, P ( · ) and C ( · ) are continuous and differentiable; (ii) P ( ) > C ( ) ; (iii) P ( Q ◦ ) = C ( Q ◦ ) for a unique quantity 0 < Q ◦ < ∞ (See textbook). Econ 210C UCSB Paper Cournot Oligopoly Each firm takes the output levels of competitors as fixed, and then decides how much to produce. Cournot Equilibrium: An output profile ( q * 1 , q * 2 , ··· , q * n ) such that q * i = BR i ( q *- i ) for each firm i , where BR i ( · ) is the best response mapping of firm i . There is a unique Cournot equilibrium under conditions (i) P ( Q ) > 0 if and only if 0 ≤ Q < Q ◦ for some finite positive quantity Q ◦ ; (ii) P ( Q ) is twice-continuously differentiable and P ( Q ) ≤ 0 for 0 ≤ Q < Q ◦ ; (iii) C i ( q i ) is twice-continuously differentiable and C i ( q i ) > 0 for all q i > 0 and for all i ; (iv) For all 0 ≤ Q < Q ◦ and for all i , there is some negative number k < 0 (may depend on Q and i ) such that P ( Q )- C 00 i ( q i ) ≤ k for all q i ≥ 0. See Gaudet and Salant RES (1991) 58, 399-404. Econ 210C UCSB Paper Bertrand Model Each firm takes the prices of competitors as given, and the decide what price to charge....
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Review 1 - Midterm Review Econ 210C UCSB Strategic...

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