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# lecture24_slides - Econ 121 Intermediate Microeconomics...

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Econ 121. Intermediate Microeconomics. Eduardo Faingold Yale University Lecture 24

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Outline of the course I. Introduction II. Individual choice III. Competitive markets IV. Market failure
Outline of the course I. Introduction II. Individual choice III. Competitive markets IV. Market failure ± Monopoly (Ch. 24, 25) ± Oligopoly (Ch. 27)

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Cournot Oligopoly N firms, facing downward sloping demand p. ² / . Firm i has cost function C i . A Cournot equilibrium is an output vector .x ³ 1 ; x ³ 2 ; : : : ; x ³ N / such that for each firm i D 1; : : : ; N , output x ³ i solves max x i greaterorequalslant 0 p ± X j ¤ i x ³ j C x i ² x i NUL C i .x i / First-order conditions: p 0 ± N X j D 1 x ³ i ² x ³ i C p ± N X j D 1 x ³ i ² D C 0 i .x ³ i /
Cournot Oligopoly Suppose all firms have the same cost function C . Then, the first-order conditions are p 0 ± N X j D 1 x ³ i ² x ³ i C p ± N X j D 1 x ³ i ² D C 0 .x ³ i / In this case, the unique equilibrium is symmetric: x ³ 1 D : : : D x ³ N D x ³ Plugging into the first-order conditions p 0 .Nx ³ /x ³ C p.Nx ³ / D C 0 .x ³ /

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Cournot Oligopoly Linear demand case: p.Q/ D a NUL bQ; C.x/ D F C cx First-order condition: NUL bx ³ C a NUL bNx ³ D MC ) x ³ D a NUL MC b.N C 1/ Total output and price: Q D Nx ³ D .a NUL MC/N b.N C 1/ ; p D a NUL .a NUL MC/N N C 1 D a N C 1 C MC N N C 1
Cournot Oligopoly Q D .a NUL MC/N b.N C 1/ and p D a N C 1 C MC N N C 1 As N ! 1 , Q ! a NUL MC b and p ! MC: That is, outcome approximates perfect competition when number of firms is very large.

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Optimal Collusion Cartel chooses .x col 1 ; : : : ; x col N / to maximize joint profit: max x 1 ;:::;x n p ± N X i D 1 x i ²± N X i D 1 x i ² NUL N X i D 1 C i .x i / F.O.C.: p 0 NUL N X i D 1 x col i ³NUL N X i D 1 x col i ³ C p NUL N X i D 1 x col i ³ D C 0 i .x col i /; all i:
Instability of Cartels Suppose all firms produce according to the optimal collusive agreement.

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lecture24_slides - Econ 121 Intermediate Microeconomics...

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