L13Oligopoly - Introduction to Microeconomics Lecture 13...

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Introduction to Microeconomics Lecture 13 Oligopoly Simon Cowan
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Outline Cournot – quantity-setting Cournot v. Collusion Stackelberg – quantity setting and move order Bertrand – price-setting Kreps and Scheinkman – capacity setting, then price setting
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Cournot Oligopoly Augustin Cournot (1838) Two Firms: a “Duopoly” Homogeneous product Firms decide on Quantities to supply Market price determined by total Quantity Supplied equal to Market Demand Firms attempt to maximise their own profits, assuming their rival’s quantity is given
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q A q B ISOPROFIT CURVES FOR FIRM A Π Π Π Π q B1 q B2 q * q B3 q B4 q * q * q * A’s REACTION FUNCTION Π < Π < Π < Π
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Where do the iso-profit curves come from? Suppose that demand is and each firm has constant marginal cost . The iso-profit of firm 1 is defined (implicitly) by ( ) 0. Let's see how depends on . Rearranging gives the A B A A B A B A p a q q c a q q c q k q q = - - Π = - - - = equation of the iso-profit ( as a function of ). = You can check by differentiation that this is concave, that for low values of it is upward-sloping and for high values of it is d B A B A A A A q q k q a q c q q q - - - ownward-sloping.
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q A q B q B4 * q B1 * q B2 * q B3 * q A4 q A3 q A2 q A1 ISOPROFIT CURVES FOR FIRM B B’s REACTION FUNCTION Π B1 Π B4 Π B3 Π B2 Π B1 < Π B2 < Π B3 < Π B4
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q A q B B’s REACTION FUNCTION A’s REACTION FUNCTION = A’s best-response function COURNOT EQUILIBRIUM q q BCournot
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At the intersection of the reaction functions, Firm A is maximizing profits given firm B’s output, and vice versa This is an equilibrium in fact a Nash Equilibrium Total output in Cournot Equilibrium is greater than monopoly output but smaller than perfectly competitive output. Therefore price is below the monopoly level and above the
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This note was uploaded on 04/12/2010 for the course ECON DEAM taught by Professor Vines during the Spring '10 term at Oxford University.

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L13Oligopoly - Introduction to Microeconomics Lecture 13...

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