L13Oligopoly - Introduction to Microeconomics Oligopoly...

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1 Introduction to Microeconomics Lecture 13 Oligopoly Simon Cowan Outline z Cournot – quantity-setting z Cournot v. Collusion z Stackelberg – quantity setting and move order z Bertrand – price setting Bertrand – price-setting z Kreps and Scheinkman – capacity setting, then price setting Cournot Oligopoly z Augustin Cournot (1838) z Two Firms: a “Duopoly” z Homogeneous product Firms decide on Quantitie to supply z Firms decide on Quantities z Market price determined by total Quantity Supplied equal to Market Demand z Firms attempt to maximise their own profits, assuming their rival’s quantity is given q B ISOPROFIT CURVES FOR FIRM A q B4 A’s REACTION FUNCTION Π A1 < Π A2 < Π A3 < Π A4 q A Π A1 Π A2 Π A3 Π A4 q B1 q B2 q A4 * q B3 q A1 * q A3 * q A2 * 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 AB AA B A BA paq q c aq q c q k qq =− − 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 A k qaq c q −− ownward-sloping. q B ISOPROFIT CURVES FOR FIRM B Π B1 Π B4 Π B3 Π B2 Π B1 < Π B2 < Π B3 < Π B4 q A q B4 * q B1 * q B2 * q B3 * q A4 q A3 q A2 q A1 B’s REACTION FUNCTION
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2 q B A’s REACTION FUNCTION = A’s best-response function COURNOT EQUILIBRIUM q A B’s REACTION FUNCTION q ACournot q BCournot Cournot conclusions z At the intersection of the reaction functions, Firm A is maximizing profits given firm B’s output, and vice versa z This is an equilibrium z in fact a Nash Equilibrium z Total output in Cournot Equilibrium is greater than monopoly output but smaller than perfectly competitive output.
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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 Oligopoly...

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