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1423class3

# 1423class3 - 14.23 Government Regulation of Industry Class...

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14.23 Government Regulation ± of Industry± Class 3 MIT & University of Cambridge± 1

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Outline • Definitions • Nash Equilibrium • Monopoly and Perfect Competition revisited • Duopoly and social welfare • Cournot, Stackelberg and Bertrand Oligopoly • Collusion • Is oligopoly a problem? • Prisoners’ Dilemma and Game Theory 2
A Nash Equilibrium The strategies x and y form a Nash equilibrium for players 1 and 2 respectively if x is the best response for 1 if 2 has chosen y and y is the best response for 2 if 1 has chosen x. 3

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Monopoly and Perfect Competition Consider the following example: Market Demand: P=25-Q Marginal Cost = Average Cost = 5 Competitive Outcome: MC=MR=P=5, Q=20; CS=200, PS=0 Monopoly Outcome: MR=25-2Q=MC=5; Q=10, P=15; CS=50, PS=100, DWL=50 4
Cournot Oligopoly • Consider two identical firms (1 and 2). Both set quantity assuming the other firm’s quantity is independent of their own choice of output. Thus the conjectural variation is zero (i.e. firm 1 assumes dq 2 /dq 1 =0). Equilibrium occurs when each firm does not want to change its output having observed what output the other firm has set. 5

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Cournot Oligopoly Price, P=25-(q 1 +q 2 ); Total costs, C 1 =5 q 1 ; C 2 =5 q 2 ; Profit, Π 1 =(25- q 1 - q 2 ) q 1 -5 q 1 Differentiate the profit function with respect to q 1 and set equal to zero to solve for marginal revenue=marginal cost. This gives the reaction or best response function for Firm 1: this gives q 1 =(20- q 2 )/2.
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