Managerial Economics & Business Strategy Chapter 9 Basic Oligopoly Models

Work through demonstration problem 9-4 (put away your books) Suppose the inverse demand function for two Cournot duopolists is given by P=10-(Q 1 +Q 2 ) and their costs are zero What is each firm’s MR? What are the reaction functions for the two firms What are the Cournot equilibrium outputs? What is the equilibrium price?

Isoprofit Curve Along each curve profit is the same Curves closer to the “monopoly output” are associated with higher profits n Monopoly outputs are at intersection of reaction function and axis (X for firm 1 and Y for firm 2) Reaches peak at intersection of reaction function Do not intersect each other

Firm 1’s Isoprofit Curve Q1Q1 Q1MQ1M r1r1  1 = $100  1 = $200 Increasing Profits for Firm 1 D Q2Q2 A B C

Another Look at Cournot Decisions Q2Q2 Q1Q1 Q1MQ1M r1r1 Q2*Q2* Q1*Q1* Firm 1’s best response to Q 2 *  1 = $100  1 = $200

What about firm 2?? Isoprofit curves are the mirror image of firm 1’s isoprofit curves

Another Look at Cournot Equilibrium Q2Q2 Q1Q1 Q1MQ1M r1r1 Q2*Q2* Q1*Q1* Firm 1’s Profits Firm 2’s Profits r2r2 Q2MQ2M Cournot Equilibrium

Impact of Rising Costs on the Cournot Equilibrium Q2Q2 Q1Q1 r 1 ** r2r2 r1*r1* Q1*Q1* Q2*Q2* Q 2 ** Q 1 ** Cournot equilibrium prior to firm 1’s marginal cost increase Cournot equilibrium after firm 1’s marginal cost increase

Stackelberg Model Cournot assumed that firms were mirror images of each other  Stackelberg doesn’t Firms produce differentiated or homogeneous products. Barriers to entry. Firm one is the leader. n The leader commits to an output before all other firms. Remaining firms are followers. n They choose their outputs so as to maximize profits, given the leader’s output. Behaves like a cournot oligopolist

What does it look like mathematically?

What happens? Knows follower will choose a point on their own reaction function n Leader chooses output on the follower’s reaction function that corresponds to their highest profits n Corresponds to the TANGENCY of the leader’s isoprofit curve to the followers reaction function