Managerial Economics Business Strategy Chapter 9 Basic Oligopoly

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 Q 2 r 1 B A C D 1 = $100 Increasing Profits for Firm 1 1 = $200 Q 1 M Q 1

Another Look at Cournot Decisions Q 2 r 1 Firm 1’s best response to Q 2* Q 2 * 1 = $100 1 = $200 Q 1 * Q 1 M Q 1

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

Another Look at Cournot Equilibrium Q 2 r 1 Firm 2’s Profits Cournot Equilibrium Q 2 M Q 2 * Firm 1’s Profits r 2 Q 1 * Q 1 M Q 1

Impact of Rising Costs on the Cournot Equilibrium Q 2 r 1 * Cournot equilibrium after firm 1’s marginal cost increase r 1** Q 2** Cournot equilibrium prior to firm 1’s marginal cost increase Q 2 * r 2 Q 1** Q 1

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 n Leader chooses output on the follower’s reaction function that corresponds to their highest profits Corresponds to the TANGENCY of the leader’s isoprofit curve to the followers reaction function