ECON 100B Lecture Notes - Lecture 7: Bertrand Competition, Nash Equilibrium, Stackelberg Competition
Econ 100B Lecture 7 - May 1, 2018
Oligopoly (Con’t)
Bertrand equilibrium
● Heterogeneous goods
● Firms compete directly against one another and once again the strategy is price
● Firms set prices simultaneously
● But firms do not sell identical products
○ Not perfect substitutes
○ The differentiation may not be driven by the nature of the product
● Regardless of the source of differentiation, selling heterogeneous goods allow firms to
exert more market power and earn more profit
● Goods are not perfect substitutes
● Each firm will have their own demand curve and the price they choose has a direct and
indirect effect on its profit
● Both demand curves are more sensitive to the firm's own price setting behavior than the
competitors’
● The demand curve of a firm is decreasing in its own price and increasing in the
competitor’s price
● Nash equilibrium is when each firm sets its price to maximize profit, taking the
competitor’s price as given
● The demand function of a firm is falling in its own price, it’s optimal response to a raise
its price when the competitor increases price of their product
● Reaction curves are positively sloped
● Price is no longer equal to marginal cost
Summary
● Cournot competition
○ Firms sell identical goods
○ They compete on quantity
○ Each firm takes the competitor's output as fixed and decides on its best response
● Stackelberg competition
○ Firms sell identical goods
○ One firm is a leader and other is a follower
○ By setting a higher quantity, leader leaves a smaller market for the follower to
cater
● Bertrand competition
○ Homogenous good
■ Firms sell identical good
■ Firms compete on prices
■ The Nash equilibrium is similar to perfect competition
○ Heterogenous good
■ Firms sell differentiated good
