Question

4. Bertrand Competition (29 points) Consider a Betrand Model. The market demand is P-130-Q, Consumers only buy from the firm charging a lower price. If the two firms charge the same price, they share the market equally. The marginal cost for firm 1 is 10, and the marginal cost for firm 2 is also 10. There are no fixed costs. A. (5 points) Would any firm charge a price below your reason. at the market equilibrium? Briefly explain B. (6 points) If firm 2 charges p.80, then what price p, will be firm l's best response? Brielly explain your reason. C. (6 points) Could (p=70, p. 60) be the Nash Equilibrium? Briefly explain your reason D. (6 points) Suppose now firm l's marginal cost is sill 10 but firm 2's marginal cost is raised to 30. All the other conditions remain the same. What is the Nash equilibrium of the new game? (You can answer it by providing an intuitive argument.) E. Bertrand with Capacity Constraint (6 points) Suppose due to the production capacity constraint no firm can supply more than 25 in this market (that is, 9.92S25). As in Part (B), if firm 2 still charges p2 -80, then what price p, will be firm l's best response? Briefly explain your reason.

Answer 1

A) No. neither firm will charge price less than 10 because if firm charges price less than 10 then firm will incur losses even it covers the entire market

b) If P2=80 then firm 1 best response is to charge price=79 and firm 1 will capture the entire market.

c) No, because firm have an incentive to change their strategy given the strategy of others.

firm 1 can decrease price to 59 and can earn larger profit given other firms charge price=60

D)bash equilibrium, firm 1 will charge price=29 and firm 2 will charge price=30 and all market will be captured by firm 1 only.