The market demand in a Bertrand duopoly is P 15 2Q and the

The market demand in a Bertrand duopoly is P = 15 - 2Q, and the marginal costs are $45. Fixed costs are zero for both firms. Which of the following statement(s) is/are true?

Select one:

a. Each firm produces 15 units.

b. None of the statements associated with this question are correct.

c. Each firm earns $337.50 in profit.

d. P = $45.

Solution

Option (d) is correct. Each firm charges Price equal to marginal cost which is $45. Suppose not. Suppose firm 1 charges price more than $45, then the demand for firm 2 will be 0 because all the consumers will go to firm 1 which is charging lower price of $45. So the best response of firm 1 should be to reduce price to $45. If firm 1 charges price less than $45, then it will capture the market as all consumers will come to firm 1. But firm 1 will incur losses because price is less than marginal cost on each unit. So firm 1 can do better by increasing price to $45, to earn normal profits. Same reasoning can be given for firm 1 also. So (d) is correct.