Bertrand Duopoly The market (inverse) demand function for a product is P=100-2Q.

Question

Bertrand Duopoly

The market (inverse) demand function for a product is P=100-2Q. Suppose there are two firms in the industry, each with constant marginal costs equal to $20. Assume that each firm can produce at most 40 units of output. Suppose further that the two firms will compete against each other just once in this market. In answering the following question, assume that a firm with a lower price than its rival will capture the entire market demand. If, in equilibrium, the two firms charge the same price, assume that they split evenly the market demand at that price. If the two firms simultaneously choose price to maximize their respective profits, what will be the Nash equilibrium (i.e., what prices will they each charge)? What will be the level of each firm’s profits?

Hint: Consider whether 40 units of output represents a binding capacity constraint.

Explanation / Answer

P=100-2Q

TR=PQ

=100Q-2Q2

MR=100-4Q

FOR PROFIT MAXIMIZATION MC=MR

20=100-4Q

4Q=100-20

4Q=80

Q=20

EACH FIRM WILL PRODUCE 20/5=4

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