Question

Suppose we have two identical firms A and B, selling identical products. They are the only firms in the market and compete by choosing prices at the same time. The Market demand curve is given by P=450-6Q. The only cost is a constant marginal cost of $15. If Firm A chooses a price of $250 what is Firm B's best response? Enter a number only, no $ sign. Hint: this is a trick question, check for what price would maximize firm B's profits.

Answer 1

Suppose we have two identical firms A and B, selling identical products. This implies that:

• If price by firm A is greater than price by firm B then Quantity sold by firm B is zero because everyone will buy from firm A.
• If price by firm A is less than price by firm B then Quantity sold by firm A is zero because everyone will buy from firm B.

If Firm A chooses a price of $250, Firm B's best response is to choose (any price less than 250). So whole demand fulfilled by firm B.

A firm will maximize profit where:

MR=MC

For MR:

P=450-6Q

TR= P x Q

TR= 450Q-6Q2

MR = differentiation of TR with respect to Q= 450-2Q

MC= 15

MC=MR

15= 450-12Q

12Q= 435

Q= 36.25

P*= 450-6(36.25)= 450-217.5= 232.5 Best response price by Firm B where it maximizes profit.