2 Suppose that firm l and firm 2 sell slightly differentiated substitute product

Question

2 Suppose that firm l and firm 2 sell slightly differentiated substitute products. Demand for firms products are given by: Q1-30-P1+P2 and Q2-30-P2+P1. Both firms have a marginal cost of 0. Suppose that the firms compete based on price. a) What is the best response function of firm 1 in this model? b) What is the best response function of firm 2 in this model? c) What is the price charged by firm 1? d) What is the quantity sold by firm 1? e) What is the price charged by firm 2? f) What is the quantity sold by firm 2?

Explanation / Answer

Q1 = 30 - P1 + P2

Q2 = 30 - P2 + P1

a) Profit (firm 1) = P1Q1 - 0 x Q1 = 30P1 - P12 + P2P1

Profit would be maximized by firm 1 when d(Profit)/dP1 = 0:

30 - 2P1 + P2 = 0 (Response function of firm 1)

b) Similarly:

Response function of firm 2 : 30 - 2P2 + P1 = 0

c) and e) Solve both equations in a) and b) to get:

P1 = P2 = 30

d) and f) Q1 = Q2 = 30

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