Question

Firms 1 and 2 each produce a product. The quantity that each firm sells depends on both its own price and the other firm’s price and can be expressed as: q1 = 1069 – 4p1 – 2.5p2 and / en q2 = 868 – 5p2 – 2p1 where p1 is the price charged by Firm 1, q1 is the quantity sold of Firm 1's product, and p2 and q2 are defined similarly for Firm 2. The constant marginal cost to firms 1 and 2 to produce a unit is c1=4 and c2=5 respectively. Firm 1's profit (W1) is defined in the standard way. Assume that Firm 1 independently chooses its price with the goal of maximising its profit W1 and that Firm 2 acts similarly, independently picking p2 with the goal of maximising W.

Determine the best response function for each firm, which specifies the price that the firm must charge for its product to maximise its profit given the price of the other firm.

Answer 1