Two companies are the only snowplow merchants in a small town. Inverse market demand curve is P = 100 - 10Q, where Q = q₁ + q₂ (Firm 1's output = q₁; Firm 2's output = q₂). Each firm has marginal costs of $25. In the Nash equilibrium in this market, Firm 1 produces ____.

Question

Quizplus · Accepted Answer

Firm 1's profit-maximizing output is q₁ = (100 - 25 - 10q₂)/20 = 5 - 0.5q₂. In the Nash equilibrium, Firm 2's output is q₂ = (100 - 25 - 10q₁)/20 = 5 - 0.5q₁. Substituting this into Firm 1's output equation, we get q₁ = 5 - 0.5(5 - 0.5q₁) = 2.5.

Two Companies Are the Only Snowplow Merchants in a Small