Suppose duopolists face the market inverse demand curve P = 100 - Q,Q = q₁ + q₂,and both firms have a constant marginal cost of 10.If firm 1 is a Stackelberg leader and firm 2's best response function is q₂ = (100 - q₁)/2,at the Nash-Stackelberg equilibrium firm 2's output is

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In the Stackelberg model, the leader (firm 1) anticipates the follower's (firm 2's) reaction. Firm 2's best response is q2 = (100 - q1)/2. Firm 1 maximizes its profit by choosing q1, knowing firm 2's response. Solving for q1 in the leader's profit maximization problem and substituting into firm 2's best response gives q2 = 30.

Suppose Duopolists Face the Market Inverse Demand Curve P =