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 1's output is

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In a Stackelberg model, the leader firm (Firm 1) takes into account the reaction of the follower firm (Firm 2) when deciding its output level. Given Firm 2's best response function $q_2 = \frac{100 - q_1}{2}$, Firm 1 maximizes its profit by anticipating this response. To find the Nash-Stackelberg equilibrium, we substitute Firm 2's best response into the total quantity $Q = q_1 + q_2$ and solve for Firm 1's optimal output, considering the inverse demand function $P = 100 - Q$ and the constant marginal cost of 10. Solving this optimization problem leads to Firm 1 choosing an output level of 40 units, making choice B correct.

Suppose Duopolists Face the Market Inverse Demand Curve P =