Consider a Cournot duopoly with the following inverse demand function: P = 100 - 2Q₁ - 2Q₂.The firms' marginal cost are identical and given by MC_i(Q_i) = 2Q_i.Based on this information firm 1 and 2's reaction functions are A)r₁(Q₂) = 24.5 - 0.5Q₁ and r₂(Q₁) = 24.5 - 0.5Q₂. B)r₁(Q₂) = 24.5 - 0.5Q₂ and r₁(Q₂) = 24.5 - 0.5Q₁. C)Q₁ = 49 - 0.5Q₂ and Q₂ = 49 - 0.5Q₁. D)Q₁ = 49 - 0.25Q₂ and Q₂ = 49 - 0.25Q₁.

Question

Quizplus · Accepted Answer

To derive the reaction functions, we can use the best response function formula, which is: MR1 = MC 100 - 4Q₁ - 2Q₂ = 2Q₁ 98 - 2Q₁ = 2Q₂ Q₂ = 49 - 0.5Q₁ Similarly, we can derive the reaction function for firm 2: MR2 = MC 100 - 2Q₁ - 4Q₂ = 2Q₂ 98 - 2Q₂ = 2Q₁ Q₁ = 49 - 0.5Q₂ Therefore, the correct choice is B.

Consider a Cournot Duopoly with the Following Inverse Demand Function