Suppose duopolists face the market inverse demand curve P = 100 - Q,Q = q₁ + q₂,and both firms have a constant marginal cost of 10 and no fixed costs.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 profit is

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We first need to solve for the optimal quantity of firm 1 as the Stackelberg leader. Firm 1 sets its quantity to maximize its profits, taking into account the best response of firm 2. This leads to the following profit function for firm 1: π1 = (100 - q₁ - q₂)q₁ - 10q₁ Taking the derivative with respect to q₁ and setting it equal to 0, we get: 100 - 2q₁ - q₂ = 0 Substituting q₂ = (100 - q₁)/2, we get: 100 - 2q₁ - (100 - q₁)/2 = 0 Solving for q₁, we get: q₁ = 30 Substituting this back into the expression for q₂, we get: q₂ = 35 The total market quantity is q = q₁ + q₂ = 65. Therefore, the market price is: P = 100 - q = 35 Finally, firm 1's profit is: π1 = (35 - 30) * 30 - 10 * 30 = 300 - 300 = 0 Firm 2's profit is: π2 = (35 - 35/2) * 35/2 - 10 * 35/2 = 306.25 - 175 = 131.25 Therefore, the total profit in the market is: π = π1 + π2 = 0 + 131.25 = 131.25 Thus, the correct answer is D) 1200, which is not an option.

Suppose Duopolists Face the Market Inverse Demand Curve P =