Let the inverse demand curve for a monopolist's product be P = 100 - 2Q and the marginal cost of production be constant at MC = 10. Which of the following is the optimal two-block tariff for the firm? A) P₁ = $70; Q₁ = 15; P₂ = $40; Q₂ = 30 B) P₁ = $60; Q₁ = 20; P₂ = $30; Q₂ = 15 C) P₁ = $80; Q₁ = 10; P₂ = $40; Q₂ = 15 D) P₁ = $55; Q₁ = 22.5; P₂ = $55; Q₂ = 22.5

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Quizplus · Accepted Answer

The optimal two-block tariff is the one that maximizes the monopolist's profit. The profit is given by:$$\pi = (P_1 - MC)Q_1 + (P_2 - MC)Q_2$$where P_1 and Q_1 are the price and quantity in the first block, and P_2 and Q_2 are the price and quantity in the second block.The monopolist's profit is maximized when the marginal revenue in each block is equal to the marginal cost. The marginal revenue in the first block is:$$MR_1 = \frac{d(P_1Q_1)}{dQ_1} = P_1 - 2Q_1$$and the marginal revenue in the second block is:$$MR_2 = \frac{d(P_2Q_2)}{dQ_2} = P_2 - 2Q_2$$Setting MR_1 = MC and MR_2 = MC, we get:$$P_1 - 2Q_1 = 10$$$$P_2 - 2Q_2 = 10$$Solving for P_1 and P_2, we get:$$P_1 = 2Q_1 + 10$$$$P_2 = 2Q_2 + 10$$Substituting the inverse demand curve, we get:$$P_1 = 2Q_1 + 10 = 100 - 2Q_1$$$$P_2 = 2Q_2 + 10 = 100 - 2Q_2$$Solving for Q_1 and Q_2, we get:$$Q_1 = 15$$$$Q_2 = 30$$Substituting Q_1 and Q_2 into the equations for P_1 and P_2, we get:$$P_1 = 70$$$$P_2 = 40$$Therefore, the optimal two-block tariff is P_1 = $70, Q_1 = 15, P_2 = $40, Q_2 = 30.

Let the Inverse Demand Curve for a Monopolist's Product Be