Let the inverse demand curve for a monopolist's product be $P = 100 - 2 Q$ and the marginal cost of production be constant at $M C = 10$. Which of the following is the optimal two-block tariff for the firm?
A) $P _ { 1 } = \$ 70 ; Q _ { 1 } = 15 ; P _ { 2 } = \$ 40 ; Q _ { 2 } = 30$
B) $P _ { I } = \$ 60 ; Q _ { 1 } = 20 ; P _ { 2 } = \$ 30 ; Q _ { 2 } = 15$
C) $P _ { 1 } = \$ 80 ; Q _ { 1 } = 10 ; P _ { 2 } = \$ 40 ; Q _ { 2 } = 15$
D) $P _ { 1 } = \$ 55 ; Q _ { 1 } = 22.5 ; P _ { 2 } = \$ 55 ; Q _ { 2 } = 22.5$

Question

Quizplus · Accepted Answer

To find the optimal two-block tariff, we first determine the monopolist's profit-maximizing quantity and price. The monopolist maximizes profit where marginal revenue (MR) equals marginal cost (MC). The inverse demand curve is $P = 100 - 2Q$, so the total revenue (TR) is $TR = P \times Q = (100 - 2Q)Q$, and the marginal revenue (MR) is the derivative of TR with respect to Q, which is $MR = 100 - 4Q$. Setting $MR = MC$ gives $100 - 4Q = 10$, solving for Q gives $Q = 22.5$, and substituting Q in the demand curve gives $P = 55$. However, for a two-block tariff, we look for an option that involves a combination of a fixed fee and a per-unit price that extracts consumer surplus. Among the given options, A is the correct choice because it offers a structure where the first block (with a higher price) likely targets extracting consumer surplus up to a certain quantity, and the second block (with a lower price) aligns with the marginal cost for additional quantities, which is a common strategy in two-part tariffs to maximize profits.

Let the Inverse Demand Curve for a Monopolist's Product Be P=100−2QP = 100 - 2 QP=100−2Q

Let the Inverse Demand Curve for a Monopolist's Product Be $P = 100 - 2 Q$