In this problem, you will be asked to derive the block-pricing scheme that maximizes profit in the case of 2nd-degree price discrimination when a monopolist faces a consumer with high demand PH = 80 − QH, a consumer with low demand PL = 50 − QL, and constant marginal and average variable cost of $10. Assume that the monopolist serves both consumer types and use TL and TH to denote the fixed fees charged to the consumers with low and high demand, respectively. For the calculations below assume zero fixed costs.
(a) Write the monopolist’s profit-maximization problem in terms of QL, QH, TL, and TH. Do not include the IR and IC constraints. You will provide them below.
(b) Write the IR constraint for the consumers with low demand.
(c) Write the IC constraint for the consumers with high demand.
(d) Using your answers in (a) and (b), write the monopolist’s profit maximization problem in terms of QL and QH.
(e) Calculate the implied profit, consumer surplus, and total welfare.