In: Economics
In this problem, you need 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 cost of $10. For your derivations, assume that the monopolist serves both consumer types and use TL and TH to denote the fixed fees (dollar amounts) charged to the consumers with low and high demand, respectively. Assume also zero fixed costs. a (15). 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 (15). Write the IR constraint for the consumers with low demand. c (15). Write the IC constraint for the consumers with high demand. d (20). Write the monopolist’s profit maximization problem in terms of QL and QH. Provide the first-order conditions and the optimal values of QL, QH, TL, and TH. e (10). Calculate the implied profit, consumer surplus, and total welfare.