Solve the following

marginal cost coincides across plants. Intuitively, this indicates that the monopolist does not have further incentives to move production from one plant to another. Exercise #7 - Price discrimination with linear costs Consider a monopoly facing inverse demand function p(q) = 100 - q, and total cost TC(q) = 4q. a) No price discrimination. Assume that price discrimination is illegal. What are the monopolist's optimal output, price and profits? b) First-degree price discrimination. For the remainder of the exercise, consider now that the monopolist can practice price discrimination. In addition, assume that this firm has enough information to practice first-degree (perfect) price discrimination. What are the monopolist's optimal output, price and profits? c) Two block pricing. Assume that the monopolist offers price discounts (i.e., two blocks of units, each sold at a different price per unit). What are the monopolist's optimal output, price and profits? d) Comparison. Compare the monopolist's profit under each of the above pricing strategies, and show that the profits in part (b) are the highest, followed by those in (c), followed by those in part (c), and by those in part (a). Exercise #8 - Third-degree price discrimination with convex costs Consider a monopolist facing two groups of costumers, 1 and 2, with inverse demand functions P1 (q) = a1 - bq and P2(q) = a2 - bq, respectively, where a, > a2 > 0 and b > 0. The monopolist has convex cost function TC(q) = c(q)? where c > 0. a) Set up the monopolist's profit-maximization problem for each group of customers. b) Find its profit-maximizing output and price for each group of customers. ) Assume that a, = taz, where t > 1. Evaluate your above results using a, = taz, and determine how the output difference across groups of customers, and the price difference, are affected by a larger value of t. d) What would happen if t = 1, so the inverse demand functions coincide for both groups of customers