1. Price Discrimination with Downward Sloping Demand. A rm Chooses how much of a good to sell to agents with downward sloping demand. Agents have utility -u(q) : vq (12/2, where q is quantity. The rm has constant marginal cost (:(q) = 2.1 Next, suppose there is mass one of agents with value U = 10 and another mass one of agents with value U : 8. d) Linear pricing. The rm charges a single price p per unit to maximize its prots. What price does it choose? How much do agents buy? How much prot does the rm make?' e) Nonlinear pricing. Suppose the rm can charge a different price p(q) for each unit q. What price function does it choose? How much do agents buy? How much prot does the rm make? f) Bundled pricing. Suppose the rm can sell two bundles (12L,qL) and (pH,qH). \\Vhat price and quantity does it choose? How much prot does the rm make