A firm chooses how much of a good to sell to agents with downward sloping demand. Agents vq - q/2, where q is quantity. The firm has constant marginal cost have utility u(q) c(q) = 2. = First, suppose there is mass one of agents with value v = 10. a) Linear pricing. The firm charges a single price p per unit to maximize its profits. What price does it choose? How much do agents buy? How much profit does the firm make? b) Nonlinear pricing. Suppose the firm can charge a different price p(q) for each unit q. What price function does it choose? How much do agents buy? How much profit does the firm make? c) Bundled pricing. Suppose the firm can sell a bundle (p, q). What price and quantity does it choose? How much profit does the firm make? mass one of agents with value v= 10 and another mass one of agents Next, suppose there with value v = 8. d) Linear pricing. The firm charges a single price p per unit to maximize its profits. What price does it choose? How much do agents buy? How much profit does the firm make? e) Nonlinear pricing. Suppose the firm can charge a different price p(q) for each unit 9. What price function does it choose? How much do agents buy? How much profit does the firm make? f) Bundled pricing. Suppose the firm can sell two bundles (PL, qL) and (PH, 9H). What price and quantity does it choose? How much profit does the firm make?