part d, e, and f only

4. Suppose that startup would like to purchase bikes from a local cyclery. The startup's utility for the bikes is given by S(q) = 100/9. The fixed costs for the cy- cleries are $100, and if the cyclery is inefficient (efficient), then its marginal costs are $10 ($5). Assume that the startup believes there is a one-third chance that the cyclery is efficient. a. What are the first-best production levels? b. What are the contracts to implement the first-best production levels? c. How much profit would the cyclery make if the startup offers a menu of contracts {(9,4), (Ft)}? d. What are the second-best production levels? e. What is the menu of contracts for the second-best production levels? f. What is the information rent of an efficient cyclery for the menu of contracts for the second-best production levels? Is this higher or lower than the profit gained for the menu of contracts for the first-best production levels? 4. Suppose that startup would like to purchase bikes from a local cyclery. The startup's utility for the bikes is given by S(q) = 100/9. The fixed costs for the cy- cleries are $100, and if the cyclery is inefficient (efficient), then its marginal costs are $10 ($5). Assume that the startup believes there is a one-third chance that the cyclery is efficient. a. What are the first-best production levels? b. What are the contracts to implement the first-best production levels? c. How much profit would the cyclery make if the startup offers a menu of contracts {(9,4), (Ft)}? d. What are the second-best production levels? e. What is the menu of contracts for the second-best production levels? f. What is the information rent of an efficient cyclery for the menu of contracts for the second-best production levels? Is this higher or lower than the profit gained for the menu of contracts for the first-best production levels