4. Suppose that IEOR startup would like to purchase bikes from a local cyclery. The startup's utility for the bikes is given by S(q) 100/q. 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. (10 points) a. What are the first-best production levels? (2 points) b. What are the contracts to implement the first-best production levels? (2 points) c. How much profit would the cyclery make if the startup offers a menu of contracts {(qi,t]), (qF, t7)}? (2 points) d. What are the second-best production levels? (2 points) e. What is the menu of contracts for the second-best production levels? (1 point) 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? (1 point) 4. Suppose that IEOR startup would like to purchase bikes from a local cyclery. The startup's utility for the bikes is given by S(q) 100/q. 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. (10 points) a. What are the first-best production levels? (2 points) b. What are the contracts to implement the first-best production levels? (2 points) c. How much profit would the cyclery make if the startup offers a menu of contracts {(qi,t]), (qF, t7)}? (2 points) d. What are the second-best production levels? (2 points) e. What is the menu of contracts for the second-best production levels? (1 point) 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? (1 point)