4. (10%) LECTURE 16This question examines menu pricing. Derik from problem set 1 is back. He now owns a sushi restaurant, and faces a problem of how to design his menu. He offers two types of sushi with increasing quality S1, S2, satisfying 0) 0, where 0 0). Solve for Derik's profit-maximizing qualities (81, 82). Are these choices socially efficient? (e) Suppose that Derik conducts a market survey about consumers' types before setting prices. Specifically, if a typical consumer is type 01, then Derik recieves a signal y with probability 1 (3,1) and receives a signal y2 otherwise; if a typical consumer is type 12, then Derik receives a signal y2 with probability and receives a signal y otherwise. Conditional on the signal that Derik receives, what prices (P1, P2) should he set for his sushis? 4. (10%) LECTURE 16This question examines menu pricing. Derik from problem set 1 is back. He now owns a sushi restaurant, and faces a problem of how to design his menu. He offers two types of sushi with increasing quality S1, S2, satisfying 0) 0, where 0 0). Solve for Derik's profit-maximizing qualities (81, 82). Are these choices socially efficient? (e) Suppose that Derik conducts a market survey about consumers' types before setting prices. Specifically, if a typical consumer is type 01, then Derik recieves a signal y with probability 1 (3,1) and receives a signal y2 otherwise; if a typical consumer is type 12, then Derik receives a signal y2 with probability and receives a signal y otherwise. Conditional on the signal that Derik receives, what prices (P1, P2) should he set for his sushis