7) Suppose I am offering you two contracts for your new position at Brown Consulting Company. In each offer, if you succeed at the job you receive a high pay and if you fail you receive a low pay. Suppose the probability of success and failure is known. The two offers are given below. P1 X1 P2 X2 Contract 1 (X1) 0.60 100,000 0.40 0 Contract 2 (X2) 0.60 50,000 0.40 30,000 a) Suppose you have a utility function that depends solely on income, () = 5 b) What is your expected income under both jobs offers? c) What is your expected utility under each job offer? d) Which job would you choose? e) Graphically represent the utility functions and the two lotteries (contract offers). f) Provide the Jensen's inequality for both of these contracts (this can be done both mathematically and illustrated graphically).

7) Suppose I am offering you two contracts for your new position at Brown Consulting Company. In each offer, if you succeed at the job you receive a high pay and if you fail you receive a low pay. Suppose the probability of success and failure is known. The two offers are given below. X P Contract 1 (X1) 0.60 Contract 2 (X2) 0.60 X 100,000 50,000 P2 0.40 0.40 0 30,000 a) Suppose you have a utility function that depends solely on income, u(I) = 5V b) What is your expected income under both jobs offers? c) What is your expected utility under each job offer? d) Which job would you choose? e) Graphically represent the utility functions and the two lotteries (contract offers). f) Provide the Jensen's inequality for both of these contracts (this can be done both mathematically and illustrated graphically). 7) Suppose I am offering you two contracts for your new position at Brown Consulting Company. In each offer, if you succeed at the job you receive a high pay and if you fail you receive a low pay. Suppose the probability of success and failure is known. The two offers are given below. X P Contract 1 (X1) 0.60 Contract 2 (X2) 0.60 X 100,000 50,000 P2 0.40 0.40 0 30,000 a) Suppose you have a utility function that depends solely on income, u(I) = 5V b) What is your expected income under both jobs offers? c) What is your expected utility under each job offer? d) Which job would you choose? e) Graphically represent the utility functions and the two lotteries (contract offers). f) Provide the Jensen's inequality for both of these contracts (this can be done both mathematically and illustrated graphically)