Mary is considering two jobs.Option (a) a job with a bank with a salary of $70,000 a year. The other option is a start-upcompany with a base salary of $40,000 with a 50% chance of a bonus of $$60000. Maryis risk-adverse with a utility function given by U=W1/2, where W is her wealth.(a) Calculate the value and expected utility of both options. What job does Marytake. [2 marks](b) What is the minimum salary in option (a) that Mary would accept in preference tothe risky job (b) [2 marks](c) Max is considering the two jobs as well. Max loves risk. His Utility function isU=W2. What job does Max take? Show all relevant calculations. [2 marks](d) Steve lives on Waiheke Island and is considering buying an e-bike, which costs$4000 to commute to work. However, he has to take the bike on the ferry everyday, where there is a risk that it will be exposed to salt spray, which could destroythe e-bike. He estimates the risk of this at 10%. He is risk-averse with a utilityfunction of U=W1/2. The salesperson tells Steve that they can offer insurance for$650. Would Steve accept the insurance? Show all relevant working. [4 marks].

Your utility function is u(c) = √c where c is consumption. Your income is W = $40, 000. With probability p = 0.05 you get sick and have medical expenses of δ = $30, 000. (a) What is your expected utility without insurance?

Prospect pair 1 -- choose between: W: (0.2, $4000) X: (0.25, $3000) Prospect pair 2 -- choose between: Y: (0.8, $4,000) Z: ($3000) Part (a): What is the expected utility for Prospect pair 1 (X)? (Note: Please enter your answer rounded to the nearest whole dollar. For example, if your answer is $1,234.89, please input 1235 in your answer box.) (1 mark) Part (b): Based on the expected utility theory, which Options (W or X) would you choose for Prospect pair 1? (Note: If your answer is Option W, you only need to input W in your answer box.) (1 mark) Part (c): Ignoring the expected utility theory, would most people choose Options Y or Z from Prospect pair 2? (Note: You only need to input Y or Z in your answer box.) (1 mark) Part (d): Please explain your rationale for your answer in Part (c) in less than 50 words. (2 marks)

Question 1Joe’s preferences are described by the following utility functionU (x, y) = xαyβwith α > 0 and β > 0.(a) Let I denote Joe’s income, and px and py denote the prices of good x and y, respectively.Find Joe’s optimal consumption bundle.

He offers an annual bonus of $10,000 for superior performance, $6,000 for good performance, $3,000 for fair performance, and $0 for poor performance. Based on prior records, he expects an employee to perform at superior, good, fair, and poor performance levels with probabilities 0.10, 0.20, 0.50, and 0.20, respectively. Calculate the expected value of the annual bonus amountMultiple choice question.$4,000$6,000$3,700

Multiple Choice QuestionMr. Smith wants to establish an emergency fund. His living expenses for his family are $1,800 per month. What is the minimum Mr. Smith should have in his emergency fund?Multiple choice question.$12,600$1,800$5,400$3,600