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)

Please illustrate when the prospect theory resembles to expected utility theory based on the following formula: Expected Utility Theory E(U) =begin inline style sum from i equals 1 to N of end style P subscript i U left parenthesis w subscript i right parenthesis Prospect Theory E(v) = begin inline style sum for blank of end style pi left parenthesis p r subscript iota right parenthesis v left parenthesis x subscript iota minus r right parenthesis pi left parenthesis p r right parenthesis space equals space p r to the power of gamma space divided by space left square bracket p r to the power of gamma space plus space left parenthesis 1 minus space p r right parenthesis to the power of gamma right square bracket to the power of left parenthesis 1 divided by gamma right parenthesis end exponent

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].

Use the following table to answer the question below.  Units Consumed Total Utility Marginal Utility0 0 —1 W 202 35 X3 Y 104 40 Z The value for Y isMultiple Choice25.30.40.45.

Consider an individual who has the following value function: v ( x )=√(x /2) for gains and v ( x )=-2 √|x| for losses. This individual is facing a lottery which consist of winning Rs. 1600 with a 25% chance, Rs. 400 with a 25% chance, and winning nothing with a 50% chance. The individual counts all outcomes as losses; that is, he takes as his reference point the best possible outcome under consideration. Suppose the weight function is p^2. What will be the expected value/utility of this lottery as per the prospect theory approach? What will be the expected value/utility of this lottery as per the RDU approach? What will be the certainty equivalent of this lottery as per the prospect theory approach?

Assume that product Alpha and product Beta are both priced at $1 per unit and that Ellie has $20 to spend on Alpha and Beta. She buys 8 units of Alpha and 12 units of Beta. The marginal utilities of the last unit of Alpha and Beta that she purchases are 40 utils and 20 utils, respectively. This indicates thatMultiple ChoiceEllie should make no change in consumption.given another dollar, Ellie should buy an additional unit of Beta.in order to maximize utility, Ellie should buy more Beta and less Alpha.in order to maximize utility, Ellie should buy more Alpha and less Beta.