4. Consider Jian Huan (JH) and Juan Camilo (JC) who are loss averse with value function...

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4. Consider Jian Huan (JH) and Juan Camilo (JC) who are loss averse with value function v(x). JH is an optimist and believes that he will receive a raise of 6,400. JC is a pessimist and believes he won't receive a raise. In fact, at the end of the year, both receive a raise of 5,000. Assume both have the following value function: v(x) a for gains (0) 2x for losses ( <0) (a) Explain who is happier, assuming they only care about the above value function. Use their expectation about the raise b (this is their reference point), and the actual raise (5000), showing your calculations. (b) Before the raise, they both could benefit from savoring the idea of (dreaming of) receiving a raise. Specifically, they receive belief utility, m(b) regarding their expectation of what the raise will be, b: m(b) = 100 b Assuming they only care about belief utility and the value function [m(b)+v(x)], explain who is happier, showing your calculations. (c) Assuming they only care about belief utility and the value function [m(b)+ v(x)], solve for the optimal expectation, 6*, to have about the raise. Show all your work (excel/Desmos/calculus etc, depending on how you solve this). HINT: You may want to consider separately expectations b < 5000 and b> 5000, given that the value function will change based on these situations. If you are going to check for individual values of b, you can focus on the range from 0 to 10,000, in multiples of 500. If you are using a calculator like Desmos.com, you can plot a function for a specific range (for example b < 5000) by adding the following after your equation: "{ 4. Consider Jian Huan (JH) and Juan Camilo (JC) who are loss averse with value function v(x). JH is an optimist and believes that he will receive a raise of 6,400. JC is a pessimist and believes he won't receive a raise. In fact, at the end of the year, both receive a raise of 5,000. Assume both have the following value function: v(x) a for gains (0) 2x for losses ( <0) (a) Explain who is happier, assuming they only care about the above value function. Use their expectation about the raise b (this is their reference point), and the actual raise (5000), showing your calculations. (b) Before the raise, they both could benefit from savoring the idea of (dreaming of) receiving a raise. Specifically, they receive belief utility, m(b) regarding their expectation of what the raise will be, b: m(b) = 100 b Assuming they only care about belief utility and the value function [m(b)+v(x)], explain who is happier, showing your calculations. (c) Assuming they only care about belief utility and the value function [m(b)+ v(x)], solve for the optimal expectation, 6*, to have about the raise. Show all your work (excel/Desmos/calculus etc, depending on how you solve this). HINT: You may want to consider separately expectations b < 5000 and b> 5000, given that the value function will change based on these situations. If you are going to check for individual values of b, you can focus on the range from 0 to 10,000, in multiples of 500. If you are using a calculator like Desmos.com, you can plot a function for a specific range (for example b < 5000) by adding the following after your equation: "{

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a To determine who is happier we need to compare their expectations about the raise b with the actual raise of 5000 JH being an optimist expects a rai... View the full answer