Question 3 Justin is currently working full time and earns $510,000. If he is promoted, he would earn $80,000. Right now his chance of being promoted is 30%. He considers getting a master degree in Economics to help improving his chance of being promoted. Suppose, there is 5% chance that he would fail to complete the degree. Without this degree, his chance of being promoted remains at 30%. However, if he gets the degree, the chance to be promoted will increase to 80%. Justin is an expected utility maximiser and his utility function over the non-negative wealth, in, is given by: Him) = x/lTJ (a) (5 marks) ls Justin risk-averse, risk-neutral, or risk-seeking? Show your work. (b) (5 marks) Compute J ustin's expected utility if he chooses not to enrol in the Master program. (c) (5 marks) Assume that the Master program is fully subsidized, i.e., it is free. Com- pute Justin's expected utility if he chooses to enrol in the Master program. (d) (5 marks} Now assume that the program is not free, what is the maximum fee, F, that Justin is willing to pay to enrol in the Master program? [Hint: Set up the equality and use any program or software to nd the value F that solves the equation. For example, https: f f www.wolframalpha.com f calculators f equation- solver-calculator] (e) (5 marks) Suppose now that the price of the master program is F = $15, 000 and, upon being promoted, Justin's new salary would be top. Find the minimum salary tap for which Justin enrols in the Master program. [Hints Set up the equation and use any program or software to nd top that solves the equation. For example, https: / f \"nvwwolfranialphacom / calculators f equat ion-solver-calculator]