Mikel has the utility function ()=112 where is the present value of his lifetime income, expressed in millions of dollars (so =1 means 1 million dollars). He currently is a surveyor, and would make 2 millions of dollars if he stuck to that career.

He is considering shifting careers to become a cameraman/video editor in the skateboarding industry. He estimated the probabilities of achieving different incomes in that path. With probability 50%, he makes 1.5 million dollars and with probability 50%, he makes 3.5 millions of dollars.

(a) What is the expected income made with the video editor career? What is Mikel's expected utility? (2 points)

(b) Does Mikel prefer to stick to his surveyor career or try the video editing career? (2 points)

(c) Find the certainty equivalent and risk premium for the video editing career. (2 points)

(d) Mikel does further research about video editing careers in the skateboarding industry, and estimates that it will correspond to the following lottery:

with probability 25%, he could make 0.5 million dollars

with probability 50%, he could make 3 million dollars

with probability 25%, he could make 5 million dollars.

What is the expected income now? What is Mikel's expected utility if he takes that path? (2 points)

(e) Find the coefficients of absolute risk aversion and relative risk aversion. (2 points)