Question

12 Suppose that Pengsoo has a utility function U(W)=√W, where W is his income in millions of dollars. If he runs his own business, he can earn 4 million dollars a year when the weather is good with probability of 1/3 and 1 million dollars a year when the weather is bad with probability of 2/3. If he chooses a fixed income job, he can earn 1.8 million dollars a year for sure. (6 points)
(12-1) Compare Pengsoo’s expected incomes in the above two cases.
(12-2) Compare Pengsoo’s expected utilities in the above two cases.
(12-3) Explain which Pengsoo would choose in the above situation.

Answer 1

1) pengoos's Expected income ( EI ) when he does his own business would be = 1/3 (4) + 2/3 (1)

EI₁ = 4/3 + 2/3 = 6/3 = 2 millions

pengoos' Income when he chooses fixed income EI₂ = 1.8 millions ( given )

2 ) As given in the question pengsoo utility func is

U(W)= W

So, Expected utility (EU) he drives when he runs his own business = 1/3 (4) + 2/3 ( 1)

EU₁ = 1/3(2) + 2/3 (1) = 1.33 millions

When pengoos's chooses fixed income of 1.8 million his utility will be

EU_{2 = 1.8 = 1.34 millions}

_{C ) If pengoo's is concerned with only income , he will choose to do business with expected probabilities and if he is concerned with utility then he will be indifferent between the two outcomes.}