Question

When W represents the size of the cash, assume the utility function of Alice is given as U(W)=√W. In other words, the size of utility that Alice gets for 40,000$ is U(4)=√4=2. If a financial product sells at the same price of 70,000$, but results in a different profit after one year, let's say one of the followings should be chosen:

A - 80,000$(100% Probability)

B - 160,000$(50% Probability), 40,000$(50% Probability)

(1)According to the expected utility hypothesis, which financial product would Alice choose and why?

(2) Also, how much profit,after one year of financial product A, should be changed for Alice to feel equal value for the two products? In other words, what is the certainty equivalent of financial product B?

Answer 1

1) As utility is given as U(W)=√W

in case A, U(8) = √8 = 2√2= 2*1.414= 2.828

in case B there are two probable outcome 160,000$ (50% probability) and 40,000$ (50% probability)

Expected outcome = 0.5*160,000 + 0.5 * 40,000 = 100,000

U(10) = √10 = 3.162

so, According to the utility function value, Alice should choose B.

2) to match the utility, the profit should be change to 100,000 in case A, i.e it should be increase by 20,000 so that the value of utility will become same.