Question

Pierce has a concave utility of wealth function, u(x). Pierce prefers prospect X to prospect Y.
Which of the following statements is therefore necessarily true for Pierce?

1. CE(X) > CE(Y).

2. U(EV(X)) > U(EV(Y))

3. EU(X) < EU(Y)

4. Y is a mean preserving spread of X.

Answer 1

Solution:

For Pierce, since utility of wealth function is concave, it means that he is a risk averse individual. So, if he prefers prosepct X to prospect Y, this certainly means that expected value from X is greater than expected value from Y.

E(X) > E(Y)

Now, if Y would have been mean preserving spread of X, then E(Y) = E(X) (this is the property of mean preserve spread). So, surely, option D is incorrect.

Furthermore, given only this much, we can't compare the certainty equivalent, and hence, the expected value of utility of the prospects. So, options A and C might be true or might not be true.

Since, we are certain that E(X) > E(Y), plotting the utility function of wealth for such risk averse individual will surely give outcome as U(E(X)) > U(E(Y)), suggesting that option B is the correct answer.