Question

Which of the following statements is necessarily false for some given (non-degenerate) risky prospect, X?

1. An individual with convex utility of wealth will have a greater value of CE(X) than an individual with concave utility of wealth?

2. When utility of wealth is linear, the numeric value (ignoring units) of CE(X) – EV(X) is equivalent to the numeric value of EU(X) – U(EV(X)).

3. A doubling of all of X’s outcomes will result in a doubling of X’s expected value.

4. A doubling of all of X’s outcomes will result in a doubling of the variance of X.

Answer 1

Solution: An individual with convex utility of wealth will have a greater value of CE(X) than an individual with concave utility of wealth?

Explanation: A non-generate prospectus induces an expected value for wellth + of x*, will surely select for x*. The reverse will be applicable for individuals with convex utility functions i.e. U''>0, and thus are termed risk-seekers