Question

12. Which of the following statements is necessarily false for some given risky prospect, X (assume that X has more than one possible outcome)? a. An individual with convex utility of wealth will have a greater value of CE(X) than an individual with concave utility of wealth? b. 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)). c. A doubling of all of X's outcomes will result in a doubling of X's expected value. d. A doubling of all of X's outcomes will result in a doubling of the variance of X.

Answer 1

Answer) Option D is the correct answer. A doubling of all x outcomes will not result in the doubling of variance. Because variance is based upon the degree of scatteredness along the mean value. If the mean doubles then the central tendency also changes. But the variation between the value remains constant.