a) If there is a 25 percent probability that Ms. Fogg will lose $1,000 of her cash on the trip,
what is the trip’s expected utility?
b) Suppose that Ms. Fogg can buy insurance against losing the $1,000 (say, by purchasing
traveler’s checks) at an “actuarially fair” premium of $250. Show that her expected utility
is higher if she purchases this insurance than if she faces the chance of losing the $1,000
c) What is the maximum amount that Ms. Fogg would be willing to pay to insure her $1,000?
f. For the CRRA utility function (Equation 7.42), we showed that the degree of risk aversion is
measured by (1
). In Chapter 3 we showed that the elasticity of substitution for the same
function is given by
Hence the measures are reciprocals of each other. Using this result,
discuss the following questions.
a) Why is risk aversion related to an individual’s willingness to substitute wealth between
states of the world? What phenomenon is being captured by both concepts?