In Equation 7.30 we showed that the amount an individual is willing to pay to avoid a
Question:
In Equation 7.30 we showed that the amount an individual is willing to pay to avoid a fair gamble 1h2 is given by p 5 0.5E 1h22r1W2, where r1W2 is the measure of absolute risk aversion at this person’s initial level of wealth. In this problem we look at the size of this payment as a function of the size of the risk faced and this person’s level of wealth.
a. Consider a fair gamble 1v2 of winning or losing $1. For this gamble, what is E 1v22?
b. Now consider varying the gamble in part
(a) by multiplying each prize by a positive constant k. Let h 5 kv. What is the value of E 1h22?
c. Suppose this person has a logarithmic utility function U 1W2 5 ln W. What is a general expression for r1W2?
d. Compute the risk premium 1p2 for k 5 0.5, 1, and 2 and for W 5 10 and 100. What do you conclude by comparing the six values?
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