Note for OTA: This corresponds to problem 7.8 in Nicholson's "Microeconomic Theory: Basic Principals". You should not need the book at all but if you do there are slides available online which contain everything in the book (a Google search should work).
We've seen that the amount an individual is willing to pay to avoid a fair gamble (h) is given by p = 0.5 E(h^2)r(W), where r(W) is Pratt's 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.
Q1. Consider a fair gamble (v) of winning or losing $1. For this gamble, what is E(v^2)?
Q2. Now consider varying the gamble in part (a) by multiplying each prize by a positive constant, k. Let h = kv. What is the value of E(h^2)?
Q3. Suppose this person has a logarithmic utility function U(W) = ln W. What is a general expression for r(W)?
Q4. Compute the risk premium (p) for k = .5, 1, 2 and for W = 10 and 100. What do you conclude by comparing the six values?
Please answer each part and explain your steps.