**Unformatted text preview: **ACTSC 372 — Assignment #4
Due Monday April 4th — 2:00 pm in the drop boxes _—-——————_——_—_____— 1. Describe all utility functions with a (positive) constant coefﬁcient of relative risk
aversion. 2. Assume your utility function is given by u(x) = 1n(x) , and assume your current
wealth is $400,000. a. How much would you pay to insure against a loss of $100,000 with
probability 0.1%? b. Now assume your current wealth is $1 million. How much will you pay to
insure against this same loss? c. Prove the following statement about a person with a logarithmic utility
function: the amount of money (as a proportion of current wealth) a
person is willing to pay to insure against a loss of 10% of current wealth
with probability p is constant. What is the constant? 3. Suppose that when a decision maker is given the following two gambles, A and B
she chooses A (i.e. she prefers gamble A to gamble B). 3 A: Win $50 with certainty B: Win $100 with probability 60%, and 0 with probability 40%. The same decision maker is then asked to choose between gambles C and D:
C: Win $50 with 40% probability and win 0 with probability 60% D: Win $100 with 24% and 0 with probability 76%. This time she chooses D. Explain why the decision maker has violated at least one
of the axioms we discussed in class. (HINT: Consider L(A,0,0.4) and L(B,0,0.4).) 4. Assume your utility function is given by u(x) = 1n(x), and assume your current
wealth is $1000. How much would you pay for an investment that pays $100 or $0 with equal probability? Would you pay more or less for this investment if
your current wealth were to increase? Explain. ...

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- Winter '09
- MARYHARDY
- Probability, Utility, current wealth