For this question, consider the quadratic VNM utility function

U(w) = a + bw + cw2

(a) What restrictions, if any, must be place on parameters a, b, and c for this function to display risk aversion? (1)

(b) Provide another utility function which represents the same preferences as U(W). (1)

(c) Given the following lottery:

L = ((1/2),(w + h); ((1/2).(w h))

This lottery is such that there are two states of the world. State 1 occurs with probability

of 1/2 and the individual wins w + h. State 2 occurs with probability of 1/2 and the indi-

vidual wins w -h. Suppose the individual is risk averse.

i. What is the expected value of this lottery (E(L))? (1)

ii. Find the expression which denes the certainty equivalent (CE). (2)

iii. Show that CE < E(L) and the risk pre-mium is positive. (2)

L - Lagrange Multiplier