Consider a consumer with utility function U = Y½.
a. Defining the coincident of absolute risk aversion by
Show that this is a decreasing function of Y. The consumer is faced with a gamble that results in a loss of 1 with probability p = 0:5 and a gain of 2 with probability 1 – p.
b. Show that there is a critical value of income Y at which the consumer is indifferent between participating in this gamble and receiving income Y with certainty. Hence show that the gamble will be undertaken at any higher income but will not at any lower income.