# Interpreting question 1 on Problem Set 3

A student asked me for a clarification of question 1 on problem set #3; this problem set is due at the beginning of class on Thursday, September 14.  Anyway, question 1 reads as follows: “A worker whose utility function U(W) = W.5 has received a job offer which pays \$80,000 with a bonus. The bonus is equally likely to be \$0, \$10,000, \$20,000, \$30,000, \$40,000, \$50,000, or \$60,000. Assume that initial wealth is \$0.”

Here’s how to interpret this problem (in terms of properly delineating state probabilities and state-contingent values for wealth): there are 7 “states of the world”, and since the bonus (over and above the salary of \$80,000) is equally likely to be \$0, \$10,000, \$20,000, \$30,000, \$40,000, \$50,000, or \$60,000, this implies that ps = 1/7 for each of the 7 states. Furthermore, since initial wealth is \$0 and the salary is \$80,000, it follows that state contingent wealth for the seven states of the world will be \$80,000, \$90,000, \$100,000, \$110,000, \$120,000, \$130,000, or \$140,000.