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.

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