What is the certainty equivalent of the new gamble

Reference no: EM132200897

Question: Now suppose Joe decides to make a plan to reduce his consumption a little in each good year in order to have a bit more money in the bad year. In particular, he decides to set aside $2,000 in every good year so that he can increase his consumption in the bad year by $18,000. The way this works is that in the years leading up to the bad year, he saves $2,000. Then in the bad year he spends his savings and then borrows enough to increase his consumption by a total of $18,000. Then, in all the rest of the good years, he pays back $2,000 of the amount he borrowed in the bad year. If he chooses this plan, Joe will lock himself into the annual saving and borrowing. Once he chooses to enter the plan, he cannot back out. 7

b-(i) What is Joe's gamble each year now, and what is the expected value of the gamble?

(ii) What is the certainty equivalent of the new gamble?

(iii) How much better off is Joe, in dollar terms, as a result of his new â€œself-insuranceâ€ plan?

(c) [Harder] Now let's ask a somewhat different question. Suppose that instead of Joe's self-insurance plan, we were to simply give Joe a lump sum of money, in good times and bad times. Show that we would have to give Joe a lump sum of $2625.50 in order to make him as much better off as simply letting him self-insure. [Hint: this is the same as saying that the gamble Joe would face after receiving the lump sum every year gives him the same expected utility as the gamble he gets by self-insuring.]

(d) Using your answers above, explain why some people are in favor of giving people tax-free savings accounts for things like unexpected healthcare expenses rather than giving them cash assistance.

Joe has a job as a plumber4 whose utility for money, Y , is ln Y . When the economy is good, Joe makes a decent living, let's say $80,000/yr. But when the economy turns bad, his income goes down, let's say to $20,000/yr. Looking ahead to the next ten years, Joe knows that there will be one year in which the economy turns bad, but he doesn't know which one.5 Suppose that interest rates are zero, so if Joe saves, he will earn no interest, and if he borrows, he will pay no interest.6 [Note: throughout this problem you will want to carry at least four decimal places when you compute logs. Otherwise you will have a very large amount of rounding error in your answers.

Reference no: EM132200897

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