# Nicole lives for two periods. In the first period she has income of 3. In the second period she will have income of zero.The interest rate and the…

Nicole lives for two periods. In the first period she has income of 3. In the second period she will have income of zero.The interest rate and the time discount rate are both zero. She cannot borrow and her utility function is U = ln c1 + ln c2. There is a government welfare program that provides a consumption floor of cmin in the second period. In other words: if she does not have enough money left over to afford to consume cmin, then the government will give her enough money so that she can afford it.

1. Obviously, for high enough values of cmin Nicole will spend all her income in the first period and just consume cmin in the second. For low enough levels of cmin she will act as if the program did not exist. Calculate the critical level of cmin at which she is indifferent between these two strategies. In other words, find that cmin for which utilities in both scenarios are the same.

2. Now suppose there is only a 50% chance she will be alive in the second period. Should cmin be higher or lower than in (1)? Find cmin.

The Russian spy Anna Chapman (aka Anya Kuschenko) lives for two periods. In each period KGB pays her \$1 million and this is her income.Her utility is U = ln c1 + ln c2. She can borrow or lend some asset between periods 1 and 2 that has a real interest rate of zero. However, there is a 50% chance that between periods 1 and 2, the ring of undercover Russian agents will get busted by the FBI, resulting in her being immediately deported from the US and all of her debts or savings being wiped out. That is, if she borrows,there is a 50% chance that she will not have to pay back the loan, and if she saves, there is a 50%chance that all her savings will disappear.

1. Set up her lifetime utility function V . Set up budget constraint(s).

2. Solve for her optimal first period consumption.Hint: Set up and solve the problem in terms of saving, s, not in terms of her consumptions, c1 andc2.