Consider an economy that is composed of identical individuals who live for two periods. Individuals maximize =n()+n() where is consumption in each period i. In each period there are N young individuals and N old individuals. Each individual receives an income of $200 in period 1 and no income in period 2 (retirement). Individuals do not want to leave behind any money (there is no bequest motive). They can save from Period 1 to Period 2.

a)How much money will they save in period 1? Now suppose that the Federal government institutes a social security system. The government takes $50 from each agent in Period 1, saves it, and gives it back in Period 2. Individuals are still able to privately save.

b)How much money will the individual save now (not counting the $50 the government took)? Suppose some individuals do not care about their retirement very much and have utility:

=ln(c1)+1/9ln(c2)

The social security system still forces them to save $50.

c)Show that these individuals will borrow money from their future (negative savings), and write down how much they will borrow.

d)Suppose these individuals are now unable to borrow. Show that the Social Security system has actually made them worse off. In other words, show that their utility without the government taking $50 from them in Period 1 and giving it to them in Period 2 is higher than their utility when the government transfers $50 from the first period to the second.