Julie lives for two periods. She works in the first, saves some of her income, and retires in the second and lives off her savings. For every coconut she saves today, she earns 1% interest (so she gets 101 coconuts in the future for every 100 she saves today). Suppose that Julie’s generation has 100 people, and that population growth is 5%. Now suppose that the government implements a pay-as-you-go social security system, forcing every person in Julie’s generation to pay 100 coconuts to a social security fund that will distribute the money to the currently old. In exchange, when Julie retires each young person will pay 100 coconuts to the social security fund, which will divide it equally among the future retirees.

a.    Compute how many young people will be working when Julie retires, how much will be the revenue of the social security system, and how many coconuts each retiree will receive.

b.    Is the government’s action welfare-improving or welfare-reducing and why?

c.    In the absence of a government, is the market outcome Pareto optimal or not? If not, what is the problem that prevents the market from delivering an optimal outcome?

d.    How would your answer for part (b) change if population growth fell to zero?