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 an interest rate of r = 2%. Julie’s generation comprises of 1,000 people and each generation grows by n% relative to the previous one. a. In the first period Julie saves 100 coconuts for retirement. How many coconuts will she have when she retires? b. 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, and the revenue will be divided equally among the future retirees. How much will be the revenue of the social security system, and how many coconuts will each retiree will receive?
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 an interest
rate of r = 2%. Julie’s generation comprises of 1,000 people and each generation grows by
n% relative to the previous one.
a. In the first period Julie saves 100 coconuts for retirement. How many coconuts will she
have when she retires?
b. 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, and the revenue will be divided
equally among the future retirees. How much will be the revenue of the social security
system, and how many coconuts will each retiree will receive?
c. What will have to be the range of values for n so that the government’s action is welfare
improving?
d. If your answer in c holds, what prevents the market from delivering an optimal outcome?
e. Demographic transitions in Japan, Europe, and the U.S. have led to a decrease in the
population growth rate below 2%, sometimes to even zero or negative rates. Given your
answer in c, what does this imply about the pay-as-you-go system relative to a fully
capitalized one?
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