Suppose a pay-as-you-go social security system where social security is funded by a proportional tax on the income of the young. That is, the tax collected by the government is yy, where y is the tax rate and y is income of the young. Retirement benefits are given out as a fixed amount b to each old consumer. Find the relationship between total social security benefits for the old and total taxes on the young. N' and N indicate the young and the old population alive in the same period, respectively. Assume that all young people receive the same amount of income. Find the lifetime budget constraint for the consumer. Assume that N' = (1 + n) N holds each period.