4. Use the social security model developed in this chapter to answer this question. Suppose that the government establishes a social security program in period T which provides a social security benefit of b (in terms of consumption goods) for each old person forever. In period T the government finances the benefits to the current old by issuing debt. This debt is then paid off in period T + 1 through lump-sum taxes on the young. In periods T + 1 and later, lump-sum taxes on the young finance social security payments to the old.
a. Show using diagrams that the young and old alive at time T all benefit from the social security program under any circumstances.
b. What is the effect of the social security program on consumers born in periods T + 1 and later? How does this depend on the real interest rate and the population growth rate?
5. Suppose a pay-as-you-go social security system where social security is funded by a propor- tional tax on the consumption of the young. That is, the tax collected by the government is sc, where s is the tax rate and c is consumption of the young. Retirement benefits are given out as a fixed amount b to each old consumer. Can social security work to improve welfare for everyone under these conditions? Use diagrams to answer this question.
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