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?