Use the social security model developed in this chapter to answer this question. Suppose that a government pay-as-you-go social security system has been in place for a long time, providing a social security payment to each old person of b units of consumption. Now, in period T, suppose that the government notices that r > n, and decides to eliminate this system. During period T, the government reduces the tax of each young person to zero, but still pays a social security benefit of b to each old person alive in period T. The government issues enough one-period government bonds, DT, to finance the social security payments in period T. Then, in period T + 1, to pay off the principal and interest on the bonds issued in period T, the government taxes the old currently alive, and issues new one-period bonds DT+1. The taxes on the old in period T + 1 are just large enough that the quantity of debt per old person stays constant, that is, DT+1 = (1 + n)DT.

Then, the same thing is done in periods T + 2, T + 3, . . . , so that the government debt per old person stays constant forever.

(a) Are the consumers born in periods T, T + 1, T + 2, ... better or worse off than they would have been if the pay-as-you-go social security program had stayed in place? Explain using diagrams.

(b) Suppose that the government follows the same financing scheme as above, but replaces the pay-as-you-go system with a fully funded system in period T. Are consumers better off or worse off than they would have been with pay-as-you-go? Explain using diagrams.