In this question, we consider a problem which arises when we switch our pension system from PAYG to FF. Suppose that a PAYG pension system is in effect until t-1 and the government switches to the FF system at the beginning of period t. This reform is not anticipated. To avoid inter-generational inequality, the government subsidizes the old in t, which is financed by issuing government bonds, and imposes lump-sum tax, 7, on the young in all subsequent generations. For simplicity, we ignore capital accumulation: k is constant over time, so are w and r. And assume n < r. (a) How much of total subsidies are required to keep the same life-time budget for generation t 1 before and after the reform? (b) The government continues to impose a constant lump-sum tax, 7, on the young forever to finance the subsidies for generation t - 1. Derive T. (c) Do you think this pension reform improves welfare?