1. Consider the following endowment Overlapping Generations model where people live two periods. Suppose people are endowed with 1-ε units of the good when young and ε units when old. Assume ε < 1/2 Each generation has the same number of people. Preferences are ln(cy) + βln(cold) where β < 1.
a. Solve out the equilibrium where the government implements a pay as you go social security system with lump sum taxes so that agents consume 1/2 when young and 1/2 when old.
b. Can the government implement a fully funded system that gives the same consumption for young and old as in the pay as you go? Show what happens to government debt if the Government borrows 1 from the first young generation.
c. What should be the government's pay as you go system be in order for there to be a fully funded system where the government could roll over its debt every period with no change in borrowing every period?