Suppose we introduce the following fully funded government pension system in an overlapping generations economy where capital pays the fixed gross rate of return . The government taxes each young person τ goods and invests the tax payments in capital (and only in capital). When old, each person receives the full return from her tax payments.
a. Find the budget constraints for a person endowed with when young and nothing when old. Argue that, for small values of , the value of has no effect on the equilibrium consumption path.
b. Use the budget constraints of the person and the government to show that the sum of private and government capital does not change if consumption does not change.
c. Describe the values of τ for which the consumption is affected.