Consider a pay-as-you-go social security plan that would collect 10 goods from each young person and distribute these goods evenly to old people. Find the effect of this plan on the wealth of future generations, consumption when young and old, private saving by the young, and investment by the young in each of the following cases. Specify as much as possible about the magnitude of the changes.
a. Population is constant and r = 1.
b. Population is constant and r > 1.
c. Population grows at the rate n > r.