1. 2. Saving and growth in a three generation model. Consider a pure endowment economy facing a given world interest rate r = 0. Residents' lifetimes last three periods, and on any date three distinct generations of equal size (normalized to 1) coexist. The young cannot borrow at all, and must save a positive amount or consume their income, y. The middle-aged are endowed with M and can borrow or save. Finally, the old have the endowment and either run down prior savings or repay what they owe before death. Everyone has the same lifetime utility function, U(cY, CM,

c) = loge + log c + log c (so = 1 here).

(a) Suppose y = (1+e)y and yo=0, where e > 0. Calculate the saving of all three generations as functions of y and e.