Consider overlapping generation economy in which each individual lives for two periods.

Population is constant. The individual’s endowments in each period are exogenous. The first-period endowment of an individual born at time t is equal to e_t, and the second-period endowment of the same individual is equal to e_t+1, where g can be negative. Each individual saves by investing in a constant returns technology, where each unit invested yields 1+r units of output in the following period.

An individual born at time t maximizes

U(c_1t,+c_2t+1)=log(c_1t)+(1+d)^-1log(c_2t+1) where d>0

Finally, the first period endowments grow at rate m so that

e_t=(1+m)e_t-1

A) How does an increase in the growth rate of income expected by one individual, g, affect his saving rate?

B) Assume that g=m, how does an increase in m affect savings?

C) In light of these results, asses the theoretical validity of the claim that high growth is responsible for the high Japanese saving rate.