Question

Here goes...

1. Consider a model in which an individual lives two periods: this period (time one) and next period (time two). This period his budget constraint requires that his consumption, c1; plus his saving, s; equals his income, y1:

c1 + s = y1:

Next period his budget constraint requires that his consumption, c2; equals his income, y2; plus the value of his saving from the initial period:

c2 = y2 + (1 + r)s

where r is a known interest rate.

The individual's problem is to maximize is

U(c1) + βU(c2)

by choices of c1; c2; and s subject to his budget constraints. What are his optimal choices ofconsumption (in both periods) and saving when
U(c) = -1/2c^2
y1 = 1000
y2 = 200
r = 0:03;
and  β = 0.97

NOTE: For this utility function, MU(c)= 1/c^3