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December 19, 2014

December 19, 2014

Posted by **Wesley** on Sunday, September 30, 2012 at 9:25pm.

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

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