Consider the three period example of a person with hyperbolic discounting, with()utility in each of

the three periods and with discount factors = 1and =1:2

( , ) = { ( ) = ( ) >

where = indicates the time of decision making, and > any point in the future seen from the

moment of decision making.

1. a)Solve the optimal choice of the person at the start of period 1,the first period-self, as a function of his budget,using the values forand.
2. b)Solve the optimal choice of the person at the start of period,the second period-self, as a function of his budget2,using the values forand. How much of the budgetKwill thesecond period-selfleave for period 3?
3. c)If the person planned out his consumption over time, would he choose to stick to his plan of action after he consumes1? (Compare what the individual chooses to do at the start of period 2 and compare that to what he planned to do at the start of period 1.)