Consider the two period problem in question 1. Suppose Dwight's utiltiy function is given by

u(c1,c2) = logc1+logc2

whereis known as the discount factor.

(a)Find Dwight's optimal choice of beet consumption today vs tomorrow. (Second

order conditions are satisfied)

(b)How does his choice ofc1change with today's income? With tomorrow's

income?

(c)Is Dwight borrowing or saving?

(d)If Dwight was not allowed to save or borrow, what would his optimal choice

be?

Suppose Dwight's contract lasted 3 periods and his utility was given by

u(c1,c2,c3)=logc1+logc2+2logc3

(e)Use your answer from 1(e). Write down the lagrangean and the associated first order conditions.

(f)Interpret these conditions using marginal arguments.