Harvey Habit has a utility function U(c1, c2) = min(c1, c2) where c1 and c2 are

Question

Harvey Habit has a utility function U(c1, c2) = min(c1, c2) where c1 and c2 are his consumption in periods 1 and 2 respectively. Harvey earns $189 in period 1 and he will earn $63 in period 2. Harvey can borrow or lend at an interest rate of 10%. There is no inflation. (Please Show work or explain. I already have the answer, just don't know how to get it )

(a) Harvey will save 60.

(b) Harvey will borrow 60.

(c) Harvey will neither borrow nor lend.

(d) Harvey will save 124.

(e) None of the above.

Explanation / Answer

total discounted ioncome from frideman hypothesis = 189+(63/1.1)

=246.2

so if he spend uniformly be C

then C+C/(1+r) = 246.2 where r=10%=0.1

=> C =128.96

hence he has to save =189-128.96

=>savings =60.03

ans:(a) Harvey will save 60

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