Consumption Theory

jermaink

New member
Joined
Nov 6, 2020
Messages
5
Hi everyone,
I'd ask you to help me with some computations.
The problem is just math.
The problem set provides several hints but I'm stuck with the Taylor expansion.
1604703891312.png

That is what I've done:

ln[U'(ct)] = ln[ ((1+r)/(1+delta)) U'(ct+1)]

Then, I thought to expand { ln[U'(ct+1)] - ln[U'(ct)] } as follows:

ln[U'(ct+1-ct)] - ln[U'(ct-ct)] + d{ ln[U'(ct-ct+1)] - ln[U'(ct-ct] } * [ ct-1-ct+ct)

Then:

ln[U'(1)] - ln[U'(0)] + d{ ln[U'(1)] - ln[U'(0] } * (ct-1)

The outcome does not make sense. Any hint?

Thanks so much
 
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