Question

5 - Homework - An example. This homework required some thought and work. If you
manage to hand in some solution, this will improve your homework statistics.
A student has a current income y1 and expects future income y2. He/She plans current
consumption c1 and future consumption c2 in order to maximize the utility function
U = ln(c1) +
1
1 + 
ln(c2) c1, c2 > 0
where  is his/her discount rate. Borrowing or lending costs/pay an interest rate of r.
Write down the consumption of the student in the future depending on the consumption
today. This means try to think about a way to express

Answer 1

This means try to think about a way to express c2 in terms of c1 (Thats the first
step)
Now find the optimal borrowing plan (plug in, what you found above and maximize the
utility with respect to c1).

Answer 2

Plz help this question got hell out of me!

Answer 3

Can you clear up the notation on that utility function?

Answer 4

\[u=\ln(c1)+(\ln(c2)/(1+\delta)\]

Answer 5

c1,c2>0

Answer 6

\[
U=\ln c_1+\frac{\ln c_2}{1+\delta}
\]And \(\delta\) is the discount rate?

Answer 7

yes

Answer 8

Out of curiosity, what course is this for?

Answer 9

BBA

Answer 10

BBA?

Answer 11

Bachelors in Business administration

Answer 12

i want this one today anyhow :(

Answer 13

n i have no freaking clue how to attempt this :(

Answer 14

That's funny, I have a Bachelor in Business Administration :P

Answer 15

lol, cool

Answer 16

I mean, through pure manipulation you can do the following:\[
U=\ln c_1+\frac{\ln c_2}{1+\delta}\\
U-\ln c_1=\frac{\ln c_2}{1+\delta}\\
(U-\ln c_1)(1+\delta)=\ln c_2\\
e^{(U-\ln c_1)(1+\delta)}=c_2
\] That's \(c_2\) in terms of \(c_1\) and U.

Answer 17

now whats the next step

Answer 18

I'm not sure, I don't think that's what they're actually looking for when they say \(c_2\) in terms of \(c_1\). The goal here is to have something where we can differentiate U wrt \(c_1\) and set it equal to zero to maximize the function.

Answer 19

now we have to differentiate wrt to c1

Answer 20

@nbouscal can you help in differentiating it as it is looking very complex

Answer 21

@across help me differentiate this wrt to c1 plz

Answer 22

@ash2326 @TuringTest plz help me differentiate it wrt to c1 plz

Answer 23

so ttired to think