#### Description

##### Exponential inter-temporal utility function question...

**Description**

New solution updates

**Question**

Exponential inter-temporal utility function question

I have this function

U(C0, C1,C2) = ln(C_0) + (?)*lnln(C_1) + (?^2)*(ln(C_2)

where? =0.8

Suppose I have $60 in period 0 (C_0). How much should they consume in each period?

Show your math. (Set the discounted marginal utility of consumption between period 0 and 1 equal, and also the discounted marginal utility of consumption between period 1 and 2 equal. That gives you 2 equations and 3 unknowns. The third equation comes from the constraint. Recall that the derivative of ln x is 1/x.)

HELPFUL INFO

Constraint

C_0 + C_1 + C_2 = 60

A SOLUTION OF A SIMILAR PROBLEM

Suppose you 7 hours of leisure spend over 3 periods (days).

U(L_0, L_2,L_2) = ln(C_0) + (?)*lnln(C_1) + (?^2)*(ln(C_2)

where? = 1/2

MU_0 = (1/2) MU_1

(1/2) MU_1=(1/4) MU_1

Constraint

L_0 + L_1 + L_2 = 7

MU_n= 1/L_n = (du/dL)

(1/L_0)= (1/2)(1/L_1)

and

(1/2)(1/L_1)=(1/4)(1/L_2)

s.t.

L_0 + L_1 + L_2 = 7

So, this simplifies to

L_0=2*L_1

and

L_1=2*L_1

So our lifetime consumption plan is

L_0= 4

L_1= 2

L_2= 1

NOTES

I'm having trouble figuring out where the 4 came from in the example problem. I'm not sure how to translate that to the problem where I have 60, instead of 7. The delta is also different and I'm not sure how to divide the 60 into three periods based on the utility function.

Additional Requirements

Min Pages: 1

Level of Detail: Show all work

Solution ID:350930 | This paper was updated on 26-Nov-2015

Price :*$25*