is 2011 ME 2

[kangkan]

Hi..can some one help with this question..

A community has a fixed stock X of oil that it has to consume over an infinite horizon. The utility function to be maximized is
U=∑tδtln(Ct)
where Ct represents consumption of the resource at time t. Also δt∈[0,1] is the discount factor for time t. Find the optimal consumption of at time t.

I have tried to apply Jensen's inequality since δtln(Ct) will be a concave function, but cannot figure out how to go beyond that.


thanks

[mrittik]

This problem is concerned with Infinite horizon. So just set up the lagrange for this L= Ut - lamda(C1+C2+......-X)...now you think

[kangkan]

thiking not working :(