Intertemporal Maximization

Posted by kangkan on Feb 12, 2014; 10:31am
URL: http://discussion-forum.276.s1.nabble.com/Intertemporal-Maximization-tp7584733.html

Hi,this question if from ISI sample paper..i am not sure how to approach it.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=U=∑▒〖(δ^t)ln⁡(C_(t)) 〗 where Ct represents consumption of the resource at time t. Also δ ( between 0 to 1) is the discount factor. Find the optimal consumption of at time t.

Is there a way to apply lagarangean when the function and the constraints are in the form of integrals?

Thanks