A dynamic problem with Pontryagin's Maximum Principle
Let the typical individual maximizes lifetime utility function be:
Flow budget constraint is given by:
Question: Find the growth rate of expenditure
Solution so far:
Now, I look ahead in the paper, and I see
First, I set up the Hamiltonian for this problem as follows:
I assume that , consumption is the same as expenditure here.
So I have
By the Pontryagin's Maximum Principle, we have the following conditions:
i. and ii.
Now, by i., I know that .
So I then have
Taking the derivative with respect to time, I have:
by ii., I have
So I guess somehow , the interest rate?
In the attachment I have a copy of the paper that this equation is on, they are on page 4 of the pdf file.
Thank you very much!!!