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Assuming that utility is forward discounted $ \rho $, lifetime utility = $ \int_{0}^{\infty} e^{-\rho t}u(c) \,dt $. And in continuous time, we also know that $ \dot{k} = y - (\delta + n)k - c$.

Given these two equations, our problem is:

$ \arg \max_{c}(\int_{0}^{\infty} e^{-\rho t}u(c) \,dt) $ such that $ c = y - (\delta + n)k - \dot{k} $

How is this solved in an optimal control context?

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  • $\begingroup$ Economic Growth, (The MIT Press) 2nd Edition by Robert J. Barro (Author), Xavier I. Sala-I-Martin (Author) $\endgroup$ Commented Jan 15, 2023 at 2:01
  • $\begingroup$ Alecos, what part of the book? And is there a pdf format? Or maybe you could summarize it in an answer, that would help... $\endgroup$
    – user43188
    Commented Jan 15, 2023 at 21:47
  • $\begingroup$ What prior research have you done? Have you googled "ramsey problem continous time"? $\endgroup$
    – BrsG
    Commented Jan 16, 2023 at 10:42

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