An exercise on discrete-time intertemporal optimization

This paper, using the different alternative methods of dynamic optimization (the Lagrange/Kuhn-Tucker (LKT) method, the substitution method, the Hamiltonian method, and the dynamic programming approach) derives the conditions that must be satisfied by the solution to the so-called Ramsey problem, hopefully in a way that can be understood by undergraduate economics students. This is done by assuming that time is discrete and that, for simplicity but without loss of generality, there are only three periods.