Consider the representative agent model, where the lifetime utility

Problem 1. Consider the representative agent model, where the lifetime utility [ e-Pru(c())at is maximized subject to the constraints k(t) = Ak(t) - c(t ) c(t) + i(t) = v(t) = Ak(t) k(t) >0 k(0) > 0 given where y(t) = per capita output c(t) = per capita consumption k(t) = per capita capital stock i(t) = per capita net investment (a) Write down the first order conditions and the trasversality condition for this problem using Hamiltonian. (b) Assume that 1-0 Show that the growth rate of consumption is given by gc = C C A - P (C) How is the growth endogenously created in this model? How do the pro- perties of this model differ from the neo-classical growth model