7. Optimal Allocations in the Neoclassical Growth Model (25 points) A consumer wants to maximize her utility over an infinite horizon. Her lifetime utility function is a.) (3 points) Derive an expression for the marginal utility of consumption in period t (i.e., MU(c,)) b.) (3 points) If she is maximizing her utility, it must be the case that in any period t, I , r '3 and o. (Show work). Find a relationship between consumption growth c.) (2 points) Suppose that she lives in a world in which consumption does not grow so What is the equilibrium real interest rate? Call this 1+r*