1. Consider an intertemporal economy with one good in each period and a representative consumer who lives forever. The consumer has preferences of the form 2 t log ct i=0 where 0 1 is a parameter that describes technological change. (a) Formulate the optimal growth problem as a dynamic programming problem by writing down a functional equation that describes the optimal value of the discounted stream of current and future utility as a function of the current capital stock, 16, and the current time period, t. (b) Guess that the value function takes the form V(k,t) = a1 + 0.2 t + a3 log(k) and solve the dynamic programming problem by nding ahaz, and a3. (0) What is the policy function kt+1 = 9091,35)