Question 3 Ramsey model with productive government (total 19 marks) Suppose we are in representative agent environment and the aim of social planner is to maximize Equation (1). Suppose that government expenditures 9e are all capital expenditures and the stock of government capital G, is a factor of production. The economy is described by Equation (2)- Equation (4) Equation (1): Eto'log(ct) Equation (2): y == Ak&Ga Equation (3): i,- Sk = kt+1-kr Equation (3): 9-8Gt = Gt+1-Ge Where & is the depreciation rate of private and public capital, is the depreciation rate of private and public capital, and A is constant. Suppose a "(1-a¹-a) > 8. And initial values of k and G are given a) Write down the resource constraint of economy and solve the social planner problem b) What are the equations that characterize steady state? c) Suppose two types of capital have the same rate of return (+1 = MPK - 8 and Tt+1 = MPG - 8. Moreover, suppose in the steady state consumption grows at rate y. What is the value of y?