Question 3 verlapping Generations Model Consider an economy in which 2 generations overlap. Time is discrete and people live two periods, people start without assets and are not able to work in the second period. The government imposes a Social Security scheme in which individuals must pay a lump sum amount q:- when young and they receive an amount {1+ru 1):]? when old. The economy has a Cobb-Douglas production function y. = \"1 {y and k are in per effective units] and the utility function for someone born at time t is given by: (#1 cm + 1H llplq'il The growth rate of the population and technology are L, = [l + all; 1 and : A,= {l + gm. II respectively. Markets are competitive and there is no capital depreciation. a] [5pts] Write down the intertemporal budget constraint, the Lagrangian and Euler Equation. b] [5pts] Write down the optimal consumption choices C 1,: and C21\" 1. c] [Spts] Calculate the wage rate {intensive form} and law of motion of capital {intensive form} assuming a = lf[2+p}. d] [5pts] Graph the steady state of the model [km = kl}