Question 3 Overlapping 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 (p when young and they receive an amount (1+rt+1)(p when old. The economy has a Cobb-Douglas production function y = kat (y and k are in per effective units) and the utility function for someone born at time t is given by: 19 10 01,1, + 1 C2.,1.+1 U: 1" 1(9 1+p16 The growth rate of the population and technology are L; = (1 + n)L;1 and : A; = (1 + g)A,1, respectively. Markets are competitive and there is no capital depreciation. a) [5pts] Write down the intertemporal budget constraint, the Lagrangian and Euler Equation. b) [Spts] Write down the optimal consumption choices C 1,1 and C2,t+1. c) [5pts] Calculate the wage rate (intensive form) and law of motion of capital (intensive form) assuming 5 = 1/(2+p). d) [Spts] Graph the steady state of the model (k m = kt)