Overlapping generations model

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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: 1-9 1-0 01,1, + 1 C2.,1.+1 U: 1" 1-(9 1+p1-6 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).

Reference no: EM133237125

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