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homework1

# homework1 - Econ 451 Homework 1(Due Jan 28 1 Consider a...

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Econ 451: Homework 1 (Due Jan. 28) 1. Consider a simple overlapping generations model as we studied in class. The economy has a constant population of N = 100. Individual are endowed with y = 10 units of the consumption good when young and nothing when old. (a) Consider the planner’s problem rst. (i) Write down the equation for the feasible set line. (ii) Draw the feasible set on a graph. Then draw a regular indi erence curve to illustrate the stationary allocation c 1 and c 2 that maximizes the utility of future generations (those who live two periods). (b) Now look at a monetary equilibrium. Suppose the initial old are endowed with a total of M units of at money. (i) Write down the rst-period and second-period budget constraints for a typ- ical individual. Combine these constraints into a lifetime budget constraint. (ii) Write down the market clearing condition in an arbitrary period t . Use this condition to nd the real rate of return of at money v t +1 =v t .

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