2. ISonsider the overlapping generations model. Let the number of young people born each period be constant, at N. There is a constant stock of at money, M. Each young person horn in period t is endowed with 3;: units of the consumption good when young and nothing when old. A person's endowment grows over time so that y; = loyal, where or ':- 1; that is. the young in the next period have a higher endowment than the young in the previous period. For simplicity, assume that in each period t, people desire to hold real money balances equal to one half of their endowment, so that more = %. {a} Write down equations that represent the constraints on rstr and second-period consumption for a typical person. Combine these constraints into a lifetime budget constraint. {i%} (b) 1'Write down the condition that represents the equilibrium in the money market in period 1. Use this condition to nd the real rate of return of at money in a monetary equilibrium. Explain the path over time of the value of at money. {15%} (c) Show that y: = {:35}in (HT-'95}