Consider the standard OLG model seen in class. People live for two periods. There is a single perishable consumption good. Each individual receives an endowment ofyunits of the good when young and nothing when old. The population evolves according toNt=nNt1, wheren= 1. The stock of money evolves according toMt=zMt1, where0< z <1:

Each period, the government imposes a tax equal togoods on each old individual. The tax must be paid in money. Each period the government destroys the money it collects.

3.a.Find and explain the government budget constraint. (2 marks)

3.b.Find an explain an individual lifetime budget constraint. (2 marks)

3.c.Find an explain the rate of return of money in a monetary equilibrium. (2 marks)

3.d.Find, explain and plot the monetary equilibrium. (3 marks)

3.e.Is the monetary equilibrium efficient? Prove it. (5 marks)

3.f.Do the initial old prefer this policy to the one that maintains a constant stock of money? Explain. (2 mark)