ECON20532
Macroeconomic Analysis 4
Spring 2019
1 Tutorial 2
1.1 Question 1
Let and for every period t, where z and n are both greater than 1. The money created each period is used to finance a lump-sum subsidy of goods to each young person.
a. Find the equation for the intertemporal budget constraint for an individ-ual in the monetary equilibrium. Graph it. Show an arbitrary indifference curve tangent to the set and indicate the levels of c1 and c2 that would be chosen by an individual in this equilibrium.
b. On the graph you drew in part a, draw the feasible set. Take advantage of the fact that the feasible set line goes through the monetary equilibrium Label your graph carefully, distinguishing between the budget and feasible sets.
c. Prove that the monetary equilibrium does not maximize the utility of the future generations. Support your assertion with references to the graph you drew of the budget and feasible sets.
1.2 Question 2
Consider the following economy. Individuals are endowed with y units of the consumption good when young and nothing when old. The fiat money stock is constant. The population grows at rate n. In each period, the government taxes each young person T goods. The total proceeds of the tax are then distributed equally among the old who are alive in that period.
a. Write down the first- and second-period budget constraints facing a typ-ical individual at time t. (Hint: Be careful; remember that more young people than old people are alive at time t .) Combine the constraints into a lifetime budget constraint.
b. Find the rate of return on fiat money in a stationary monetary equilib-rium.
c. Does this government policy have any effect on an individual's welfare?