Let Nt = nNt−1and Mt = zMt−1 for every period t,where z and n are both greater than one. The money created each period is used to finance a lumpsum subsidy of a ∗ t goods to each young household.

1. Find the equation for the budget set of an individual in the monetary equilibrium. Graph it. Solve and arbitrary indifference curve which would be tangent to the budget set at the optimal consumption bundle (c ∗ 1 , c∗ 2 ).

2. On the graph you drew for part 1, draw the feasible set. Take advantage of the fact that the feasible set will got through the monetary equilibrium (c ∗ 1 , c∗ 2 ). Label the graph carefully, and distinguish between the feasible set, and the budget constraint.

3. Prove/show that the monetary equilibrium does not maximize the utility of future generations. Support your argument with references to the graph you just drew.