Let N_t = nN_t-1 and M_t = zM_t-1 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 a^*_t of goods to each young person.
a. Find the equation for the budget set of an individual 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 (c^*_1, c^*₂). 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.