Problem #1: Consider an overlapping-generations economy with money. The generation of initial old comprises N individuals. The gross growth rate of the population is n = 1. The young are endowed with y = 5 units of goods each whilst the old do not receive an endowment. The utility function of each generation t is u(CL.t, C2,t+1) = Cit + 2\\C2+1. Assume that the initial old are endowed with M/N units of money per capita. 1. In the monetary equilibrium, what are the per-period budget con- straints of an individual ? 2. Derive the intertemporal budget constraint for a given real rate of re- turn on money. 3. Derive the optimal choices of consumption cyr and c2+1 as a function of v. and ut+1. Show that these demand functions are homogeneous of degree zero and interpret this finding. 4. Why can p/P +1 be interpreted as the real return on money? 5. What is the aggregate demand for real money balances of the young generation in t as a function of the real return on money? What is the aggregate supply of real money balances of the old generation in t