Using our generalized model of the monetary OLG economy, assume that the nominal money supply grows at a rate :2 :2: U and that the population grows at a rate 1i. Each period, monetary injections are supplied equally across the old individuals, A2,; I} 0. Assume that the old individuals have endowments 82 = 0 and that each young individual receives 6] endowments of the consumption good. 1. Solve for the optimal trade-olir condition between consuming when you and con- suming when old. 2. Provide a denition of a competitive monetary equilibrium. 3. If the economy is in a stationary equilibrium, how is the rate of return from nominal money holdings related the growth rate of the money supply and the growth rate of the population? 4. What is the golden rule growth rate of the nominal money supply for this economy? 5. Explain why having a growth rate of the nominal money supply for this economy that differs rom the golden rule growth rate of the nominal money supply results in an equilibrium allocation of consumption that is suboptimal. To understand this point, think about individual returns to saving versus the feasible rate of return that the aggregate economy can achieve by transferring resources between the young and old individuals at a point in time