Consider a two-period-lived overlapping generations economy with the following features: for all agents born at time I and later, u (c c c-l I , l. In addition, assume thatn = z = l, that all agents born at time I and later are endowed O', O), and that the initial old hold M > O units of fiat money in aggregate. b. d. Solve for this economy's stationary Golden Rule allocation. That is, find the values of that maximizes c;l subject to q + % S y. The simplest approach is to use the feasibility constraint to substitute for c2 in terms of in the utility function. Within the framework of a monetary equilibrium, solve the utility maximization problem of a young agent born at time t. Therefore, find the demand functions for {q J that maximize cf$l subject to (i) qa + v,mr S y and (ii) taking and as positive and given. A useful way to solve this problem is to follow the approach taken in the Appendix to Chapter 2. Thus, let qt = (that is, time t real balances) and so now write the time t and t+l budget constraintsas +4 S y and _EL q, . Next, use these two expressions to substitute for and in the utility function in terms of qr. This will leave you with the utility function now depending only upon qr. Maximize this function with respect to qr. You can then solve for qr and from this for and CHI. Be sure to use the chain rule where needed. Assuming stationarity, solve for the equilibrium rate of return on money in this economy. Solve for the values of {q,2} that hold in this economy's stationary monetary equilibrium. These will be quantities because we are assuming the rate of return equals its equilibrium value.