Consider the following economy with generational overlap
5. Take into account the next economic system with generational overlap. One agent is born at every date t > 1 and lives at dates t and t + 1. A single perishable good is obtainable for consumption at every t. Every agent has preferences represented by a utility operate In./7, ln.i.t.t+i, the place and denote portions consumed by the agent born at t when younger and when previous respectively, and endowment (5.2). There may be additionally an preliminary previous agent who lives solely at date 1, has an growing utility operate and is endowed with one unit of the great. (a) Discover the Golden Rule allocation. [20%] For the rest of the query, assume that a authorities modifications the cash provide, so If,' = zi±iM, the place zt+, > zero, and the change is effected by an actual lump-sum tax/switch on brokers when they're previous; av+.1 denotes the worth of the tax/switch paid at date t + 1 by the agent born at date t and a,four.1 = (b) Arrange the optimization downside confronted by an agent in a aggressive economic system with monetary-fiscal coverage as described above. [15%] (c) Acquire the primary order situation(s) for the issue arrange in (b). [10%] (d) Acquire the nonlinear distinction equation within the variable //7 the place //7 := •IiL and 197 is the equilibrium value degree in interval t. [15%] (e) Let 1 = z — four/three. Discover the stationary financial equilibrium allocation. [10%] (f) Let = four/three if t = 1. three.5. • • • and z1= three/eight if t = 2.four.6. • • • . Discover a financial equilibrium allocation. [20%] (g) Can you establish whether or not the allocation you present in (f) is a Pareto optimum allocation? Please justify your declare. [10%] END OF PAPER