2 Consider the following cashinadvance model. Lifetime utility of the representative household is given by :3 Elvis) - \"(Hill t=U Copyright 2020 v01 @3 University of Southampton Page 2 of II 3 ECON3OIDW1 where ,5 6 (0,1) is the discount factor, 6 is consumptionI and n\" is labour supply. u is strictly increasing, strictly concave, and differ entiable. 'u is increasingI convex, and differentiable. Furthermore, we assume the following lnada conditions: lim,,_,{]v'(n"') = U and lim,,s_,1u'{n\"') = 00. Where 1 is the time endowment. The consumer's problem is to maximize utility subject to a "cash inadvance constraint" PIECE S 1715 + Am; V1 (4) where R, is the price of goods in terms of money, m; is the money stock the consumer has at the beginning of the period, and Amt is a lump sum transfer by the government or central bank. The consumer also faces a budget constraint: mt+1 + Pact 5 mg + Amt + afgn? Vt. (5) w; is the real wage and R1113 the nominal one. The agent buys goods or saves in money my\" so that she can make purchases in the next period. Firms produce with labour through the following production func tion: _ A d y: \"r where y; is output in period t, A is a parameter, and 73.? is labour input. Firms solve the usual profit maximization static problem maxrr = An;i wing Assume that the money injection Amt made by the monetary au thority to the representative agent is such that the stock of fiat money grows at a constant factor: rug+1 me = a. (a) Three key features of money are medium of exchange, store of value, unit of account. Identify the key equation in the model above that gives money a role as a medium of exchange and motivate your answer. (b) Show whether money is superneutral. (c) Define and solve the problem of a benevolent planner in this environment. (d) Find the growth factor of money 3 that is efficient in the sense that it makes the planners allocation a competitive equilibrium