Solution - York University

equilibrium rate of return to fiat money:budget constraint in equilibrium is:v t+1v t= n z> 1. Thus the resulting lifetimec 1 + z n c 2 ≤ y + z n aCompare the lifetime budget constraint to the resource constraint. Since z > 1, theyare different and thus the decentralized solution does not obey the golden rule. Thereason is that inflation makes people hold less money than they otherwise would.The graph you have to put down is in Fig.1. Clearly money is not superneutralbecause the growth rate of money affects real allocations.(c) A policy of fixing the price level means setting z = n. If the money supply is setto grow at the same rate as the economy (population growth rate) then the rate ofreturn to fiat and the price level will both be constant. In this case the resourceconstraint is the same as before: c 1 + c 2n≤ y. The lifetime budget constraint thoughbecomes: c 1 + c 2 ≤ y + a. The golden rule allocation is still not achieved. Theargument is similar as before. See pp. 57-59 for the details. The graph you needis provided in Fig.2. Note that the initial old still prefer the golden rule over thispolicy too.(d) The first and second period budget constraints are:c 1,t + v t m t + k + t ≤ yc 2,t+1 ≤ v t+1 m t + αk t + a t+1The rate of return to money in a stationary allocation is:v t+1v t= n z> 1, while therate of return to capital is α < 1. Since, α < n , according the principle of rate ofzreturn equality, only fiat money will be held and thus k = 0 in equilibrium.(e) (8 marks) Recall that in part (d) we showed that money will be held only. Since thereis no capital, we have to show the effects of these policies in a monetary economyonly. With government expenditures you can show that the resource constraint peryoung person is:c 1 + c 2n + g n ≤ y.If the government decides to finance the expenditures through seignorage then thelifetime budget constraint for an individual is:c 1 + c 2zn ≤ y4