Question 2 Consider an overlapping generations model with the following characteristics: individuals are endowed with y units of the consumption good when young and nothing when old. The fiat money supply changes according to Mt =zMt-1 and the population grows at rate n for every period t, according to Nt =nNt-1 where z and n are greater than i. The money created in each period is used to finance a lump-sum subsidy of at+1 goods to each old person in period t+1. Prove that the monetary equilibrium (c1*,c2*) does not maximise the utility of future generations. ii. Under what condition of monetary expansion would this economy achieve the optimal allocation of resources? Explain your answer.
Question 2
Consider an overlapping generations model with the following characteristics: individuals are endowed with y units of the consumption good when young and nothing when old. The fiat money supply changes according to Mt =zMt-1 and the population grows at rate n for every period t, according to Nt =nNt-1 where z and n are greater than
i. The money created in each period is used to finance a lump-sum subsidy of at+1
goods to each old person in period t+1. Prove that the monetary equilibrium (c1*,c2*) does not maximise the utility of future generations.
ii. Under what condition of monetary expansion would this economy achieve the optimal allocation of resources? Explain your answer.
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