In an economy at its steady state, real GDP, Y, increases at the rate g+n, where g isthe technological growth rate and n is the rate of population growth.The monetary base M is equal to nominal GDP divided by the velocity of money Vi.e. M = PY/V where P is the price level. Thus, assuming the velocity of money isconstant, the growth rate of the monetary base will be (approximately)ΔΜ= +g+nMwhere is the inflation rate.The velocity of money is determined by the functionV = V°ebiThe nominal interest rate i is determined by i = r" +7, where the natural real interestrate r" is constant in steady state and taken as given.Assume that n = 0, g = 0.03, r" = 0.05, b =1, and Vo = 20.(a) What is the seignorage as a fraction of nominal GDP, when inflation is T = 0.01?(b) What is the seignorage as a fraction of nominal GDP, when inflation is a = 0.10?(c) What rate of inflation maximizes seignorage?(d) What is the maximal seignorage as a fraction of nominal GDP?

We are going to solve this question using single variable optimisation technique.

In an economy at its steady state, real GDP, Y, increases at the rate g+n, where g is the technological growth rate and n is the rate of population growth. The monetary base M is equal to nominal GDP divided by the velocity of money V i.e. M = PY/V where P is the price level. Thus, assuming the velocity of money is constant, the growth rate of the monetary base will be (approximately) %3D ΔΜ =*+g+n M where is the inflation rate. The velocity of money is determined by the function V = V°ci The nominal interest rate i is determined by i = ph +x, where the natural real interest rate r" is constant in steady state and taken as given. Assume that n= 0, g = 0.03, r" = 0.05, 6 = 1, and V° = 20. %3D %3D %3D (a) What is the seignorage as a fraction of nominal GDP, when inflation is a =0.01? (b) What is the seignorage as a fraction of nominal GDP, when inflation isT = 0.10? (c) What rate of inflation maximizes seignorage? (d) What is the maximal seignorage as a fraction of nominal GDP?

In an economy at its steady state, real GDP, Y, increases at the rate g+n, where g is the technological growth rate and n is the rate of population growth. The monetary base M is equal to nominal GDP divided by the velocity of money V i.e. M = PY/V where P is the price level. Thus, assuming the velocity of money is constant, the growth rate of the monetary base will be (approximately) %3D ΔΜ =*+g+n M where is the inflation rate. The velocity of money is determined by the function V = V°ci The nominal interest rate i is determined by i = ph +x, where the natural real interest rate r" is constant in steady state and taken as given. Assume that n= 0, g = 0.03, r" = 0.05, 6 = 1, and V° = 20. %3D %3D %3D (a) What is the seignorage as a fraction of nominal GDP, when inflation is a =0.01? (b) What is the seignorage as a fraction of nominal GDP, when inflation isT = 0.10? (c) What rate of inflation maximizes seignorage? (d) What is the maximal seignorage as a fraction of nominal GDP?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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