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 ofi.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)moneyVΔΜ=*+g+nMwhere is the inflation rate.The velocity of money is determined by the functionV = V°ehiThe nominal interest rate i is determined by i = r" +T, 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, 6 =1, and V" = 20.(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 is a =0.10?(c) What rate of inflation w maximizes seignorage?(d) What is the maximal seignorage as a fraction of nominal GDP?

We will use single variable maximization method to answer this question.

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 Le. 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) money V ΔΜ M +g+n where is the inflation rate. The velocity of money is determined by the function V V°e The nominal interest rate i is determined by i = r"+T, 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. (a) What is the seignorage as a fraction of nominal GDP, when inflation is = 0.017 (b) What is the seignorage as a fraction of nominal GDP, when inflation is a 0.10? (c) What rate of inflation w 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 Le. 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) money V ΔΜ M +g+n where is the inflation rate. The velocity of money is determined by the function V V°e The nominal interest rate i is determined by i = r"+T, 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. (a) What is the seignorage as a fraction of nominal GDP, when inflation is = 0.017 (b) What is the seignorage as a fraction of nominal GDP, when inflation is a 0.10? (c) What rate of inflation w 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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