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?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![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)
ΔΜ
= +g+n
M
where is the inflation rate.
The velocity of money is determined by the function
V = V°ebi
The nominal interest rate i is determined by i = r" +7, 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, 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?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5af2719b-7d19-437c-a166-896bad9eead5%2F078017fc-acbb-4919-a8b7-d744a2d69505%2Fzo97jsc_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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)
ΔΜ
= +g+n
M
where is the inflation rate.
The velocity of money is determined by the function
V = V°ebi
The nominal interest rate i is determined by i = r" +7, 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, 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?
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