1. The Fisher relationship relates the real interest rate, rt, to the nominal interest rate, it, as well as thecurrent and future price of goods measured in terms of money, Pt and Pt+1. It is given by:PtPt+11 + rt = (1 + it);(a) Conceptually define how r, and it differ from one another. Given this, provide some intuition forwhy the Fisher relationship as written above must hold.(b) Define the (gross) expected inflation rate as 1+ +1relationship approximately implies:Ttit - +11+rt ==Pt+1. Use this to show that the FisherPt(c) Suppose that, in the medium to long run, the real interest rate satisfies:1 Yt+1B Yt1Define B =where p > 0. Take logs to derive an approximate relationship between the real interest1+prate, p, and the expected growth rate of output. Argue that the real interest rate is increasing in p andincreasing in the expected growth rate of output. Provide some intuition (based on competitive equilibriumin an endowment economy) for your answers.(d) If, as immediately above, the real interest rate in the medium to long run is independent of theinflation rate, and if expected inflation equals actual inflation in the medium to long run, what is the primarydeterminant of the level of the nominal interest rate in the medium to long run? Is your answer consistentwith what we observe in the data?

(According to Bartleby guidelines we are allowed to answer only 1 question at a time if not…

Answered: (a) Conceptually define how r, and it…

(a) Conceptually define how r, and it differ from one another. Given this, provide some intuition for why the Fisher relationship as written above must hold.

Brief Principles of Macroeconomics (MindTap Course List)

8th Edition

ISBN:9781337091985

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter6: Measuring The Cost Of Living

Section: Chapter Questions

Problem 9PA

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Concept explainers

Risk and Uncertainty

Uncertainty refers to a situation when there is one possible outcome of a decision but where the probability of occurrence of each particular outcome is not known or cannot be estimated.

Question

1. The Fisher relationship relates the real interest rate, rt, to the nominal interest rate, it, as well as the
current and future price of goods measured in terms of money, Pt and Pt+1. It is given by:
Pt
Pt+1
1 + rt = (1 + it);
(a) Conceptually define how r, and it differ from one another. Given this, provide some intuition for
why the Fisher relationship as written above must hold.
(b) Define the (gross) expected inflation rate as 1+ +1
relationship approximately implies:
Ttit - +1
1+rt =
=
Pt+1. Use this to show that the Fisher
Pt
(c) Suppose that, in the medium to long run, the real interest rate satisfies:
1 Yt+1
B Yt
1
Define B =
where p > 0. Take logs to derive an approximate relationship between the real interest
1+p
rate, p, and the expected growth rate of output. Argue that the real interest rate is increasing in p and
increasing in the expected growth rate of output. Provide some intuition (based on competitive equilibrium
in an endowment economy) for your answers.
(d) If, as immediately above, the real interest rate in the medium to long run is independent of the
inflation rate, and if expected inflation equals actual inflation in the medium to long run, what is the primary
determinant of the level of the nominal interest rate in the medium to long run? Is your answer consistent
with what we observe in the data?

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