Interest Rates and Inflation

TL;DR

This paper derives a delay differential equation linking interest rates and inflation, providing simulations and solutions, with implications for economics, mathematics, and physics.

Contribution

It extends previous work by deriving a new delay differential equation relating interest rates and inflation, including detailed analysis and simulations.

Findings

Derived a delay differential equation from the Fisher relation.

Provided computer simulations of the equation.

Presented an exact solution and analysis of the model.

Abstract

This article is an extension of the work of one of us (Coopersmith, 2011) in deriving the relationship between certain interest rates and the inflation rate of a two component economic system. We use the well-known Fisher relation between the difference of the nominal interest rate and its inflation adjusted value to eliminate the inflation rate and obtain a delay differential equation. We provide computer simulated solutions for this equation over regimes of interest. This paper could be of interest to three audiences: those in Economics who are interested in interest and inflation; those in Mathematics who are interested in examining a detailed analysis of a delay differential equation, which includes a summary of existing results, simulations, and an exact solution; and those in Physics who are interested in non-traditional applications of traditional methods of modeling.