The Problem of Modelling of Economic Dynamics in Differential Form

TL;DR

This paper critiques traditional macroeconomic models, highlighting their inaccuracies, and proposes using Fredholm linear integral equations of the second kind with parameter-dependent kernels to better describe economic dynamics.

Contribution

It introduces a novel approach of applying Fredholm integral equations to model economic zigzags, addressing limitations of differential equation models.

Findings

Traditional differential models are insufficient for economic dynamics.

Fredholm integral equations can effectively describe economic fluctuations.

The proposed method offers a more representative reflection of economic realities.

Abstract

Traditional models of macroeconomic dynamics are fundamentally incorrect. The reason lies in a misunderstanding of peculiarities of the analysis of infinitesimal quantities. However, even those types of solutions that are envisaged by the above-mentioned models are nonrepresentative in the sense of the reflection of realities. It became obvious that the techniques of the theory of linear differential equations were insufficient here. Accordingly, the scientists' attention switched to the theory of nonlinear differential equations. At the same time, balance and, accordingly, the model with matrix properties are objectively inherent in the economic system. For the reduction of this model to a differential form, there exist rather elementary means that proved to be unclaimed. Macroeconomic rhetoric - the power of the accelerator, a lag on the part of demand, etc. - accompanied by the use of a lot of abstract coefficients prevailed. However, there is no organic interrelation between matrix and nonlinear differential equations. On the contrary, it can be said that linear theory of integral equations originated in matrix analysis. The Fredholm linear integral equation of the second kind with a parameter-dependent kernel proves to be rather representative with regard to the class of possible solutions. It seems that it can be used for the description of any zigzags of the economy. The price one has to pay for this is the nontriviality of existing theory.