Critical value of the total debt in view of the debts durations

TL;DR

This paper investigates the critical total debt levels leading to borrower bankruptcy by analyzing debt distributions, fractal dimensions of economic systems, and applying entropy and chemical potential methods.

Contribution

It introduces a novel approach to determine critical debt values based on fractal dimensions and dual calculation methods, linking economic system properties to debt thresholds.

Findings

Critical debt values depend on the fractal dimension of the economic system.

Two independent methods yield consistent critical debt thresholds.

Debt thresholds vary with the velocity of money circulation.

Abstract

Parastatistic distribution of a total debt owed to a large number of creditors considered in relation to the duration of these debts. The process of debt calculation depends on the fractal dimension of economic system in which this process takes place. Two actual variants of these dimensions are investigated. Critical values for these variants are determined. These critical values represent the levels after that borrower bankruptcy occurs. The calculation of the critical value is performed by two independent methods: as the point where the entropy of the system reaches its maximum value, and as the point where the chemical potential is zero, which corresponds to the termination of payments on the debt. Both methods lead to the same critical value. When the velocity of money circulation decrease, it is found for what dimensions critical debt value is increased and for what it is decreased in the case when the velocity of money circulation is increased.