Abstract - Why Money Trickles Up

This paper combines ideas from classical economics and modern finance with Lotka-Volterra models, and also the general Lotka-Volterra models of Levy & Solomon to provide straightforward explanations of a number of economic phenomena.

Using a simple and realistic economic formulation, the distributions of both wealth and income are fully explained. Both the power tail and the log-normal like body are fully captured. It is of note that the full distribution, including the power law tail, is created via the use of absolutely identical agents. It is further demonstrated that a simple scheme of compulsory saving could eliminate poverty at little cost to the taxpayer. Such a scheme is discussed in detail and shown to be practical.

Using similar simple techniques, a second model of corporate earnings is constructed that produces a power law distribution of company size by capitalisation.

A third model is produced to model the prices of commodities such as copper. Including a delay to capital installation; normal for capital intensive industries, produces the typical cycle of short-term spikes and collapses seen in commodity prices.

The fourth model combines ideas from the first three models to produce a simple Lotka-Volterra macroeconomic model. This basic model generates endogenous boom and bust business cycles of the sort described by Minsky and Austrian economists.

From this model an exact formula for the Bowley ratio; the ratio of returns to labour to total returns, is derived. This formula is also derived trivially algebraically. This derivation is extended to a model including debt, and it suggests that excessive debt can be economically dangerous and also directly increases income inequality.

Other models are proposed with financial and non-financial sectors and also two economies trading with each other. There is a brief discussion of the role of the state and monetary systems in such economies.

The second part of the paper discusses the various background theoretical ideas on which the models are built.

This includes a discussion of the mathematics of chaotic systems, statistical mechanical systems, and systems in a dynamic equilibrium of maximum entropy production.

There is discussion of the concept of intrinsic value, and why it holds despite the apparent substantial changes of prices in real life economies. In particular there are discussions of the roles of liquidity and parallels in the fields of market-microstructure and post-Keynesian pricing theory.

Abstract - Wealth & Income Distributions
This paper combines ideas from classical economics and modern finance with the general Lotka-Volterra models of Levy & Solomon to provide straightforward explanations of wealth and income distributions. Using a simple and realistic economic formulation, the distributions of both wealth and income are fully explained. Both the power tail and the log-normal like body are fully captured. It is of note that the full distribution, including the power law tail, is created via the use of absolutely identical agents. It is further demonstrated that a simple scheme of compulsory saving could eliminate poverty at little cost to the taxpayer.

Abstract - Pricing, liquidity and the control of dynamic systems in finance and economics

The paper discusses various practical consequences of treating economics and finance as an inherently dynamic and chaotic system. On the theoretical side this looks at the general applicability of the market-making pricing approach to economics in general. The paper also discuses the consequences of the endogenous creation of liquidity and the role of liquidity as a state variable. On the practical side, proposals are made for reducing chaotic behaviour in both housing markets and stock markets.

To download 'Dynamic Systems', please click the link below (0.5Mb, 29 pages text, 8 figures.):

Abstract - Wealth, Income, Earnings and the Statistical Mechanics of Flow Systems

This paper looks at empirical data from economics regarding wealth, earnings and income, alongside a flow model for an economy based on the general Lotka-Volterra models of Levy & Solomon. The data and modelling suggest that a simple economic system might provide a tractable model for giving an exact statistical mechanical solution for an 'out of equilibrium' flow model. This might also include an exact mathematical definition of a 'dissipative structure' derived from maximum entropy considerations. This paper is primarily a qualitative discussion of how such a mathematical proof might be achieved.

To download 'Statistical Mechanics' please click the link below (0.75Mb, 25 pages of text, 14 figures):