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.
