Business cycles and chaos.


As we observe the global economy is in what is described by various commentators as in a catastrophic regime.Mathematically this is also correct as the inversion from global growth to global contraction is a velocity inversion ( ie a dissipative phenomena also known as dampening)
(V TO -V)=(T TO-T)

How far the contraction will go at present is not well understood.As we observed in the previous post as the global markets were approaching instability,the derivatives and hedge funds "fueled" the bifurcation by distorting the commodities markets.We can understand this in terms of the inversion of the gamblers paradox also known as the St Petersberg paradox.( for which there are never winners doubling up is financial suicide eg the Nick Leesing syndrome )

In the most recent central bank update I can find the Reserve Bank Governor of New Zealand call this the greatest destruction of wealth ever.

Credit related losses $2 trillion
Equity markets $30 trillion
Housing market $4 trillion
Lost productivity $3 trillion

There may be some distance to fall as some estimates of the derivitives market have been quoting liabilities of 600b us.The Housing prices in the US have fallen further in some areas with now the median price of houses in the US city of Detroit at around 7500 US$.This is around 10 % of the median price of a dwelling in Soweto,

It may be tough to get financing for a new car these days, but in Detroit you can buy a house with a credit card.

The median price of a home sold in Detroit in December was $7,500, according to Realcomp, a listing service.

Not $75,000. Remove a zero—it's seven thousand five hundred dollars, substantially less than the lowest-price car on the new-car market.

This brings us to the problem of ETS,carbon markets etc.As we observe the instability is chaotic and endogonous changes will exasperate that eg

Business Cycles, Bifurcations and Chaos in a Neo-Classical Model with Investment
Dynamics

Stephane Hallegatte, Michael Ghil Patrice Dumas Jean-Charles Hourcade

Abstract

This paper is motivated by the rising interest in assessing the effect of disruptions
in resources and environmental conditions on economic growth. Such an assessment
requires, ultimately, the use of truly integrated models of the climate and economic
systems. For these purposes, we have developed a Non-Equilibrium Dynamic Model
(NEDyM) by introducing investment dynamics and nonequilibrium effects into a
Solow growth model. NEDyM can reproduce various economic regimes, such as
manager- or shareholder-driven economies, and permits one to examine the effects
of disruptions on the economy, given either an assumption of steady-state growth
or an assumption of business cycles with transient disequilibrium. We have applied
NEDyM to an idealized economy that resembles in certain respects the 15-state
European Union in 2001.

The key parameter in NEDyM is investment flexibility. For certain values of this
parameter, the model reproduces classical business cycles with realistic characteristics; in particular, NEDyM captures the cycles' asymmetry, with a longer growth phase and more rapid contraction. The cyclical behavior is due to the investment{profit instability and is constrained by the increase in labor costs and the inertia of production capacity. For somewhat greater investment flexibility, the model exhibits chaotic behavior, because a new constraint intervenes, namely limited investment capacity. The preliminary results presented here show that complex behavior in the economic system may be due entirely, or at least largely, to deterministic, intrinsic factors, even if the economic long-term equilibrium is neo-classical in nature. In the chaotic regime, moreover, slight shocks { such as those due to natural or man-made catastrophes { may lead to significant changes in the economic system.

This paper introduces a modeling framework for macroeconomic growth dynamics
that is motivated by recent attempts to formulate and study \integrated models" of the coupling between natural and socio-economic phenomena. These attempts are driven, at least in part, by public debate about global issues, such as anthropogenic climate change. The challenge is to describe the interfaces between human activities and the functioning of the earth system over the very long term. In this context, economists have used primarily longterm growth models in the Solow tradition, relying on the idea that, over time scales of decades to centuries, the golden-age paradigm is an acceptable metaphor. This approach appears, however, to be increasingly at variance with the nature of the policy debates in the field. Advocates of stringent emission limits are concerned about the cost of damages caused by climate change, while their opponents worry about the cost of greenhouse gas abatement. But balanced growth models that incorporate many sources of flexibility tend to suggest that the damages caused by disruptions of the natural | i.e., physical and biological | planetary systems, as well as the mitigation policies proposed to prevent these disruptions, will entail only \a few percent" of losses in gross domestic product (GDP) over this century (IPCC, 2001). Both categories of activists tend thus to suspect that the figures suggested by current models underestimate either type of costs, since real economies rarely manifest a tendency to steady-state behavior

Hence a Priori to any legislative reactionary response to Climate Mitigation taxation regimes or cap and trade or whatever the dialectics "of the day is" the science of the mathematics must be robust and predictable,of which to date it has not eg Stern.ie it had no predictable qualities.

eg V. G. Gorshkov, A. M. Makarieva, B.-L. Li*

Comprehending environmental and economic sustainability: Comparative analysis
of stability principles in the biosphere and free market economy


Abstract
Using the formalism of Lyapunov potential function it is shown that the stability
principles for biomass in the ecosystem and for employment in economics are
mathematically similar. The ecosystem is found to have a stable and an unstable
stationary state with high (forest) and low (grasslands) biomass, respectively. In
economics, there is a stable stationary state with high employment, which
corresponds to mass production of conventional goods sold at low cost price, and an
unstable stationary state with lower employment, which corresponds to production
of novel goods appearing in the course of technological progress. An additional
stable stationary state is described for economics, the one corresponding to very low
employment in production of life essentials such as energy and raw materials. In this
state the civilization currently pays 10% of global GDP for energy produced by a
negligible minority of the working population (currently ~0.2%) and sold at prices
greatly exceeding the cost price by 40 times. It is shown that economic ownership
over energy sources is equivalent to equating measurable variables of different
dimensions (stores and fluxes), which leads to effective violation of the laws of
energy and matter conservation.


In other words if instability of the energy markets already exists (excessive pricing) and is instrumental in creating a global meltdown,how will an enhanced taxation regime not fail to extend the Economic inversion from years to decades