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Biophysical limit and metabolic growth:
New understanding of modern division of labor andsustainable economies()[Peking University, Beijing; Fudan University, Shanghai]
Copyright: Ping Chen, 2023

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1. Introduction
Current ecological crises are driven by excess consumption, which has been justified byneoclassical theories of unlimited growth. The theory of metabolic growth provides a better
alternative to understand biophysical limits of economic growth and ecological constraints of themodern division of labor. It should be noted that among the founding tenets of classical economics
is the Smith theorem that the division of labor is limited by market extent. Malthus, of course,
whatever one thinks about the overall argument he provides, at least realized there could becompetition between resources and population, and this issue subsequently influenced the works.
,
business cycle,.
Furthermore, the nonlinear dynamics of the division of labor and the theory of metabolic growth
reveal lifecycles (more exactly, wavelets) in the co-evolution of ecology-technology-culture. This
ecological systems or the trade-off between stability and complexity in which general equilibrium
frameworks break down under increasing returns to scale. Clearly, given the predicaments of themodern period, coordination of nations is a more critical issue of the global division of labor than.
,science philosophy should be brought to the fore in combination with complexity economics.

2. Neoclassical Theories of Unlimited Growth and Metabolic Growth Theory with Ecological
Constraints
Two neoclassical growth theories on exogenous and endogenous growth provide theories forunlimited growth (Solow 1970; Romer 1986), and these promote excess consumption without
appropriate recognition of biophysical limit. It is widely understood that mainstream economics
cannot deal with the current ecological crises, including global heating, population explosion, andenergy and food shortages.
In contrast, the theory of metabolic growth introduces a nonlinear network of population dynamics
for limited economic growth (Chen 2014). The simplest ecological model of growth was the logistic
model with an S-shape, which was verified in studies of the origin of the division of labor of social
animals (Chen 1987). See Fig. 1.

93real-world economics review, issue no. 106
subscribe for freeFigure 1. The theory of metabolic growth and the Logistic wavelet.

The blue line represents obsolete technology or industry that declines into a logistic wavelet under strong
competition from emerging technology (represented by the green line by a logistic growth curve with an Sshape). The envelope (red line) describes macro growth cycles as the sum of competing technologies at themeso level.

It can be argued that two classical theories shed new light on complexity economics, and thesecan be used to better understand the biophysics foundation of limited growth. The Smith Theorem(,,
III; Stigler 1950). Malthus, meanwhile, draws attention to resource capacity as a constraint on
population (Malthus 1798). Subsequent work develops a general Smith theorem or Smith-MayChen theorem (May 1974; Chen 2014) based on nonlinear ecological networks rooted in
population dynamics. Here, competing technologies are limited by three factors. First, resource
capacity, (e.g., land or natural resources) which management science refers to as scale economy.
Second, biodiversity, which indicates the scope of economy. Third, the magnitude of environmental
fluctuations, such as natural disasters and wars. These provide aspects in which there is a tradeoff between stability and complexity.

3. New Basics of Economic Ideas and Concepts
It can be argued that the theory of metabolic growth provides new foundations in economics basedon five reasons. First, a biophysical foundation to economic growth introduces industrial structure
into the economic framework. Technological competition mainly occurs at the meso (i.e. medium
structure) level. Accordingly, the Keynesian micro-macro model can be extended into a three-level
framework of micro-meso-macro economics. Here, the biological perspective is essential for mesoeconomics (Chen 2005). It i,,
in population dynamics (Schumpeter 1939; Chen 2010).

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Second, the AK model of the neoclassical production function can be replaced by a dynamic modelof evolving returns to scale. Any technology has a lifecycle with four stages: an infant R&D stage,an early or young stage of increasing returns, an adult stage of constant returns, and an aging
stage of decreasing returns and subsequent death. This involves a changing role for governments
.
(
,
.
).
,
regulatory policy faces a critical choice: dominant economic power may protect obsolete
technologies, while innovative sectors will demand institutional reform to advance risingtechnologies. How these are deal with provides for new understandings of economic justice andfair competition.
Third, as any ecological economist is aware, basic assumptions of neoclassical economics violate
the biophysical foundation of economics. For example, the Arrow-Debreu general equilibrium
model excludes increasing returns and the non-convex set, which is the typical feature of S-shapelogistic growth with ecological constraints. Furthermore, the Lucas theory of rational expectations
and micro-foundations is a slave model of population without individual degrees of freedom, andthis is in tension with the principle of large numbers (Lucas 1972, Chen 2002). One might also notethat the representative agent model in econometrics and finance is based on a random walk or
Brownian motion model with a single particle, and this clearly does not accord with the behavior ofhumans as a social animal. The better alternative model of the financial market is a population
model of the birth-death process, rather than variations on the Black-Scholes model of option
pricing (Chen 2005). Market fluctuations are driving by gaming between bull and bear camps rather
than random shocks of a representative agent. Insofar as this is achieved then it becomes possible
to diagnose financial crises and provide an early warning (Tang and Chen 2014, 2015).
Fourth, the linear demand function with infinite wants cannot be justified by human nature of.
,unlimited in some ways but are conditional (Maslow 1948). Moreover, modern diseases like obesityand diabetes are stimulated by the kind of conspicuous consumption long identified by original
institutionalists (Veblen 1899) and anthropology can provide an alternative ecological perspective
on civilization diversity and learning (Harris 1978; Gowdy 1997; Chen 1987, 2014).
Fifth and finally, the theory of metabolic growth can reveal the core mechanisms of colonialism
and geopolitical conflict, which is rooted in market-share competition for energy and natural
resources played out through the globalization of the international division of labor. Clearly, market
exchange cannot solve persistent conflicts such as war in the Middle East (Coase 1960; Chen
2007). It is also notable that the idea that transaction costs tend to fall, proposed by Coase, ischallenged by empirical evidence, since the U.S. economy increased its transaction costs from
25% of GDP in 1870 to 50% of GDP in 1970 (Wallis & North 1986). The point being made here,
albeit briefly, is that international conflicts are ultimately ecological in nature and crisis prone.
Coordination of nations is, therefore, more critical than market forces in dealing with global heatingand ecological crises (Chen 2021, 2024).

95

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4. Economic Complexity vs. Neoclassical Simplicity
Complexity science originated from astrophysics when Henri Poincaré discovered the three-bodyproblem had no analytical solution in 1899. The discovery and development of deterministic chaosin the 1960s to 1990s found wide evidence that nonlinear deterministic systems only have limited
predictability. Ilya Prigogine further recognized the important role of irreversibility in biologicalthermodynamics equilibrium. In reality non-stationarity is dominant in time series economics but
absent in controlled experiments in physics and biology. In this sense economic complexity is more
complex than physics and biology. In any case, the study of economic complexity reveals thefundamental flaws of neoclassical simplicity in three ways (Chen 2019, 2024).
First, the three-body problem is radically different from a one-body, two-body, and infinite-bodyproblem. Three and many-body problems are more complex and often without analytical solutions,while in economics the representative agent model, the two-player model in game theory andinternational finance, and the mean-field model in statistics are all equivalent and deficient as anequilibrium framework. For example, a two-country exchange model can calculate the exchange
rate and interest rate parity, but this is not so for three or more major currencies. This is also why
the option-pricing model has a fundamental flaw since it is based on a single-particle model ofBrownian motion without collective behavior.
Second, nonlinear stochastic processes may have a multi-peak distribution such that highmoments cannot be ignored during phase transition, and this is the root of financial crises (a pointthat will make more sense to readers conversant in finance). The polarized presidential election in
the U.S. shows a typical polarization with dual-peak distribution, which is a sign of bifurcation at
the cross-point of coming crise.
Third, nonlinear trends in macro and financial indexes are the main difficulty in macro
econometrics. Somedium business cycles by the HP filter (Chen 1996). Yet macro management is better aimed at
frequency rather than amplitude observation, and this is often used in medical diagnosis.
,
heartbeats.
Finally, the following six tables provide a summary of issues for interested readers and provide acomparison of different levels of complexity (Chen 2024).

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Table 1. Simplicity and Complexity in Math Economics
Issue

Simplicity

Complexity

One-body, two-body,infinite bodyThree-body problem

One

Multiple

Convex

Non-convex

Returns to scale

Decreasing returns, constantreturns

Increasing returns

Utility/Production

Unlimited, log-linear functions

Logistic functions

Deterministic

LinearNonlinear

Stochastic

Markovian

Non-Markovian

Time series

Stationary

Non-stationary

SystemClose/Convergent

Open/Divergent

Boundary

No cell, no state

Multi-level boundaries

Structure

Homogeneous

Non-homogeneous

Number of players
Number of equilibriums
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Table 2. Simplicity and Complexity in Economic Concepts
Concept

Simplicity

Complexity

Optimization, convergence,stability

Evolution, diversity, uncertainty

Unique stable equilibrium

Multiple stable/unstableequilibrium states

Cost-minimization, predictability

Creativity, innovation,
opportunity

Infinite predictability

Finite predictability

Rational, fully predictable

Nonlinear changing trends,
open competition

Labor choice of recession

Interactions between trends &major players

Equilibrium

General equilibrium,
disequilibrium

Non-equilibrium, multibiological rhythms

Economics

Two-level of micro-macro

Three-level of micro-mesomacro

Volume conservation

Volume expansion/contraction

Exogenous(independent central bank)Endogenous(constraint central bank)Invisible hands without policy

International competition &domestic change

Order

Efficiency

Expectations

Money

Policy98

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Table 3. Simplicity and Complexity in Science
Discipline
Math

Simplicity

Complexity

Linear difference equation

Nonlinear differential & mixedeqn.

Linear system with single layer

Nonlinear system with trade-off

Systems

between stability andcomplexity
Perfect, imperfect gas, fluid,
solid

Nonlinear, non-equilibrium
physics

Hamiltonian system

Dynamical system without
optimization

Equilibrium structure

Dissipative structure

Equilibrium thermodynamics

Evolutionary thermodynamics

Disorder=heat death

Changing order out of chaos

Vector & Tensor field

High-dimensional networks

Harmonic waves

Non-Eucleadian wavelets

Chemistry

Linear chemical reactions,Nonlinear chemical reactions

Biology

Biostatistics, game theory

Population dynamics, social
animal

Psychology

Behavioral psychology

Evolutionary psychology

Linearized neural cell

Brain structure and complex
networks

Physics

Neural science

Hierarchical structures99

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Table 4. Neoclassical Simplicity and Pseudo-physics
TheoryConcept

Math

Pseudo-physics

General equilibrium

Scalar field

Point state without
time & space

Unique priceLinear pricing

Infinite speed for priceadjustment

Rationality

Preference

Isolated man

No social interact. &learning

Friction

Disequilibrium

ShocksFrictions from struct. &boundaries

CrusoeIndividualism

Representative AgentSelfish against natureof social animal

Convergence

Equilibrium Order

Heat death=disorder=

Price

OptimalMaxim entropy inthermodynamics
GreedyDD& SS curve

Constraints ofphysiology & ecology

Transaction costs

Zero-transaction costs

Inertial motion, nochanging speed

Complete market

Perfect information

Perpetual motion
machine I.

Perfect competition

No monopoly firms

No classification offirms and consumers

ShocksRandom, Brownian

Perpetual motion
machine II.

Finance

Arbitrage-free

Option pricing

Single particle without
population

Exchange Rate

Bilateral parity

Parity theorem

Uncertainty ininternational
competition

Efficiency

Random series

FD whitening filter for
price signals

Expectations

Error-free prediction

Infinite computing
powerConsumer

Firm

Econometrics

EMH

Rational
Perpetual motion
machine III

No financial crises

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Table 5. Competing Models of Complexity
Classification

Theory / Model

MeasureExamplesComputation

Fractal, Levy

Fractal dimension

Coastline, geographic

SystemNetworks

Dimension, structure

Ecology, WWW, AI,
big data

Physics

Sandpile, spin-glass

Scaling

Snowflake, turbulence,

Chemistry

Dissipative structure

Strange attractor

BZ reaction

Biology

Organism

Structure, life cycles

Species, cell, cell
membrane

Imitation, pandemics

Multi-peak distribution

Ising model

Traffic, city

Flow structure

Two-fluid mode, city
evolution

Color chaos,Correlations, trend

HP filter, freewaymodel

BD process

High moments

Phase transition of
viable mkt

Epistemology

Mind-structure

Piaget cognitive
psychology

Maslow hierarchy

Multi-layer needs

Fractal, Levy

Fractal dimension

Coastline, geographic

SystemNetworks

Dimension, structure

Ecology, WWW, AI,
big data

Physics

Sandpile, spin-glass

Scaling

Snowflake, turbulence,

Chemistry

Dissipative structure

Strange attractor

BZ reaction

Biology

Organism

Structure, life cycles

Species, cell, cell
membraneSociology

Economics

Brain

Computation101

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Table 6. Open Issues of Complexity Science
Concept

SchoolTheoryExamplesSelf-organization

BAC

Dissipative structure

Origin of life, Divisionof labor,

Self-organization

SFI

Edge of chaos

ABM, artificial life,
artificial market

Austrian

Holistic knowledge

Endogenous money
without state

KeynesWartime economy

Endogenous moneywith state

Biological clock

Schumpeter

Multiple waves

Business cycles likeheartbeats

Scaling laws

EPS

Power laws

turbulent flow, highfrequency tradeSocial temperature

EPS

Trade balance

Immigration throughboundaries?

Spontaneous order

Note: BAC for Brussels-Austin-Chinese school, SFI for Santa Fe Institute, EPS for econophysics (Chen 2019,2024).

5. Conclusion: Developing a General Theory of Physics-Biology-Economics
The development of complexity economics revives the dream of a general theory in economics,
first proposed by Einstein in physics, and later suggested by Keynes in economics (Galbraith 1994;
Chen 2024). It does so in conformity with the problem of biophysical limits rather than in ignorance
or isolation from them. One might note that science has a hierarchical structure, and this is
described in figure 2 below.

102real-world economics review, issue no. 106
subscribe for freeFigure 2. Hierarchical Structure for Symbolic System and Material World
Complexity

Brain Science
Psychology
Systems

EconomyBiologyMathChemistry
Physics

Simplicity

Symbolic System

Material World(Left) The inverse pyramid of the symbolic system from simplicity to complexity.
(Right) The pyramid structure of the material world from bottom to top layer.

It can be argued that figure 2 speaks to a new understanding of philosophy of science. Physics isthe very foundation of all scientific branches because organic life still obeys the laws of physics
but is not explanatorily exhaustive. Clearly, a physics-biology approach ought to be a foundationof real-world economics and any grand unification theory should have a hierarchical knowledge
structure. Mathematics meanwhile must be appropriate to its application.
Basic assumptions in the linear-equilibrium formulation of neoclassical economics are essentially
utopian theories based on perpetual motion machines (Chen 2024). Ecological dynamics
introduces nonlinear and non-equilibrium perspectives into ecological economics. Complexity
sciences develop new tools for evolutionary economics and institutional economics with structuralchanges and diversified development. We need a new (Popperian) philosophy of science tounderstand the evolutionary tree of human knowledge. For example, the neoclassical model of
efficient market is a special case of calm market while financial crise is the special regime ofturbulent market in the phase-transition model based on birth-death process (Tang and Chen
2015). I contend that existing mainstream and heterodox economics can be better understood as
special cases in different branches of the general evolutionary tree of human history.

103

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Author contact: p.chen87@gmail.com; pchen@nsd.pku.edu.cn___________________________SUGGESTED CITATION:
Ping Chen, Biophysical limit and metabolic growth: New understanding of modern division of labor and sustainableeconomies ,real-world
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