The Symmetry Assumption in Transaction Costs Approach
Symmetry Breaking in Evolutionary Thermodynamics of Division of Labor
China Center for Economic Research at Peking University in Beijing, China
Center for Political Economy at Fudan University in Shanghai, China
Draft: June 30, 2007
Coase raised fundamental questions on the firm nature and market solution for social
conflicts. However, confusion was around the symmetric intonation of transaction costs,
the ill-formulated Coase Theorem, and the false analogy in physics. Fundamental issues
in the transaction costs approach can be elaborated by the symmetry assumption in
equilibrium economics and symmetry breaking in evolutionary dynamics. The Coasian
belief of decreasing transaction costs by market competition is against historical
experiences of the division of labor and basic law in thermodynamics. The creative nature
of the firm and selective role of institution can be understood by Maxwell’s demon of
living boundaries and increasing complexity in industrial economy.
Key Words: transaction costs, Coase Theorem, symmetry principle, symmetry breaking,
Inspiration and confusion surround the concept of transaction costs. Under the term
“Coase theorem” in the Palgrave Dictionary of Economics and Law, the article began
with a startling question (De Meza 1998):
“Is this statement (Coase Theorem) profound, trivial, a tautology, false,
revolutionary, wicked? Each of these has been claimed.”
There are three sources of confusion concerning the Coase theory. First, Coase
himself never gave a clear definition of transaction costs and a rigorous statement of the
Coase theorem. Therefore, different interpretations generated conflicting implications.
Second, Coase made a false analogy between the Coasian world of zero transaction costs
and the physics world without friction. Third, Coase claimed that his approach was
nothing new, but a simple application of price theory. Cheung found a fundamental flaw
in Stigler’s formulation of the Coase theorem, and reformulated it in terms of the
symmetry assumption between consumption and investment (Cheung 1998). Cheung’s
work helps us to rethink hidden symmetry assumptions in equilibrium economics (the
narrow interpretation of neoclassical economics), which excludes non-convexity,
instability, and diversity.
We will first examine different versions of the Coase Theorem; then discuss the
symmetry principle and symmetry breaking in physics, biology and economics, and the
fundamental differences between equilibrium and evolutionary perspectives. We will
show that the Coasian belief of decreasing transaction costs by market competition is
against historical experiences of division of labor and basic law in thermodynamics. The
creative nature of the firm and selective role of institution can be understood by
Maxwell’s demon in living boundaries and increasing complexity in industrial economy.
Finally, we will explore the creative nature of the firm and the selective role of institution
from an alternative approach to evolutionary dynamics.
1. The Coase Theorem and the Symmetry Assumption in Equilibrium Economics
Different formulation of basic ideas may be a bridge to new thinking. Physicists did
not realize Newton’s hidden assumption on absolute time and space until Einstein
reformulated mechanics in the form of relativity theory. The basic message from the
symmetry principle in mechanics is the existence of equilibrium order, which is described
by stability in dynamical systems. The fundamental idea of symmetry breaking in
thermodynamics is a time arrow or history in living order that is the origin of diversity in
nature and society.
Many controversies around the Coase Theorem are rooted in the Coasian world with
zero transaction costs that conflict with basic laws in physics and basic concepts in
economics. We will reexamine the Coase approach and his cases by symmetry analysis.
1.1. Controversies on the Ill-formulated Coase Theorem
There are two versions of the Coase Theorem. The first version was made by
Stigler in 1966 but Coase accepted it with a strong reservation (Coase 1988a p.174-
“Stigler dubbed the ‘Coase Theorem’: ‘… under perfect competition private
and social costs will be equal.’ … it would seem that the qualifying phrase ‘under
perfect competition’ can be omitted”
A similar version was given by Cooter: “The initial allocation of legal entitlements
does not matter from an efficiency perspective so long as they can be exchanged in a
perfectly competitive market” (Cooter 1987).
Coase preferred to replace the textbook condition of perfect competition with his
trade mark of zero transaction costs (Coase 1960, p.104, Coase 1988a, p.14):
“… the ultimate result (which maximizes the value of production) is
independent of the legal system if the pricing system is assumed to work
For better understand the original idea of the Coase Theorem, we reformulate it in
terms of the modified Cooter version that social conflicts can be solved by bilateral
exchange, since its economic efficiency is independent of institution and regulation in the
(Coasian) world with little transaction costs.
However, this idea was criticized by Samuelson, because of an “insoluble bilateral
monopoly problem with all its indeterminacies and non-optimalities” (Coase 1988a p.159,
Coase defended his position with three arguments. First, he tried to disarm his critic
by claiming in the opening statement his Nobel lecture that “I have made no innovations
in high theory” (Coase 1992). It reminds us that any flaw in Coase theory should be
traced back to the very foundation of equilibrium economics. Second, he took the
Friedman argument for an efficient currency market by asserting that non-negotiators
“have little survival value” in reality (Friedman 1953, Coase 1988a, p. 161-162).
So far the debate focused on the empirical issue on whether the Coasian world with
zero-transaction costs made any sense in the real world. Many economists and legal
scholars considered transaction costs were high in the real world, therefore institution and
regulation did matter (Cooter 1987). However, Coase insisted that “transaction costs are
not significantly affected by the change in the legal position regarding liability, which
will commonly be the case,” so that he had serious doubt to any regulation including
antitrust law, environment regulation and legislature on commercial bribery (Coase 2004,
1979). We will start with theoretical problems in the Coasian world, and then study his
1.2. Impossibility of the Coasian World in Physics
When Coase first came to Chicago, he tried to change the research direction in
industrial organization without a success. In his own words (Kitch 1983):
“When I first came to Chicago, in the industrial organization shop, people
used to talk about monopoly and concentration. … and I used to say then that
monopolizing was a competitive industry… But as no one ever listened, I gave
up saying it.”…. (Then he changed his marketing strategy. His social cost paper
got immediate attention by using a title he did not like: “social cost” used by
“I don’t think the concept of social cost is a very useful one, and I don’t
refer to it. But it did indicate to people what I was talking about.”
This is a good example that marketing strategy is aimed to catch a larger market share
but is done by increasing transaction costs (i.e. using the misleading title of “social cost”
but real meaning is “private cost” instead).
This time, the Coasian world of zero transaction costs became a magical argument
against government regulation by using a physics analogy (Coase 1988a, p.14):
“A world without transaction costs has very peculiar properties. As Stigler has
said of the ‘Coase Theorem’: ‘The world of zero transaction costs turns out to be
as strange as the physical world would be without friction. Monopolies would be
compensated to act like competitors, and the insurance companies would not
exist.’ “(Stigler 1972, Coase 1988a, p.14). “In the absence of transaction costs,
there is no economic basis for the existence of the firm. ….. the assumption of
private property rights can be dropped…. it costs nothing to speed them up, so
that eternity can be experienced in a split of second.” (Coase 1988a, p.2, p.14-15).
As trained as a physicist, can we accept that the Coasian world is a good abstract for
relevant reality? The answer is NO. It is absolutely a bad abstraction, since it violates
basic laws in physics. Specifically, Coase made four grand errors in physics:
First, an inertial world without friction is not a “strange world” but a good
approximation of physical movements in space, which has been confirmed by accurate
prediction of planet motion and repeated success of launching artificial satellites. Later
we will see that the Coase theorem often makes conflicting policy suggestions without
clear analytical power.
Second, zero information cost could not happen in a physical world. According to the
uncertainty principle in quantum mechanics, any transmission of information must
consume some minimum amount of energy (Brillouin 1962). So-called perfect
information in economic models only implies a chess-like game with rigid rules and
finite choices. It has nothing to do with marketing war in business, which is filled with
false information and misleading image.
Third, there is no possibility of infinite speed even without friction, since the theory
of relativity sets the light as the speed limit. Therefore, the static model of demand and
supply curve is not capable of explaining macro dynamics including business cycles and
Forth, the nature of transaction costs is useless high entropy waste such as heat and
CO2 while the nature of production cost is useful low entropy materials such as raw
material and electricity (Ayres 1998). An organization or institution with zero transaction
costs implies a heat engine without release any wasted energy in the form of heat
dissipation. This engine cannot be made since it violates the second law of
In short, Coase even failed to understand elementary physics. The Coasian world
cannot serve as a theoretical argument for the Coase Theorem.
1.3. Confusing Economics of the Coase Theorem
Let us assume that Coase could drop the false analogy in physics but still maintain his
popularity among economists. Can we get economic insight from the Coase Theorem in
We may first examine the issue of the Coase conjecture that a durable goods
monopolist would adopt a marginal pricing (Coase 1972). Like his 1960 paper on social
costs, it triggers a new round of controversy without a clear conclusion (Fehr and Kühn
1995). Coase himself may realize that it contradicts his earlier finding that marginal
pricing was difficult to work even for public utility, since he excluded his 1972 paper
from his 1988 collection (Coase 1972, 1946, 1988a). There is a remarkable divergence
between single equilibrium picture based on demand-supply approach and multiple
equilibriums in game theory. Both approaches are based on representative agent models.
So far, economists have not develop a working approach similar to statistical mechanics
and molecule kinetics, which can answer the question how interacting particles can reach
an equilibrium level of speed or temperature without the need of a homogenous group.
When Coase accepted Cheung’s definition of transaction costs as institution cost,
Coase did not realize that Stigler (and himself) and Cheung had conflicting
interpretations of competitive price.
For Cheung, if transaction cost is zero, monopolies would have perfect information of
consumer’s preferences, so that they could exercise perfect price discrimination (Cheung
It is known that the concept of competitive equilibrium is based on arbitrage free
opportunities, which in turn implies linear pricing (Ross 1976). Perfect price
discrimination is nonlinear pricing or different price for different people. It rules one
price law in perfect competition, which is the core of market fairness by property right
school and self-corrected stability in equilibrium economics (Alchian 1987).
Therefore, the Coasian world is not a consistent theory in economics too. We have to
find a new perspective in studying the transaction costs approach.
1.4. Cheung’s Reformulation Based on the Symmetry Assumption
To save the Coase idea of transaction costs, a symmetry assumption was proposed to
reformulate the Coase Theorem (Cheung 1998):
“The transaction costs paradigm in which I was brought up – and here I am
sure Coase fully shares my view – has the merit that it entails only the simplest of
economic tools. In fact, this paradigm contains no new theory whatsoever to
Only three fundamental propositions are present in the (transaction costs)
paradigm. First is the postulate of constrained maximization. Second is the
downward sloping demand curve, which (because there is no need to separate
consumption and investment activities) also covers diminishing marginal
productivity. Third is the notion that cost is the highest-valued option foregone.”
Originally, Coase only proposed one specific symmetry: “the reciprocal nature of the
(externality) problem” where “both parties (say, the polluter and the victim) cause the
damage” (Coase 1960). Cheung further identified the hidden symmetry assumption in
equilibrium economics: the symmetry between consumption and investment, or the
symmetry between demand and supply, which was justified by the principle of
diminishing marginal returns.
1.5. The Symmetry Principle in Classical Physics and Equilibrium Economics
The symmetry principle plays a fundamental role in the theory of equilibrium physics.
It is known that basic laws in physics can be characterized by some types of symmetry.
There are two fundamental symmetries in classical physics: time symmetry from the
law of energy conservation, and space symmetry from the law of momentum
conservation, which are valid in Hamiltonian systems, i.e. the world without friction.
Symmetry principles in classical physics have important implications: stability and
reversibility. In another words, history does not matter in simple Hamiltonian dynamics.
A simple structure with a high degree of symmetry can be constructed, including a
perfect gas, crystal, or fluid.
Symmetric construction is widely used in modeling a laissez-faire economy. For
example, linear demand and supply curves have visible symmetry in economic textbooks.
Especially, the popular Cobb-Douglas utility and production function have symmetric
forms. Information symmetry is implied in perfect competition. Symmetric formulation
of players in game theory, consumers and producers in the micro model and macro
models are widely used in economic theory.
The symmetry argument also played an important role in the debate against the
Keynesian economics. For example, Keynes’ monetary theory of unemployment violated
the symmetry property in mathematical economics, since demand and supply function
with price and quantity should be homogeneous function of degree zero (Leontief 1936).
Technically speaking, symmetry between demand and supply is assured by a
downward demand curve or a decreasing return to scale. Coase could justify his
reciprocal relation between farmer and rancher only if the rancher’s cattle business was
operating under diminishing returns.
The question remains whether the Coase-Cheung symmetry principle has solid
foundation in theory and reality?
2. Symmetry Breaking in Evolutionary Thermodynamics and Division of Labor
The macro world greatly differs from the micro world in physics, which is
characterized by symmetry breaking in thermodynamics. A time arrow played a
constructive role when life emerged as a symmetry breaking process in open systems
(Prigogine 1984). Fundamental causes of a time arrow are rooted in nonlinearity and the
Life evolution has shown a series of symmetry breaking process: say, from point
symmetry in drop-like creatures in the sea, to line symmetry of a higher kind in plants
and animals. Similarly, social evolution such as the division of labor, war and revolution,
is also a symmetry-breaking process. The symmetry principle in equilibrium thinking and
symmetry breaking in evolutionary thinking provide a theoretical platform for debates
among different school of thoughts (Foster 1993).
2.1. Asymmetry in Economic Complexity and Market Disequilibrium
All economic complexity, irrational behavior, and market failure can be traced to
some form of asymmetry of dynamic mechanism. For example: information asymmetry
in exchange and loss aversion in decision making is responsible for market failure and
irrational behavior (Akerlorf 1970, Kahneman et al. 1990). Asymmetry in demand and
supply can be visualized by an S-shaped demand curve and a Z-shaped supply curve
(Becker 1992, Dessing 2002). Asymmetric power also appears in game theory in the
study of cooperation and conflicts.
The most remarkable feature in an industrial economy is the asymmetry between
consumer numbers and firm numbers, which signals the tremendous power of industrial
organization (Chen 2002).
Cheung once reframed the Coase question on the nature of the firm in such a dramatic
way: “Why, in a free-enterprise economy, would a worker voluntarily submit to direction
by an entrepreneur or an agent instead of selling his own output or service directly to
customers in the market?” (Cheung 1987).
Any unemployed worker could easily perceive the asymmetric power between poor
labor and an organized capital. No worker would submit to a self-appointed boss without
compensation above his previous income as self-employed. The common-sense answer to
the nature of the firm is certainly creating value, rather than reducing transaction costs!
Coase reversed the order simply because equilibrium economics denies the existence of
profit in a closed system without innovation.
Stable price equilibrium in the Arrow-Debreu model is relevant to atomic economies
without product cycles, product innovations, supply chain and networks. For an industrial
economy, symmetry breaking between consumption and investment resulted from round-
about production and product cycles (Hayek 1935, Chen 2006).
2.2. The Creative Nature of The firm and the Asymmetric Aspects of Transaction
In the case of GM acquiring its supplier Fisher Body, Coase did not gave any
empirical evidence on the scale of transaction costs, but did provide two clues of other
factors: First, GM’s previous contract with Fisher Body was based on the mark-up
pricing rather than marginal pricing; its profit was fixed at 17.6% of cost. Second,
reducing business uncertainty seemed a main motivation in acquisition (Coase 1937,
1988b, 1988c, 2000). His argument for transaction costs was a theoretical assumption
that the firm size was determined by the balance between deceasing transaction costs and
increasing organization costs within the firm. This logic implied non-convexity of
varying (first increasing then decreasing) returns to scale, which was a visible departure
from his belief in diminishing returns in price theory. It is also an inward looking view of
corporate strategy, or a firm theory without competitor.
The Coase concept of transaction costs has two implicit assumptions: one was that
transaction costs were symmetric to both sides of exchanges; the other was that market
competition would drive down transaction costs, just like the similar mechanism for
Coase ignored possible asymmetric aspects of transaction costs in market competition
(Vogel 1987, Glaeser, Johnson, and Shleifer 2001). For example, deregulation policy
could reduce transaction costs for producers, but increase information asymmetry and
transaction costs for consumers. The firm boundary itself implies an increasing
information barrier to outsiders but a decreasing information barrier to insiders. There are
numerous examples of increasing transaction costs under market competition. For
conservative producers, reducing marketing cost as overhead would increase current
profit; but for aggressive producers, increasing marketing expense as a strategic
investment might increase market share. For high tech firms like Microsoft, marketing
costs may be even larger than production and development costs.
To have a new understanding of the origin of the firm, we may consider a similar
question in biology: What is the origin of life?
It makes no sense to say that the emergence of life is driven by reducing entropy
production, rather than increasing adaptability or learning at the costs of increasing heat
emission. As Georgescu-Roegen pointed out (Georgescu-Roegen 1976):
“Thermodynamics is at the bottom a physics of economic value … and the
Entropy Law is the most economic in nature of all natural laws. … The Entropy
Law is the taproot of economic scarcity.”
The cost-benefit analysis is meaningful only if the cost can be compared with the
value being created. We may better consider the other side of the coin: the creative nature
of the firm in Schumpeter economics, since transaction costs are difficult to measure in
the dissipative process. Firms create value or increase organizational capability by several
means: developing a scale and scope economy, increasing innovation in developing new
products and new services, decreasing risk and uncertainty, say, controlling external
shocks in vertical integration and diversifying risk in horizontal integration, etc (Chandler
Economics of contracts and governance did reveal some factors in incentive
mechanism and internal control (Cheung 1964, Williamson 1979, Hart 1995, Holmström
and Roberts 1998). However, in the simpler case of sharecropping, it was found hard to
make a choice between different forms of contracts, say, wage, rent, or sharecropping,
based on a comparison of transaction costs. It was relatively clear for decision making
based on risk analysis (Cheung 1969, Stiglitz 1974).
Here is a dramatic example in recent events. During economic transition in the former
Soviet Union in 1990s, Russia’s real GDP declined 43% and Ukraine 61%, but their
currencies devalued more than 5000 times and 70000 times respectively (Chen 2006)!
Even if you know your business and your market, how could you predict that the shock
therapy in liberalization would generate inflation spiral and break down your cash flow?
Does the Coase Theorem can estimate the magnitude of coming transaction costs for
financial market deregulation?
If the nature of the firm and its governance is design of contract (Cheung 1983,
Williamson 1979), we may consider a new conductor who takes over an orchestra with
music score at hand. For some reason, he fired all the members of the old orchestra and
recruited new members for his own team. Do you expect that this orchestra would
perform as well as before?
2.3. The Wallis-North Paradox and Historical Trend of Division of Labor
All grand theories in economics seek inspiration from history. There seem two ideal
candidates for the Coasian market with minimum transaction costs: “hunting bands” and
“(financial) markets in which transactions are highly regulated” (Coase 1988a).
However, the Coase belief of a decreasing trend in transaction costs was challenged
by the Wallis-North paradox, it showed that the aggregate transaction costs in the US
grew from about 25 % of GDP in 1870 to more than 50% in 1970 (Wallis and North
1986). This finding is consistent with self-organization theory and complexity science but
a paradox for the transaction costs paradigm (Forster 1993, Chen 2005).
To explain China’s recent reform by the transaction costs approach, Cheung proposed
a different scheme; it assumed that a market transition was a process from infinite
transaction costs with trade barrier before, and much less transaction costs after reform
(Cheung 1986, 1998). If we compare the simplistic life style in Mao’s era before the
1970’s and an affluent variety in Deng’s market economy, the increasing trend of
transaction costs is visible from a rapid growth of marketing, accounting, lawsuits, and
regulations along with rapid economic growth. In any case, there is no possibility of a
decreasing trend of transaction costs suggested by the transaction costs approach.
If we accept that the primitive tribe has little information and asymmetry and least
marketing cost, then the transition from the hunter-gatherer society to proto-type market
needs a quantum jump in transaction costs rather than an increasing trend. This scenario
is a counter-historic view of human civilization. It is noted among economists
“Thermodynamics is at bottom a physics of economic value – as Carnot
unwittingly set it going – and the Entropy Law is the most economic in nature
of all natural laws.”
Transaction costs may have a small U-shaped dip or wavelike movements with
technology progress, in addition to an upward trend. However, the whole history of the
division of labor has been characterized by increasing discovery of new resources and
increasing consumption of energy along with increasing release of waste and heat.
Government inaction is a dangerous policy for pollution, SARS, and global warming.
How can we imagine a Coasian world with decreasing transaction costs?
2.4. Barriers to Exchange and Sources of Social Conflicts
Coase simply disregards the possibility of persistent conflicts without a negotiated
solution, he argued that “traits (of neither buy nor sell)… have little survival value”
(Coase 1988a). Therefore, we should discuss the barriers to exchange and the sources of
Coase did make significant contributions in promoting a market solution for public
goods and externality. With symmetry analysis, we can easily judge the working
condition for bilateral bargaining with some limitations, since competitors are near
symmetrical in auction radio frequency, selling pollution rights, or operating a lighthouse
(Coase 1959, 1974, Noam 1988).
In contrast, there was much doubt about the Coase solution for social conflicts, such
as a noisy neighbour, pollution, and animal trespassing (Rusmusen 1998). Empirical
studies found no empirical evidence for the Coase assumption of symmetric relation.
First, non-convexity, such as an increasing return to scale and fixed costs, can be a
significant cause of symmetry breaking in bilateral bargaining. In the case of California’s
animal trespassing law, ranchers would increase cattele without bounds if they had the
property rights. Historically, switching the property rights from pro ranchers to pro
farmers did change people’s behavior and the agriculture structure in California (Vogel
Second, the downward sloping demand curve is reasonable only for a positive utility
generated by pleasure. For a negative utility such as noise or pollution, the demand curve
must be upward if the polluter had no pollution rights and had to pay compensation to the
victim. There is no symmetry between the polluter and the victim. In addition, free legal
service (in the sense of reducing transaction costs) may encourage lawsuits rather than
further settlements outside the court (Simpson 1996). The real issue for proper regulation
and government action is not a simple argument for choosing smaller transaction costs,
but a careful balance among market efficiency, social stability, and economic
Third, income and wealth effects are essential factors in social cost (Hurwicz 1995).
Friedman pointed out that the condition for downward sloping demand was invariance of
real income, not nominal income, which implied a macro foundation on the non-existence
of unemployment (Friedman 1953, Cheung 2001a, Chen 2002). This condition sets
further constraint to the Coase proposal of government inaction, since social stability
demands government policies in managing business cycles, including monetary, fiscal
and tax policies.
Fourth, power asymmetry may lead to a breakdown of the political Coase theorem
(Acemoglu 2003). Economic intrestets for a privileged group may outweigh the welfare
of the majority of people.
Finally, political and ideological factors of conflicts and war also have an economic
source. The endogenous root of a business cycle, in the form of excess capacity or
banktrupcy, is the price paid for creative destruction. There are tremendous sunk cost and
learning uncertianty associated with replacing technologies (Chen 2005). Strategic
competition, not price competition, greatly increases transaction costs in an innovation
From the above analysis, we can see that Coase made little cases which had
convincing evidence for supporting the Coase Theorem, the Coase Conjecture, or the
Coase belief. Coase made a constant call of observing the real world, which got a cold
review on Coasian economics (Rusmusen 1998):
“Poor Professor Coase, What ironies he has inspired! He is known
almost exclusively for three papers: … (1937, 1960, 1972). Each of these is
theory, albeit verbal theory, with almost no empirical content. Yet for many
years Coase has called for an increase in the amount of intelligent
descriptive empirical work in economics, and has shown how to do it with
his own careful case studies. These case studies are little cited, but they are
even less initiated.”
Intrestingly, Samuelson, one of the founders of neoclassical economics, had much
better assessment in the limit of current economics (Samuelson 1995):
“Allocation of property rights – and how they are to be defined - matters
mightily. They are the chips in the game of dickering, threatening, and
litigating. …… Only in certain Santa Claus situations – constant returns to scale,
infinite divisibility, free entry, dispensed ownership of each grade of factor,
shared knowledge, complete markets – only then will Smithian self-interest be
compelled to achieve Pareto-Optimality.
To try to capture all that which contributes to deadweight loss under the
verbal rubric of “transaction costs” weakens a useful concept without gaining
understanding of incompleteness of markets, asymmetries of information, and
insusceptibilities of various technologies to decentralized pricing algorithms.