An Origin of

the Neoclassical Revolution: Mill’s“Reversion” and its Consequences
Y. Shiozawa
Rough draft 2015.8.1
First draft 2016.8.3
Second draft 2016.10.7
This is the second draft of a paper before English revision. The first version was
titled Mill’s Reversion and an Origin of Neoclassical Revolution / An Internalist View
(and uploaded in RG). This is planned to be published in 2017 as a chapter of a bookthat commemorates 200 years after the publication of David Ricardo’s Principles of

Political Economy and Taxation (the first edition). When the final version is
published, it will be announced in the comment to this working paper.
2016.11.15§1. Introduction

2§2. The nature of neoclassical revolution

2§3. Essential difference between classical and neoclassical economics 6§4. The neoclassical revolution in a wider historical perspective 14§5. Mill’s unintended “solution”

18§6. How is Mill’s “solution” misplaced?
§7. Mill’s “solution” and after

29§8. William Stanley Jevons

34§9. Francis Ysidro Edgeworth

43§10. Alfred Marshall23

46§11. Alternative way outs? / Senior, Mangold and Sidgwick 54§12.What was the neoclassical revolution? Implications for Future Research 59
Acknowledgement
References

60

62

Figure 1

21

Figure 2

23

Figure 3371§1. Introduction
In the history of economics, we can detect two major price theories: one is classicaltheory of value and the other is neoclassical theory of value. The change fromclassical to neoclassical was the biggest turn in the history of economic theories
and is called neoclassical revolution. Factors which paved the way to theneoclassical revolution are numerous. Many explanations were made fromexternalist point of view, i.e. explanations from the social, political, andphilosophical backgrounds. Here I present an internalist explanation, i.e. one by the
logic of scientific or theoretic development. I argue that, when John Stuart Mill tried
to solve the international value problem, he was forced to revert from classicalprinciple of cost determination of value to a special form of the law of demand andsupply. This marked a crucial turning point. The aim of this paper is to prove thiscontention.
The paper is composed in the following way. Section 2 explains the nature ofneoclassical revolution. Section 3 complements section 2 by making essential
difference of two value theories more visible. Section 4 argues the nature ofRicardian revolution and situates the neoclassical revolution in a new perspective.
Section 5 spots the point of origin of neoclassical revolution and section 6 explains
why Mill’s “solution” and his thesis for reversion were misplaced. Section 7 gives a
bridge between Mill and three founding fathers of British neoclassical economics.
Three following sections give individual accounts of Jevons, Edgeworth andMarshall in this order. I will show that all three fathers were deeply influenced byMill's misleading solutions. Section 11 shows that there were possibilities ofalternative way outs. Section 12 summarizes the paper and gives some hints forfurther investigations.

§2. The nature of the neoclassical revolution
I have not explained how Mill’s “solution” was misdirected. It is the task of section 6.
Before proceeding to this task, let us see the consequences of Mill’s “solution.” Mybold conjecture is that this was the very point of turn from classical economics toneoclassical economics, or in other expression conversion from plutology(economics of production) to catallactics (economics of exchange). I owe to J. R.
Hicks (1974, 1976) this characterization of the neoclassical revolution. This must be
the main feature of the neoclassical revolution. Hicks explains this as follows:2while the classical economists looked at the economics system primarily fromthe production angle, the catallactists looked at it primarily from the side of
exchange. It was possible, they found, to construct a ‘vision’ of economic life
out of the theory of exchange, as the classics had done out of the social
product. It was quite a different vision. (Hicks, 1976, p.212) 1
Hicks defines plutology and catallactics as the difference of the focus of attention.
This is an important difference that contrasts two attitudes but it may induce amisunderstanding that plutology or economics of production does not think about
exchange. This is a pure misapprehension.
The main difference between economics of production and that of exchange lies on
the understanding how the values of goods are determined. As I will argue in thenext section, the core of economics is the theory of value. Classical theory of value,
best represented by the Ricardian theory, contends that values are determined byproduction conditions. Neoclassical theory of value assumes that theory of value ispossible without any reference to production conditions. Pedagogically it starts
from a pure exchange situation. As an inevitable consequence of this abstraction,
psychological factors become dominant. It depends too much on the individual
agent’s ability to deal with total economic processes. There comes the necessity toassume infinite rationality for the agents.
The neoclassical theory of value may be a universal theory that is valid for any
economic era and situation, but not a good theory of capitalist economy where
producers play predominant roles. The classical theory of value presupposes acapitalist production, or a market economy whose principal players are industrial
firms that produce commodities (goods and services) by employing workers andmachines. 2 The neoclassical revolution was not only a change of the focus ofattention, but a change of logic and structure in the theory of value.
When we talk about neoclassical revolution, we have to take into account that, atthe time of neoclassical revolution, economics was not yet a unified discipline that
Hicks preferred to use the term “catallacticist” instead of “marginalist.” I use theexpression “neoclassical revolution” to indicate that the revolution comprises much
more wide changes of economic thinking.
2 For more detailed account of classical theory of value, see Shiozawa (2015).
1

3

economists in different countries have the same framework of research. Indeed,
economics of French speaking countries or that of German speaking countries hasvery different history than that of English speaking countries. In this chapter, I only
examine an origin of the neoclassical economics in the United Kingdom. In theContinental Europe emergence ofneoclassicaleconomics

and

thus

the

neoclassical revolution took very different courses and we have to observe themfrom a totally different angle even if we admit that neoclassical revolution was an
instance of simultaneous discoveries.
The emergence of neoclassical economics in the UK is a subject most often
examined and argued. However, as I have indicated above, majority of explanations
were made from externalist views. I advance in this chapter a conjecture that theneoclassical revolution was led mainly by the internal logic of economics. This istotally an internalist view.
This internalist view is necessary because of the peculiarity of the neoclassicalrevolution in the UK. If the neoclassical revolution is a turn from economics ofproduction to that of exchange, we have to admit that this reverses the order ofhistorical development. In a very old time where trade was only made between
communities, exchange rates may have no close relations to the cost of production.
Exchanged things were surpluses of communities’ necessity. The peculiarity of theneoclassical revolution is that it came after the industrial revolution. The industrial
revolution was the most conspicuous event which took place in the time of classicalpolitical economy. Why did neoclassical economics, which came after the industrial
revolution, ignored this extraordinary phenomenon? It must be even then apparent
that tremendous rise of commercial activities is supported by rapid increase of
production volumes. Externalist view does not explain this most conspicuous fact.
This chapter advances a conjecture that the neoclassical revolution was a logicalprocess in the development of economic theories. We contend that neoclassicalrevolution was prepared by John Stuart Mill’s study when he wanted to solve an
unsettled problem left by Ricardo. It was the question of theory of value in theinternational trade situation. As this is a conjecture which came to my mind recently(in four or five years ago), and as the stake is extraordinarily big, I do not claim that
this chapter provides sufficient evidence to prove my conjecture. It requires
enormous work in the history of economics and I have to ask some others to try to4verify or falsify my conjecture. This section remains a rough description of what
may have possibly occurred.
John Stuart Mill did not abandon the very core of classical value theory but he wasobliged to make a structural reform on the logic of value theory. There were threemoments for it. The most important category of commodities that does not obey thelaw of the cost of production was labor (Mill, Library III.2.19). The second was thejoint cost cases (Mill, Library III.16). International values formed the third category(Mill, Library III.16.14). Mill had to admit, if reluctantly, that the law of demand andsupply as an anterior and more fundamental law than the cost of production theoryof value. This was the first consequence of Mill’s “solution”. Ricardo once declaredthat “[t]he opinion that the price of commodities depends solely on the proportionof supply to demand, or demand to supply, has become almost an axiom in political
economy, and has been the source of much error in that science.” (Ricardo: Sraffa
p.382; Library 30.3) Mill knew this and had to reconcile Ricardo’s theory of valueand his new “solution”. What Mill did was to admit the law of demand and supply as
more fundamental and logically anterior to the cost of production theory of value.
Mill stopped at this point, for this was the maximal possible concession he could
make. But economists after Mill did not. They had searched to make their theory
more coherent and unified. Here comes the second consequence of the Mill’s“solution”.
If the law of demand and supply is more fundamental, it is natural to apply this law
uniformly and universally. My suspicion is that English founders of neoclassicaleconomics were influenced by the Mill’s “solution” and his conclusion. Jevons,
Marshall, and Edgeworth show more or less indicative evidences for this suspicion.
As Jevons is thought to be the person to have led the marginalist revolution,
examination of Jevons will inevitably be longer than Marshall and Edgeworth.
I do not deny that other factors intervened in the arrival of the neoclassicaleconomics. Spread of optimization techniques (in mathematics), tradition ofutilitarianism (in philosophy), deep-rooted tradition of demand and supply thinking(in economics), popularization of the concept of functions, and finally the generaldecline of Ricardian economics. Mirowsky (1989) argued that "energy" concept
was crucial to the arrival of neoclassical economics.

5

All these factors must have worked indeed. But we should ask how direct thesefactors worked in the formation of exchange economics in place of production
economics. Their influences are indirect, whereas impact of Mill’s “solution” was, I
believe, more direct than others. Above all, Mill was logically forced to accept thatthe law of demand and supply is anterior and more fundamental than the cost of
production theory of value. If we admit that the cost of production theory of value
was the center core of the classical economics, it was this internal logic that drove
economics of production to that of exchange. All other factors are external to thelogic of economics. I agree that the change of society or sciences drive economics
to a new direction. However, if economics is an independent science, we shouldsearch internal logic that produced the neoclassical revolution. As it is called
revolution, it was really a fundamental change of logical structure of economics. It
is strange if there is no internalist explanation. My conjecture is one of those scarceinternalist explanations. 3
As far as I know, no one has ever claimed that Mill’s “solution,” or his situation
setting was one of key factors that forced the arrival of neoclassical economics. I
believe this conjecture deserves a scrutiny.

§3. Essential difference between classical and neoclassical economics
The core of an economic theory is the theory of value. The theory of value exposesin a most abstract form how an economy works. It exhibits the vision of a specifictheory. There are many different aspects between classical and neoclassicaleconomics but the essential difference appears in theories of value. Consequently,
in this section, I discuss the difference of two value theories and contrast them.
When we compare two theories of value, classical and neoclassical, the first thing
to do is to define what the classical theory of value is, because there is no unified
understanding on what it is. As for neoclassical theory of value, there would be noserious confusions. Neoclassical theory of value comprises various strands ofHicks (1976) asked himself how we can explain the rise of catallactics. He examinedsome possible explanations such as reaction to socialism and the change in the realworld, but he denied these as major factors and advanced a thesis that the main appealof catallactics lies in its intellectual quality. Walras made it possible to thinks of
economic system as a system of interactive markets and Menger as an adjustment ofmeans to ends. Hicks estimates that Jevons did not completed his system. In this sense,
Hicks tries to understand the neoclassical revolution on an internalist standpoint but
he does not mention the point I argue in this chapter.
3

6

economic thoughts from Marshall and Walras to Arrow and Debreu. However, they
have a common core. They are all theories of prices. They put paramountimportance on the function of prices. Prices permit the whole complex economy towork, effectively and efficiently. The core of these theories is composed of twoparts: one is the utility theory of value and the other is demand and supply
equilibrium. No specific structure is required as the theory holds for all situations.
Classical theory of value has no such unified theoretical core as the neoclassicaleconomics has. In the era of classical economics, laws of demand and supply
existed. Utility was an important component for many economists. Therefore, main
components of neoclassical economics existed already in the time of classicalpolitical economy. I do not try to unify various strands in a single framework. If I doit, it would be a total confusion. Instead, I pick up the most typical theory and define
it the classical theory of value. I have chosen Ricardo as such a representative.
Many people will agree with me. Indeed, Ricardo’s theory of value is a culminationof various classical theories. However, there are still many misunderstandings onwhat Ricardo’s theory of value is.
As Ricardo’s theory of value, many economists may think of the labor theory ofvalue. As Marx adopted it at the core of his theory, many Marxists would think it
granted but my idea is different. My definition of Ricardo’s theory of value, andconsequently of classical theory of value is the cost of production theory. This
claim has textual evidence. Ricardo himself added in the third edition of his
Principles a note explicitly claiming this. In fact, he wrote:
Mr. Malthus appears to think that it is a part of my doctrine, that the cost andvalue of a thing should be the same---it is, if he means by cost, “cost of
production” including profits. (Ricardo: Sraffa, p.47; Library, I., n.7)
The idea is similar to what Marx later argued in terms of production price. We haveno space to argue this interpretation here. Read Takenaga (2016) for a moredetailed textual examination. As for the possibility of developing Ricardo’s idea as amodern theory, see Shiozawa (2016).
Essential feature of cost of production theory of value is its objective charactercompared with the subjective character of the neoclassical theory. By the word7

objective we mean that the value of a commodity is determined by social conditions.
The core contention of cost of production theory of value is that prices areprimarily determined by the cost of production including profit. In a more modern
terminology, this is to say that prices are determined by the full cost principle. If weuse mathematical expression, the price vector p is given by a system ofsimultaneous equations:(I + M){ w a0+ A p} = p.

(3-1)

We skip the notations of symbols used here, because they are not used in thefollowing. Those who are interested in this expression are required to consult mypaper (Shiozawa, 2016, equation 6).
Many factors are involved in the determination of cost of production. First,
production techniques. As a part of knowledge, production technique has asubjective aspect, but a production technique can be specified by input-output
relations which are measured objectively. When all inputs that are necessary for the
production of a unit of product are known, the cost can be calculated objectively. 4
The expenditure for a kind of inputs is the value times the quantity of the input. If
we know the value of all inputs including wages, we can calculate the total
expenditure. It is noteworthy that the expenditure is totally observable quantity
which has little relevance with toils and pains even if human work is involved 5. The
cost is the sum of all expenditures that were necessary to the production multiplied
by a markup factor. The markup factor is 1 plus the markup rate. The total
expenditure is to sum up all expenditures and the full cost of the product is the total
expenditure times the markup factor, or 1 plus the markup rate. The markup rate is
fixed by custom or by calculation for the moment of consideration. We can argue
how markup rate changes by the change of market conditions, for example by thechange of competitive conditions. 6
However, to determine the cost of production for all products in an economy is not a
4 For simplicity, we assume that production is linear, i.e. inputs and outputs are directly
proportional.
5 There is no necessity to ask if it is proportional to toil and pain (or real cost after
Hollander). See Chapter ** (Tabuchi 2017 in this volume).
6 See for a short account Shiozawa (2016) under the heading How are markup rates
determined?. Matrix M in equation (3-1) is the diagonal matrix whose j-th diagonal is
the markup rate mj for product j.

8simple operation, because costs depend on values. Here we have a logical cycle. To
define the cost of a commodity, we should know the value of all inputs. At the timeof Ricardo, system of equations was not widely known and we can easily believe
how difficult it was for Ricardo to build a cost of production theory of value. This
explains partly why Ricardo often talked about cases where the product is madeonly by labor. He could include indirect labor but he could not give a precise formulaas equation (3-1).
What was more difficult was the question of choice of production techniques.
Imagine a situation when you have two production techniques which give the same
product. In that case, the superiority of a production technique depends on values.
When you know all the input prices, it is the simple question of adding up. However,as a theory of value, you have to determine values by costs and the costs ofproduction depend on values. How does a system of production techniques come tobe chosen in such a way that all chosen techniques have the least production costamong techniques that produce the same product?
This is a theorem which was found and proved in the mid 20th century. It was Paul
Samuelson who discovered this theorem and named it “substitution theorem” at
first

and

later

“non-substitution

theorem.”Samuelson

only

provedthetwo-commodity case and Koopmans proved the three-commodity case and K.
Arrow the general case (Koopmans, 1951). Confusion of the naming shows
Samuelson did not understand the real meaning of the theorem. I prefer to call thistheorem minimal value theorem, because this assures the existence of a system of
production techniques that gives the minimal value system given the wage rate. 7 In
mathematical expression(I + M){ w a0+ A p} ≧p.

(3-2)

for all production techniques and equality holds for a system of production
techniques that covers all kind of products. Readers of this book will easily noticethat the fundamental theorem of the new theory of international values (Chapter 1,

It is widely quoted that minimal value or non-substitution theorem holds only when
no fixed capital goods exist. This is a serious misunderstanding because the theorem isvalid in the situation that durable capital goods keeps their efficiency within the
depreciation period and are discarded afterwards. See Shiozawa (1975).

79theorem 3.4 equation iii) is a simple generalization of (3-2). 8 Sraffa (1960) gave noremarks on this theorem, although he explicitly treated the question in Part III
Switch in Method of Production. 9
As I have argued in Shiozawa (2016), classical theory of value has taken a complete
form, only in the latter half of the 20th century. Evidently this is in contradiction toJohn Stuart Mill’s contention that the classical theory of value is complete by 1848
(Mill: Library III.1.2). Although Ricardo could not develop a theory of simultaneous
equations or know the minimal value theorem, he knew by his deep insight that thevalue of a commodity stays constant regardless of sudden changes of the demandor the supply of the commodity and this in the presence of plurality of production
techniques. He knew that “prices always vary in the market, and in the first instance,
through the comparative state of demand and supply” (Ricardo: Sraffa 119 Library
6.28). However, he knew also that the market price comes back to the natural value,i.e. to the cost of production, after the first disturbance settles down.
In Ricardo’s theory of value, demand and supply play no role except that they are
only disturbing factors. The values are determined by production conditions
together with normal profit margins. If demand changes, production changes
correspondingly. If the production adjustment proceeds, the market price returns to
the value. 10 In this way, supply and demand have little to do with the determinationof values. This abstraction of demand and supply relations from the theory of value
is remarkable, because this is to recognize that the essential feature of modern
economy is the primal independence of values and quantities. Values are
determined by production conditions which are mainly technological. Quantities are
regulated by the demand that is requested at the value of the product. This was thereal content of the Ricardian revolution. In an industrial society, Ricardo observedthat it is the conditions of production that determine value relations. In fact, if thedemand of a product changes with whatever reason it may be, the volume of
In Chapter 1, A is the matrix of net production coefficients modified to an equivalentsystem. In this chapter, A denotes the matrix of input coefficients. Equation (iii) can be
rewritten in this chapter’s notation exactly in the same form as (3-2) if vector w is
replaced by a scalar w.
9 Sraffa may have been aware of this theorem in the form of what he dubbed“Borkiewicz’s dictum”. See Gehrke and Kurz (2006).
10 This became much more conspicuous because production adjustment speed became
faster in many industries. Modern industrial firms since the 20th century have lessnecessity to appeal to the price adjustment to adapt themselves to the demand changes.
810

production can change and adjust it to the changed state of the demand. As far as
cost of production remains constant, there is no reason that prices changes.
Few economists, in his time and after him, understand this. Ricardo must have akind of quantity adjustment ideas. In fact, he argued in this way:
the proportion between supply and demand may, indeed, for a time, affect themarket value of a commodity, until it is supplied in greater or less abundance,
according as the demand may have increased or diminished; but this effectwill be only of temporary duration. (Ricardo: Sraffa pp.383, Library 30.1)
It is clear that Ricardo assumed that the supply of a commodity or the production
would soon be adjusted to the demand. If not, there is no reason that the pricewould come back again to the original price (natural price). In this sense, Ricardo
had in his mind a quantity adjustment mechanism if it was quite different from what
we imagine by this term. Classical theory of value presupposes that the supply
adjusts to the change of the demand. This is typically a situation of the capitalist
economy. Few economists in his time understood that at the back of Ricardo’s
theory of value a special supply attitude is assumed. It was not written explicitly but
is a principle that is twined with Ricardo’s price theory (Shiozawa 2016). It is theprinciple of effective demand at the firm level.
It is here necessary to note that even after Ricardo few people including economists
did not understood this very core of Ricardian theory of value. I will argue this pointin the next section. The vision that prices regulate discrepancies of supply anddemand was an old common knowledge. Ricardo objected to this common sense.
John Stuart Mill was a good and loyal interpreter of Ricardo but he was the firstman who noticed that the cost of production theory of value did not hold in the caseof international trade. Probably after a long reflection, he claimed but cautiouslythat we must “revert to a principle anterior to that of cost of production, and fromwhich this last flows as a consequence,—namely, the principle of demand andsupply” (Mill 1844, Library I.19. Similar expression appears in Mill 1848, Library
III.16.5). After Mill, three founding fathers of neoclassical economics (i.e. Jevons,
Marshal and Edgeworth) all accepted Mill’s contention and began to argue in termsof demand and supply.

11

My main contention in this chapter is that Mill’s “solution” was in fact misdirected
and the Mill’s conclusion that recommended the reversion to the law of demand andsupply misguided the economics to the neoclassical revolution.
Mill opened a tradition to examine an interior vertex of the production possibility
frontier. It is the point that I named Mill-Jones point. The tradition continued untilvery recent days as we shall see in section 6. I myself have been a victim of thistradition when I was trying to write a paper which took form in Shiozawa (2007).
This paper was intended to be a successor to my paper in 1985 (written in
Japanese) and more than 20 years I tried continuously to find a theorem whichmight give sufficient conditions for the existence of interior vertices in the models
of input trade. Shiozawa (2007) was written when I found a theorem (Theorem 3.4),
which I cannot say was a very insightful one. Soon after that, I was liberated fromthe fixed idea and my obsession fell down. I observed the situation and I finallycame to know that John Stuart Mill in the mid-19th century and Ronald Jones in the
mid 20-th century were completely misguided by an obsession of price adjustment.
A naive simple method to rebuild the international value theory is to focus not on theinterior vertex but on the points in the interior of facets. When I acknowledged this, I
started to write papers which would compose Shiozawa (2014). The new theory ofinternational values was an extension of the cost of production theory of value. It
meant for me a revival of classical theory of value.
After 1960’s long discussions were made on the nature of neoclassical economics.
Manyeconomists

revealedthatmicroeconomics

comprises

vital

flaws.

Sonnenshein-Mantel-Debreu theorem (inadequacy of representative agents) 、
ubiquity of bounded rationality (impossibility of optimization), non-existence ofauctioneer (ubiquity of bilateral exchanges), capital reverse and reswitching(non-existence of scalar quantity of capital), inconsistency of the neoclassicaltheory of firms (irrelevance of marginal productivity theory), and many othermiscellaneous flaws (Beinhocker2006, Keen 2011, Shiozawa 2016). All these flaws
come from the basic structure of neoclassical economics. It relies on the individual
agents’ ability to adjust everything instantaneously. Such an adjustment may bepossible for a small economy composed of two or three persons and a few kinds ofgoods. This is the reason why neoclassical economics textbooks prefer to talkabout Robinson Crusoe. All these defects are the results of

its basiccharacteristics: economics of exchange. In opposition to economics of production,12

it intends to be a universal theory of economic activities. This abstract nature ofneoclassical economics induced it to rely too much on the individual human ability,
because it could not assume any social structure that supports economic activitiesof human individuals. Ricardo’s cost of production theory of value assumes aconcrete economic structure. This it the reason why it is dispensed to assume
omnipotent and omniscient human agents as it is generally done in neoclassicalmicroeconomics. The stake of the option between two value theories is extremely
great.
The main stream macroeconomics

now normally

examines

if

it hasa

microfoundation. However, this does not assure in any means that it is a sane
economics. Some economists pointed that the macroeconomics of these thirty was
spectacularly useless if it is not positively harmful. Minor inventions to adjust andmodify macroeconomic models cannot save this state of the art, because it isbased on fundamentally flawed microeconomics. As far as microeconomics stays
intact, microfounded macroeconomics remains fictive entity deprived of any reality.
It is now time to change our paradigm.
This paradigm change necessitates a new theory of value. Fortunately, it exists
already. It is the classical theory of value. We can start from it. The classical theoryof value had once a grave weak point. It lacked the theory of international values.
John Stuart Mill tried to attack this problem and he conceded to the law of demandand supply, because he could not build a theory of international values on theextension of Ricardo’s theory of domestic values. The question of international
trade was too important to neglect as exceptions. As we will see, this paved the way
to neoclassical economics. But now, the theoretical situation has changed. We havea theory of international values which is an extension of the classical theory ofvalue. The classical theory of value had to cede the place of orthodoxy of
economics once to neoclassical economics but now can take it back.
In the sequel, we will examine how neoclassical economics emerged from classicaleconomics in the United Kingdom. As I have warned it, I will not treat theneoclassical revolution in Continental Europe or any other places. Before
embarking on concrete examination, it will be useful to situate the neoclassicalrevolution in a wider historical context. We can thus link wormlike procession ofindividual theoretical efforts and a bird-eye view of the history of economic

13

theories.

§4. The neoclassical revolution in a wider historical context
The main feature of the neoclassical revolution was a change from plutology tocatallactics. It was the change from economics of production to that of exchange.
However, this revolution is not a simple revelation of a new truth. In view of classicaltheory of value, neoclassical theory of value is retrogression to an old common
sense. Almost one and a half centuries have passed since the arrival ofneoclassical economics. During those years, many components were introduced torefine it. First the concept of marginal utility. Then marginal products. preference
order, isoquant curve, decreasing returns to scale, law of diminishing returns (dueto input substitution), smooth production functions, constant elasticity functions,representative agent, (unbounded) rationality, rational expectations and manyothers. Do they prove a tremendous development of economics? Or are they anaccumulation of rubbishes which are attached to rescue and beautify the vital flawsof neoclassical economics? Neoclassical revolution must be situated in a wider
historical context. For this purpose, let us compare the history of economics withthat of sciences.
In the history of sciences, many wrong ideas were accepted as truth for a long
period. Many of school textbooks only tell how true theories were discovered bygreat scientists. However, as Thomas Kuhn (1962, Chapter 1 in particular)
emphasized it, truer history is more sinuous and full of deviations. Sciences develop
toward a wrong direction for a prolonged period. Wrong ideas persist and evendevelop in cases. Progress of a science is not necessarily a “development byaccumulation”. Once an intellectual tradition establishes, if it is true or not, it
continues in some cases for a long time before it comes out to be understoodwrong.
Phlogiston theory in chemistry survived more than a century until Lavoisierestablishes oxidation theory of combustion. Aether hypothesis as conveying
medium of light continued more than three centuries until Einstein announces his
special relativity theory. Sometimes an erroneous hypothesis came to bestrengthened by some most proficient scholars. In the case of Aether, Newton
played such a role by assuming "aethereal medium" to explain refraction and14diffraction.
In the time of a science revolution, something different occurs. Kuhn called it
paradigm change. Many parts of an old theory are overthrown at the same time. The
neoclassical revolution in economics is much more peculiar than common science
revolutions. My view on the history of economics is quite inverted from the common
understanding. There was once an essentially correct theory but it succumbed to a
new theory. The latter proliferated more than one and half centuries and now theold theory is resurrecting as a new hope. Even in the history of sciences we havenot many similar stories. Only one story I can cite is heliocentric theory. Everybody
knows that geocentrism occupied the mainstream of the astronomy for a long timeand reverted by Copernicus and others. This Copernican revolution paved the way
to Newtonian physics. However, heilocentrism was not a new idea in a strict sense.
We knew that a Greek philosopher named Aristarchus of Samos preachedheliocentrism in the Alexandrian age before Claudius Ptolemy wrote or edit

Almagest. Ptolemic system remained unchallenged more than one thousand years
until the arrival of modern science age. Unfortunately, Aristarchus’s paper was lostin the history and it was only transmitted that an idiosyncratic scholar called
Aristarchus advanced a theory that the earth goes around the sun.
If we consider this story, Ricardo is comparable to Aristarchus of Samos. Since thetime of John Stuart Mill until today, a geocentrism called neoclassical economics
occupied the mainstream of economics and Ricardo was the subject matter for
historians of economic theory. We are now expecting a Copernican revolution ineconomics.
Some may object to my comparison pointing that Ricardo was much more importantand influential economist than Aristarcus of Samos as astronomist. Indeed, Ricardo
was once the most reverend economist in England. Keynes once wrote in his

General Theory that “Ricardo conquered England as completely as the Holy

Inquisition conquered Spain.” (Keynes, 1936, p.32, Chapter 3, Section 3) Of
course, this is a Keynesian rhetoric. It does not prove how Ricardo was accepted in
the 19th century. Ricardo may have some strong influence on economic policies but
policies and theory are different things. I doubt if Ricardo’s theory of value wasreally understood by a wide range of his contemporary economists.

15

If Ricardo was established as a firm orthodoxy, it is incomprehensible why
oppositions to Ricardo’s theory flooded just after his death. A second classeconomist like Robert Torrens and members of Political Economy Club could claimthat all the great principles of Ricardo had been abandoned as erroneous by 1831
(Dobb, 1973, Chapter 4). In England, there were a few economists who understood
Ricardo’s theory of value. We may count James Mill, John Ramsey McCullock andJohn Stuart Mill among them. Ricardo’s contemporary economists such as Malthus,
Jean-Baptiste Say never agreed with or did not understand Ricardo’s theory ofvalue. Nassau Senior, whom I will mention briefly in Section 11, was fundamentally
against the Ricardo’s theory of value (Bowley, 2003[1937], pp.17-19), although histheory is difficult to understand as an integral whole. Ricardo’s objectivist theory
never really entered in France (Faccarello, 2014). German-speaking world case is
not very different from France. Major interpreter did not go further than J. B. Say(Gehrke 2014). This fact partly explains why Karl Heinrich Rau preceded
Marshallian cross for many years 11. Marx praised Ricardo as his precursor andsuperb analyst of capitalist system but never understood (perhaps intentionally) his
cost of production theory of value. If Dobb’s estimate is correct, Ricardo’s theoryof value gloried only about 10 years. Even if we count all years after the publicationof Ricardo’s Principles until the arrival of the marginal revolution, it is about 50
years. Neoclassical years now count about three times as long as Ricardian years.
Ricardo was an ephemeral phenomenon.
Aristarchus of Samos was once a famous mathematician and astronomer, but hewas almost completely forgotten by the arrival of Claudius Ptolemy and after that hewas the object to be cited as a strange doctrine claimed before Ptolemic system. If
we observe Ricardo from a long distance, Ricardo is quite similar to Aristarchus. He
is famous as an extreme case of classical political economy, but few economists
studied his theory of value seriously.
Keynes’s parable of Holy Inquisition is indicative. He only mentions the lack ofaggregate demand concept in Ricardo. He was not fair to cite Ricardo in this way.
Keynes wanted to make clear contrast between Say and Ricardo in one side andMalthus on the other side 12.
Baug (2001 p.159) reports that "the first appearance of subjective value theory and ademand and supply diagram-with price on the vertical axis as in Marshall-was in the
fourth 1841 edition of Rau's Grundsatze der Volkswirtschaftslehre (1826)."
12 Keynes cites as economists in the side of Malthus, K. Marx, Silvio Gesell and Major
1116

He was right when he said that considerations on effective demand were lacking ineconomists before him. If Keynes really understood Ricardo’s theory of value and if
he had asked advices from P. Sraffa, he could have build his theory of effective
demand in a completely different scheme. As I am claiming in elsewhere, theory ofeffective demand can and should be constructed on the basis of classical theory ofvalue (Shiozawa 2016, section 7; 2017). 13 Keynes missed his chance to define hisconcept of effective demand on a more firm basis if he accepted Ricardo’s theoryof value. Cambridge tradition did not permit him to do that. In the beginning of the20th century, Ricardo’s idea was completely wiped out even in Cambridge, England.
Ricardo lived in reality in “the underworld” for a long time and remained as a holder
of as curious theory as heliocentrism before Copernicus. My aim in this chapter is
to show how this happened despite of appraised authority of John Stuart Mill.
Young Mill tried to understand Ricardo’s problem and give a “solution” for it. His
solution was the real bifurcation point between classical and neoclassicaleconomics. In the following sections I will show how Mill’s “solution” was misguided
and how his “solution” determined the path of economics after him.
Let me add few more words on Ptolemaic system. I remarked that there is aparallelism between Aristarchus of Samos and heliocentrism in one part andRicardo and his cost of production theory of value. This parable inevitably implies
that neoclassical economics is compared to geocentrism. In these comparison,
they have many common points. We know that Ptolemaic geocentric system is afinely constructed exact science. After Copernichus’s book On the Revolutions of

the Celestial Spheres was published in 1543, many eminent astronomers remained
to support geocentric system. Tycho Brahe (1546–1601) was one of them. He was aDanish noble and could construct precision machinery for the celestial observation.
Aided first by a Danish King and then by a Holy Roman Emperor, he could build
observatories, in Denmark and later in Prague. At his life time, he was the mostprecise and comprehensive observer of the celestial world. This reputation
attracted Johannes Kepler to work as assistant to Brahe for a short time. At thistime there were many astronomers who supported heliocentric system, including
Douglas who remained in the underworld.
13 John Stuart Mill argued that "The demand for commodities determines in what particularbranch of production the labour and capital shall be employed." (Mill, I.5.24) This expresses
the similar idea as Sraffa’s principle of effective demand. For more details, see Shiozawa(2017).
17

Kepler, but Brahe continued to retain geostatic system. With small variation of
Ptolemaic system, he could coherently predict the planetary movements within theobservational error range. Heliocentric system became more precise thanPtolemaic system only when Kepler discovered his three laws of planetary motion.
Ptolemaic system was a complex system. Planets move on a circular epicycle
whose center moves around on a deferent, the circle with its center near to theearth (the offset is called eccentric). They move at a constant angular velocity
viewed from an equant point which is also displaced from the center of the deferent.
By this complex configuration he could explain motions of planets, including
retrograde motion and change of brightness. To improve the preciseness of
prediction, Ptolemy and later astronomers added epicycles to epicycles. In this way,
Ptolemaic system became more and more complicated each time a new adjustment
was added. In a time some seventy cycles and spheres were employed.
Ptolemaic system and its history are quite similar to the actual neoclassicaleconomics. Neoclassical economics can generate various models and can adapt
them to any observed data. It is only less precise than the Ptolemaic system.
Theoretical components such as marginal utility, marginal products, preference
order, isoquant curve, decreasing returns to scale, and etc. are similar to deferent,
eccentric, epicycle, equant and others. These components are invented in order tokeep neoclassical system coherent without enquiring the deep meaning of theseabstract entities. In the course of one and half centuries it accumulated too many
irrelevant theoretical components. Now many economists acknowledge that theneoclassical system has become too complicated and apologetic and contains no
deep insights. Key concepts of Ptolemaic system such as deferent, eccentric,
epicycle lost value just after the Newtonian revolution. Just like that, after a
Copernican revolution in economics, those key concepts such as marginal utility,
marginal products, preference order, isoquant curve, and etc. will loose their
meaning and will be thrown away in the museum of oblivious concepts.

§5. Mill’s unintended “solution”
There is no reason to doubt John Stuart Mill’s good faith when he wanted toadvance Ricardo’s theory one step forward. Ricardo explained how a trade ispossible with gains from it for both countries when a country is more productive in18

absolute terms than the other country in both industries. In his explanation,exchange rate was simply given and it was different from that of both countries
when they produced without foreign trade. Ricardo’s system comprised threetheories of domestic values: prices of reproducible goods, prices of non-producible
goods and theory of rents and price of lands. In chapter 7 On Foreign Trade, he
added a fourth element: prices in international trade.
Ricardo knew well that “the rule which regulates the relative value of commodities
in one country, does not regulate the relative value of commodities exchanged
between two or more countries” (Ricardo, 1952, p. 133; Library VII.10?). However,Ricardo did not or could not produce any theory concerning how the international
values are determined. 14
As we will see later, the famous illustration using four magic numbers is a repetitionof the logic that Viner (1937, p.440, Library ) named “18th century rule”. Viner isreferring to Martyn’s reasoning, but it is doubtful if it is appropriate to call thereasoning as “18th century rule,” because Martyn (1701) (or Martyn 1720) was not awidely distributed pamphlet and remained obscure until the 19th century when it
was re-published by McCulloc (1856). It is true that Adam Smith (Smith 1765,
Library IV.2.11-12) gave a similar argument as Martyn’s but there is no evidence that
Smith read Martyn’s pamphlet. 15
Another point that requires an adjustment in the traditional explanation is that
Ricardo had discovered the rule to determine specialization pattern by taking ratiosof two coefficients and comparing them. In view of the footnote Ricardo (1951,
p.136 , Liberty) made, it is possible that Ricardo compared the two ratios. However,
it is doubtful if Ricardo thought the task to determine the specialization pattern anessential part of his trade theory. He gave an example in which we can easily
determine it but Ricardo himself was thinking a situation where countries are notcompletely specialized. As he discussed in later part of the chapter, Ricardo wasconsidering the case where many commodities are traded simultaneously. We findno mentions to treat these cases.
See Tabuchi (2017?) for the details on how Martin was re-discovered and on theinterpretation of Ricardo’s argument in his chapter on foreign trade. See also Shiozawa(2016b, section 7).
15 See Maneschi (2002) for the history of acceptance of the pamphlets. The author ofpamphlets was not known until Christine McLeod (1983) established author’s identity.
14

19

Despite of all these ambiguity, Ricardo’s example was ingenious. Paul Samuelson
rightly named it Ricardo’s four magic numbers. John Stuart Mill started to learn
Ricardo from his boyhood. He was particularly interested in problems that hebelieved Ricardo had left behind him. One such problem was to determine the termsof trade. The terms of trade are an expression to indicate the relative prices
between export and import goods. In the two-commodity case terms of trade are
the same as relative price or value of two goods in the international market.
As Yukizawa (1974), Ruffin (2002) and Maneschi (2002; 2003) made it clear, 16
Ricardo simply supposed international exchange values that are different fromthose of domestic exchanges. However, he did not give any hint on how thesevalues are determined and how they are related with each other. He simply
remarked that “the same rule which regulates the relative value of commodities in
one country, does not regulates the relative value of commodities exchanged
between two or more countries.” (Sraffa 133, Library 7.10).
Mill found that the terms of trade is not determined in Ricardo’s Principles. His
judgment was right. It is reasonable and justifiable that Mill set the problem insearch for the logic that determines the relative value of commodities. Mill might
have tried to generalize Ricardo’s cost of production theory of value into thisinternational exchange situation. On this point, we have no record which tells how
he thought on this. Even if he wanted to do it, it would be a difficult work because, inthe time of John Stuart Mill, there were no theories of convex polytopes and linear
inequalities. 17
Without any suitable mathematical tools, Mill and his followers were obliged to workon a simple 2-country, 2-commodity economy. If it was possible to imagine
many-commodity case, general analysis of such a case would be highly difficult inthe middle of the 19th century. In fact, as we shall see later (in section 11), there
were two or three economists who wanted to go beyond 2-commodity case.
However, they could not elucidate the reason why 2-commodity and 3- or morecommodity cases are different and where the difference comes about.

16
17

Fore the detailed history on this connection, see Tabuchi (2016).
True solution required these theories as it was revealed by Shiozawa (2014),
20

The trouble with 2-country, 2-commodiy case lies in the fact that there is on the
production possibility set only one point where both countries obtain gains fromtrade. It was the situation of complete specialization. Geometrically it is an internalvertex (extreme point) of the production possibility set and unique point in thepositive quadrant (or first quadrant). Mill and his followers did not recognize that
this is a singular circumstance which appears only for 2-country, 2-commodity case.
We can easily explain how Mill was enforced to consider the economic situation that
he has no special intention to examine. Figure 1 gives a standard world production
possibility frontier for the case of two-county, two-good case.

Good 2

Figure 1

C
World PPF

Prices in
Domain 2
D

Domain 2
Price Variation Band
B
PPF
for P

Prices in
Domain 1
Domain 1

PPF for EOAGood １Figure 1
The production possibility frontier (PPF) is the set of maximal points of the
production possibility set (PPS). The frontier of two-country, two commodity
economy has two segments: segment AB and segment BC. This feature orconfiguration does not change when the coefficients change. Let us omit two points
at the coordinates, because they are degenerated cases. Any point between A andB has a price vector which is identical to the price vector in country P. Any point
between B and C has a price vector which is identical to the price vector in country
E. In both cases, one country enjoys no gains from trade, because the prices are the21same as those of closed economy for one country. 18 Mill excluded these cases
because he thought that trade should be beneficial for both countries. Thatsituation occurs only at the point B. On that point, both countries P and E can enjoy
gains from trade. Mill thought that this is the point to examine and asked how termsof trade is determined at that point. Young John Stuart did not know how grave
meaning this simple reasoning has for the destiny of economics.
Point B is a point of complete specialization. A country has only one commodity
which is competitive in the world market. In this situation, when the labor input
coefficients are fixed and each country has a determined quantity of labor (or labor
power), the quantity of the product a country can produce competitively isdetermined. In Mill’s example (Mill, 1848, Library III.18.6-17.), Germany specializes
in linen and England specializes in broadcloth (III.18.4). If the model is interpreted
strictly, then Germany employs all workers to produce linen and England employs
all workers to produce broadcloth (Ricardo did not imagined such an extreme case).
As the labor power is determined, the quantity of linen that Germany produces andthe quantity of broadcloth that England produces are determined. In other words,
Mill was lead to observe an economy where two countries engage in the productionof one commodity and total amount of the product is determined by the input
coefficients and amount of labor force.
This is the situation that Mill found himself in as his international trade example. Thisis but a pure exchange economy. The above story is of course a logicalreconstruction. No explicit words appear in Mill (1848). Nominally, we haveproductions in Mill’s trade economy. However, the amount of production ispredetermined and a country can get other commodity only by the exchange of
their product. If we pick up the situation where two sides engage in negotiation, it is
the same situation where two sides negotiate with each commodity in their backyards.
John Stuart Mill was thus guided by his good faith from Ricardo’s production
economy to pure exchange economy, which is by their characters totally different
From the figure itself, it is note clear that wage rates of both countries are
determined uniquely at the same time as prices. The international value systemcomprises wages of all countries and it is uniquely determined when the world demandlies in the interior of a facet, or on an open domain of the frontier. See Theorem 3.4,
Chapter ×× of this book.

18

22

from what Ricardo examined.
How Mill solved the determination problem of terms of trade is not of the firstimportance. The most important fact is that Mill displaced the problem fromproduction economics to exchange economics. He unconsciously did this. I contend
that this was the very point where economics of production of the classical political
economy was replaced by economics of exchange in the neoclassical tradition.
After Mill, most of trade theorists continued to examine the situation that Mill had
set and could not escape from it except for a few exceptional cases.

§6. How is Mill’s “solution” misplaced?
Now it is time to argue Mill’s “solution.” Was it a really solution to the Ricardo’s
problem of constructing a theory of international values. Was Mill’s “solution” aunique possible solution to the theory of international values? By no means! Mill’s“solution” was an observation of an exceptional case. Mill and many othereconomists in international trade theory mistook this exceptional case as arepresentative situation of international trade. Let me explain first by a figure.

U

Figure 2

Good 3A Minimal Model of the
Ricardian Trade Theory

Domain 2

T

VO
Ridge 1

Ridge 2S

Good 2

Domain 3
Domain1
Q
Good 1R

2 country, 3 goods case

Figure 2
Figure 2 presents the world production possibility frontier (PPF) in the case of23

2-country, 3-commodity case. It is named minimal model of the Ricardian trade
theory. I will justify this denomination soon.
The world PPF of Figure 2 consists of three facets (open domains), eight ridges andsix vertices. The first observation is that there is no vertex in the interior of thepositive orthant. No point like B in Figure 1 exists. We call such internal extreme
point Mill-Jones point 19. Formal definition of Mill-Jones point is any vertex of theworld PPS that lies in the interior of the positive orthant. Let us call such a point of
PPF interior vertex. Coordinates of such a point must be all positive and is anextreme point of the world PPS (We omit the modifier “world” here after).
As we have observed, there exists no Mill-Jones point in Figure 2. One may thinkthat this is a mere incidence, but it is not. No trade model has Mill-Jones point if thenumber of commodities exceeds the number of countries. An internal vertex
represents a situation of complete specialization. This means that every country
has only one commodity which is competitive in the world. Then, there is a
one-valued mapping from set of countries to the set of commodities. Therefore, if aMill-Jones point exists, the number of commodities is equal to or less than thenumber of countries. In Figure 2 case, the number of commodities is greater than
the number of countries and it is impossible to have an internal vertex. In general, if
the number of commodities is greater than the number of countries there exists noMill-Jones point.
There are vertices at the boundary of the PPS. At these points, one or morecoordinate vanishes. It means that one or more commodity is not produced at all.
These are degenerated cases and we do not consider them, because they are thesituation where some commodities are not produced at all. We cannot say that the
number of produced commodities is 3 in this situation.
Mill-Jones points or interior vertices do not exist when the number of commodities
is greater than the number of countries. This simple proposition went unnoticed
nearly 150 years after J.S. Mill. But it has an important consequence. We can countabout 200 countries or economies in the world. The number of commodities,
19 Some call this point “Ricardo point” or “Ricardo’s Limbo point”. Because these are not a suitable

naming, I do not adopt this naming. The reason of my naming is given later.

24

although it is difficult to count them exactly, easily exceeds millions. For example, aprice book of the Gosplan in the former Soviet Union, it is said, contained more than
20 millions of items. We may assume any developed economy trades and produces
more products than that. We may safely assume that the number of commodities isbigger than the number of countries. Non-existence of Mill-Jones points means that
there is no pint at which prices can move freely within an open range. People after
Mill continued to try to determine prices on the assumption that they have somemargin of free movement, but there is no such possibility when the number ofcommodities is bigger than the number of countries.
What happens in a point other than Mill-Jones point? If we see Figure 2 again, we
easily know that most point of the PPF lies in either of three domains. In Domains 1
and 3, the prices are proportional to those of a country. J.S. Mill excluded thissituation considering that if trade continues, both countries must have certain gains
from trade. In the two-country, two-commodity case, such a point is unique. It is
point B of Figure 1. In case of two-country, three-commodity case, we have a wide
Domain 2. Any point in Domain 2 has a system of international values which remains
constant as far as the point stays in Domain 2. This system of international values isdifferent from either of two countries’ domestic values and two countries (andemployed workers in both countries) can enjoy gains from trade.
There is a possibility that the world production or demand comes on one of two
interior ridges RV and RT. We can exclude the points on the border of the frontier,as they are degenerate points. At a point on RV, for example, the prices can vary but
they must remain perpendicular to the ridge RV. The degree of freedom of thoseprices is only one dimensional. Moreover price changes have no effects to move thedemand and the production of the world. The price variation changes the exchange
ratio between good 1 and a combined set of goods 2 and 3 but has no effect tochange the demand from a point on RV to another point on RV. In fact, Ridge RV isparallel to ridge TU and to the plane that is supported by axes OS and OU. All points
on RV have the same quantity of good 1. The same explanation holds for ridge RT.
Then, price adjustment does not work at any point on the frontier.
Domains 1 and 3 are the cases which are sometimes studied as big country cases.
Although Domain 2 in Figure 2 stands in a similar situation like point B of Figure 1,
they present very different characteristics. At point B the prices moves freely within25

a certain range (the degree of freedom is the same as the number of commodities
minus 1) and the world production is fixed. At any point in Domain 2, the pricesystem remains constant and the world production can change freely in the domain.
These characteristics are quite similar to the classical value theory. There is only
one value system and supplies can be adjusted to any effective demand as far as it
stays in Domain 2.
Now the whole picture becomes clear. Mill examined a two-country, two-commodity
case believing that the model gives a representative situation and fell in an
unexpected trap.
He did not imagine that the situation changes drastically and in an essential way
when the number of commodities is bigger than the number of countries. If we
admit that the number of commodities exceeds the number of countries, theminimal model of international trade should be 2-country, 3-commodity case. This is
the reason that I call Figure 2 minimal model of the Ricardian trade theory.
John Stuart Mill started a tradition to consider complete specialization case. It
meant at the same time to examine a pure exchange economy, because in such acase the product and the volume of each country’s production is determined andthe countries (or representative agents) negotiates the exchange ratios between
commodities. This tradition has been succeeded by economists after Mill and it
remained so even at the middle of the 20th century.
In 1950’s there was a kind of resurrection of Ricardian trade theory. Following theworks of Graham, Lionel McKenzie and Ronald Jones extended the Ricardian modelfrom 2-country, 2-commodity case to many-country, many commodity cases. This
was a great step forward in the Ricardian tradition but the tradition was conservedby them. McKenzie wrote three-odd papers on Ricardian trade model and Jones
followed him. Their works marked a new era as their analysis was based on the newmathematical tool developed by the activity analysis which was a topical trend atthat time. Curiously, McKenzie treated the cases where the number of countries isequal or greater than the number of commodities. Jones (1961) discovered afamous formula that I will explain briefly soon after. The formula gives the necessary
and sufficient condition that a pattern of full specialization is realizable (“efficientassignment” in Jones’s terminology). This formula proves that there is at most one
internal vertex in the case of N-country, N-commodity case. Jones also considers

26

unequal cases, i.e. the case where the number of countries is not equal to thenumber of commodities. However, as his definition of “class” (Jones 1961, p.164)
shows, he is interested in cases where the number of countries is greater than thenumber of commodities. Why did McKenzie and Jones examine such singularperverse cases, whereas a common sense or a simple observation tells that numberof commodities is far greater than the number of countries?
Jones’s formula is expressed in the form of next theorem.
[Jones Theorem](Jones’s formula) 20
Let aij be labor input coefficients for country i to produce commodity j. Suppose
there are N countries and N commodities. Then the following two conditions areequivalent:(1) There exist positive wage rates w1, w2, … , wN which satisfy

w1・a11 < w2・a12, w3・a13,・・・ , wN・a1N;
w2・a22 < w1・a21, w3・a23,・・・ , wN・a2N;
・・・

wN・aNN < w1・aN1, w3・aN3,・・・ , w(N-1)・aN(N-1).
(2) For any permutation τ of N indexes which is different from identity,

a11・a22・ ・・・ ・aNN < a1τ(1)・a2τ(2)・ ・・・ ・aNτ(N).
The second condition can be translated that left side product is the strict minimum
among permutation products in the form of the right side. The condition (1) isequivalent to the existence of internal vertex or positive extreme point.
This is a beautiful generalization of Mill’s formula (comparison of two ratios fromfour magic numbers) for comparative advantage. In Mill’s case, country 1
specializes in commodity 1 and country 2 specializes in commodity 2 when two
ratios satisfy the following relation:

a11 / a12 < a21 / a22.

(5-1)

Here a ij are labor input coefficients. The above condition is equivalent to

a11 / a21 < a12 / a22.

(5-2)

These two conditions are in this turn equivalent toa11・a22 < a12・a21.

(5-3)

Jones proved the proposition (1)⇒(2), but it is doubtful if Jones proved the inverse
proposition (2) ⇒ (1). Jones (1961). See Shiozawa (2015) Section 10.

20

27

Jones theorem tells that above three equivalent conditions (5-1), (5-2) and (5-3) arealso equivalent to the existence of positive numbers w1 and w2 which satisfies theconditions

w1・a11 < w2・a21 and w2・a22 < w1・a12.

(5-4)

This equivalence theorem can be demonstrated as follows. If positive numbers w1
and w2 which satisfy (5-4) exist, multiplying both sides of the two inequalities, andeliminating w1・w2 from both sides, we get (5-3). The converse holds too. In fact, if
assume condition (5-2) holds, take positive numbers w1 and w2 in such a way that

a11 / a21 < w2 / w1 < a12 / a22.
Then we can derive the first inequality from the left inequality of (5-4) and thesecond inequality from the right inequality of (5-4).
The left inequality of (5-4) means that the cost of production of commodity 1 incountry 1 is cheaper than the cost of production of commodity 1 in country 2. Inother words, the production of commodity 1 in country 1 is more competitive than incountry 2. In the same way, the right inequality of (5-4) implies that the productionof commodity 2 in country two is more competitive than in country 2. With wage rate

w1 and w2 which satisfy (5-4), we get an economy in which country 1 specializes incommodity 1 and country 2 specializes in commodity 2. Thus the above equivalence
theorem implies that real cost and money cost approaches are in fact equivalent in
the case of 2-country, 2-commodity case.
Jones theorem gives a sufficient condition for the existence of a Mill-Jones point.
The theorem also implies that if Mill-Jones points exist at all, they are unique. We
can thus observe a keen interest on Mill-Jones point at the time of Ronal Jones.
However, as we have observed, no such point exists when the number ofcommodities N is bigger than the number of countries M. If M=N, there exists at
most one Mill-Jones point. If M>N, there may exist many Mill-Jones points. In fact,
there are in a general case as many Mill-Jones points as the number of “classes”. If
Jones knew all these facts, why did he not consider the non-existence case? It mustbe easy for him to reason that internal vertex does not exists in the case M<N. This
strange fact proves how the tradition Mill opened was strong and binding.
Mill started a well established tradition that he may not have intentioned. Mill was
guided to this tradition simply by the easiness of examination, but the stake was big.

28

This simple examination marked the start of new economics later named
neoclassical economics. Jones was a deep thinker but was fully immersed in the
tradition of neoclassical economics. He was too preoccupied by the priceadjustment framework to see the most common cases. They were not suitable toprice adjustment paradigm and they were exclude from observation. In the time ofclassical political economy, this was not such an established tradition. John StuartMill, intended or unintended, set the problem which was not solved by Ricardo andthus started new economics of exchange.

§7. Mill’s “solution” and afterJohn Stuart Mill posed his question. How solved it is not important. What matters is
how he posed it. We know his solution well. The international values come to anintermediate point of two extremes that are values of each of two countries. He
showed how, at a value, two countries would exchange their products against the
products of the other. Existence is not discussed in a modern way. In sections 6 to 8
that were added in the third edition, Mill started arguing the question of multiple
equilibria, but he did not give any sufficient condition for the a solution to be unique.
These questions are studied by Alfred Marshall and we will give a short comment in
the section on him.
Despite of this inadequate character of Mill’s “solution”, I have no intention toreprimand the lack of exactitude of his solution. At the time of John Stuart Mill i.e.
at the middle of the 19th century, mathematics itself was still intuitive than logical.
Even many-year later, Jevons and Walras were satisfied by counting the numbers ofequations and unknowns. What is more important and crucial to the history of
economics is what he believed to have established in his Principles. It is sometimes
difficult to distinguish the influence of his “solution” to the unsettled trade questionand other observations he made in the course of his economics formation. Although
I admit that the followings may not be exclusive result of his “solution”, we canobserve that Mill made a tremendous step forward towards the economics of
exchange in the course of considering and examining the international value
problems. Here is a list of propositions that Mill came to affirm in the course of thisexamination:(1) It is not the absolute advantage of an industry but comparative advantage that
determines the pattern of trade and specializations. (Principles III.18.60; Essays I.2,

29

I.9)
(2) The law of demand and supply is anterior and more fundamental to the law of
cost of production (Principles III.16.5; E I.19).
(3) The price regulates itself in such a way that demand will be equal to supply(Principles III.18.15, a citation from Essays I.32; Essays I.23).
(4) Supply and demand are but another expression of reciprocal demand.
(Principles III.18.24)(5) Demand depends on value (or price). (Principles II. ; Essays I.38)(6) Equation or equilibrium of international demand is the equality of exports andimports. (Principles III.20.5; Essays I.52, I.72)(7) Each country completely specializes in the production of one commodity.
(Principles III.18.4; Essays I.6)
(8) 2-country, 2-commodity analyses can be generalized without fundamental
change of logics. (Principles III.18.17, III.18.20, III.18..22, III.18.61, III.18.63;

Essays )Mill believes that proposition (1) is what Ricardo wrote in his Foreign Trade chapter.
However, as it was made clear, Ricardo did not explain in this way at least on his
four magic numbers (See Yukizawa 1974, Maneschi 2003, Foccallero 2015, Tabuchi2016). 21 This is practically John Mill8s invention. And yet his idea is still influencing
the international trade thinking. Proposition (2) became a kind of manifesto for theneoclassical revolution. In Principles Mill advances this statement in a chapter 16,
Book III, Some Peculiar Cases of Value, but he put it here, in my guess, to attenuate
too drastic an announcement for many Ricardian loyalists including Mill himself.
However, what Mill prepared in the International Value chapter was not thismanifesto alone.
Proposition (3) was the real content of proposition (2). In the Prinicples, there is no
explanation what is the principle of demand and supply, but in Essays Mill explainsthat the principle of demand and supply means that price or exchangeable value
depends on demand and supply (Essays I.23-24). In the Principles, Mill makes nosuch hint before International Value chapter except two minor comments i.e. a partthat was omitted in the third edition where he spoke of the adjustment of wages
Ricardo’s footnote on shoe maker and hat maker (Sraffa 1951 p.138) is more
ambiguous. He may be thinking as we normally do by taking two ratios of two different
industries, each for two countries.
21

30

(note #84) and he talks about adjustment of prices of two jointly produced products(Principles III.16.15). On the contrary, he emphasizes the opposite causal relation at
the beginning of the Book III:[T]he value of things which can be increased in quantity at pleasure, does
not depend (except accidentally, and during the time necessary for
production to adjust itself,) upon demand and supply; on the contrary,
demand and supply depend upon it. (Principles III.3.7)
The notion that value depends on supply and demand already appears in the Essays(I.23). The essays were written in 1829-30 (P.1), but examination on how gains fromtrade are divided between trading countries went back to early 1820’s when Millwas still teen agers. Mill knew very well that the principle of cost of production was
the core of Ricardo’s whole doctrine. He discovered by his study on theinternational trade questions that this central dogma had a deep crack. Knowing
this from his young days, Mill remained at surface a loyal adherent of Ricardo’s
theory. He proposed that we should revert to a more general and fundamental lawof demand and supply. In the Principles, this proposal was placed only after themain argument on values was over and just before the important two International
Trade chapters. Despite of this careful presentation of his new doctrine, students
after him have found that this is the key point that may revolutionize the wholesystem of economics.
What Mill named peculiar cases may have given some influence on adopting the
new doctrine. For example, Alfred Marshall studied the cases of joint cost of
production in his early days when he started to study economics as his major
research field. However, the importance of international values is without
comparison. As we will see in the coming three sections the three pioneers ofBritish neoclassical economics have picked up international trade problem as oneof major research targets.
International trade situation as it was set by John Stuart Mill was more helpful thanwe imagine in the formulation of neoclassical economics. Mill may have not been
well aware of the effects of complete specialization, even though he clearly states
this point as proposition (7). In a 2-country, 2-commodity case, what each country
produces and how much it produces are determined as we have observed in31section 5. This introduces a pure exchange situation. It is evident that this situation
setting paved the way to the economics of exchange.
In addition, this situation helped to establish the symmetry of demand and supply.
In this 2-person 2-good pure exchange economy, supply is in fact the demand ofanother good. As Mill put it, supply and demand are in fact an expression ofreciprocal demand. This helped much the formulation of supply curve, because thesupply was symmetric counter part of the demand. The notion of demand curve orfunction was easily formulated by the utility maximization. Supply curve or function,
when the production intervenes, was much difficult to formulate. Marginal principle
was first introduced for utility, but its introduction in production was retarded many
years. We know how Marshall struggled to harmonize supply curve with the
production conditions. He invented the notions as internal and external economies.
He barely succeeded to explain increasing supply curve by excluding economies ofscale within a firm. Such kind of complication did not existed in the case ofreciprocal demand.
When we acknowledge that demand depends on prices, it is easy to know that
supply depends on prices in the case of reciprocal demand. This acknowledgement
established symmetric framework of supply and demand. Although it seems Mill did
not arrived at the notion of demand and supply function with prices as independent
variables (Yoshii, in this volume), there was only a step to that. What was lacking forMill was the mathematical concept of a function in general. In the time of John
Stuart Mill, an idea of function in general was not very common. Mathematicians
may have used such an abstract concept, but for non-specialists a function was
something expressed by algebraic expressions. 22 It must be difficult for Mill toconceive the relation between the demand and the price as a function.
Mill’s concept of equilibrium of international demand was a bit special one. It meant
the trade balance and in this sense equilibrium did not signify the equality ofdemand and supply as it means in the modern sense. We will see in section 10 (p.48
in the draft) that he must be thinking of a kind of cybernetic process. However, thePrinciples wiped out some of traditional misconceptions. As Mill put it, many
This explains in part why A. A. Cournot (1838) had introduced the concept of demand
function as early as 1838. Cournot was trained as mathematician, In addition,mathematics education was much developed in France than in England in the first halfof the 19th century.

22

32persons assumed that value depends on the proportion between the demand andthe supply. He pointed that it is not the proportion but the equality of them (III.3.5).
However, this equilibrium concept may have induced a grave slip when Millconsidered the situation where more than 2 country or 2 commodity cases are
examined. He suggests that these cases can be treated just as the same way as thecase of 2-country 2commodity case (III.18.17; III.18.61), but it seems he did notreflected on these questions deeply. He claims that the introduction of third country
or commodity does not alter the theory. He is right in one sense. In his
understanding total value of exports and imports must be equal. He is preoccupied
in this equality or trade balance and does not think how the specializations aredefined in these situations. It is difficult to suppose he has any concrete idea inmind, because this question remained difficult question even at the middle of the20th century. Curiously, Mill does not mention explicitly that his two by two caseanalysis can be generalized to many country or commodity cases in the first of
Essays. It is probable that he knew the difficulty when he was working of thespecialization and had forgotten some twenty years later when he started to write
the Principles.
As a simple conclusion of this chapter, we may say that International Value chapter
prepared most of the neoclassical frameworks and marked a clear shift from
economics of production to that of exchange. In chapter 3 of book 3, he statedclearly that value of things does not depend upon demand and supply, but demandand supply depend upon it. In chapter 18 of the same book, Mill set a situation
where the exchange value adjusts itself so that the demand and the supply become
equal. In the former, the mechanism that brings the supply equal to the demand was
the change of production volume. In the latter, the production was put off and apure exchange situation was introduced. In this state, two parties have certain
quantity of each of two commodities. In the course of long explanations, a clear
change of adjustment mechnism occurred and the causal orientation was reversed.
Without mentioning this change ofadjustment mechanisms, and without

investigating why this change of adjustment occurred, Mill declares that the law ofdemand and supply is more general than that of cost of production. As we have
explained in section 6, there was a grave oversight. We will see in the following
three sections how this oversight guided late comers to the construction of
economics of exchange. More precisely it was the economics where the exchange
plays the major role whereas production is interpreted just as a variant of exchange

33

(production as exchange with the nature).

§8. William Stanley Jevons
In the case of Jevons, my judgment is symptomatological. There is no textual
evidence that Jevons was influenced by Mill’s “solution”. Despite his apparent
hostility and contending attitude against John Stuart Mill, and although there are no
direct evidences, it is highly probable that Jevons unconsciously accepted Mill’sfundamental framework in international trade.
Let me start my argument by citing two interesting papers. One is Donzelli (2007)
and the other is Aldrich (2000). Donzelli claims that Jevons did not develop law ofdemand and supply. Aldrich (2000) argues the reasons of non existence ofJevonian revolution in international trade theory.
Let us see what Donzelli (2007) questions:
One of the most surprising features of Chapter 4 of TPE [Theory of Political

Economy] is that, in spite of the reiterated emphasis laid by Jevons on the
allegedly fundamental role played by the so-called "laws of supply anddemand" in his theory of exchange, no formal demand-and-supply analysis isactually employed by the author in deriving such theory nor, in spite of what
Jevons himself occasionally claims, can be deduced from the formal
statement of the theory, as can be found in TPE. (Donzelli 2007, p.2)
It is true that expressions “demand function” and “supply function” do appear in
Jevons (1871) (See also White, 1989; Nakano, 2009). In the Preface to the second
edition, Jevons refers to what we call “demand function” when he talked about
Cournot, but he cite it as “a function of the price, or D = f(p)”. Even in hismathematical theory (1874) no such expression appears. Jevons was trained as
natural scientist, particularly good in chemistry, and had a concept of function in
general. He uses the term such as “function of utility” but he never used theconcept of “demand function” or “supply function” in his principal book as his own
concept. What does this mean?
A simple explanation is that Jevons did not think in terms of demand and supply

34

functions. If Donzellii (2007) pointed this fact, he is right. Then, what did Jevonsmean by the laws of supply and demand? 23 In the Preface to the second edition of
his Theory, Jevons cites Lardner (1850) that he found in it a “mathematically andgraphically” treated example of the laws of supply and demand. The chapter 13
indicated by Jevons is an account of receipts and profits. 24 A diagram appears in
p.249. Lardner discusses how the tariff influence the profits and argues that there
is a maximum point of profit when the tariffs are continuously increased from a very
low value to higher values. These must be a good example of mathematicaltreatment of profit analysis and it must be true that Jevons got an “idea ofinvestigating Economics [sic] mathematically”. However, it is difficult for us to seethat this is related to a law of demand and supply. What Lardner argued there is acalculation of profit maximization.
In the body of the book, expression of “laws of supply and demand” appears ten
odd times. In any of them, there is no detailed explanation about the laws. Many ofthem indicate that the laws of supply and demand are the consequences of law ortheory of exchange (Theory, Library I.2, I.24, IV.39). The most detailed account of
the laws appears in Chapter I Introduction. In the second appearance Jevons
explains: “The ordinary laws of supply and demand treat entirely of quantities ofcommodity demanded or supplied, and express the manner in which the quantities
vary in connection with the price.” (I.5) This explanation of the law of demand andsupply does not seem to differ much from the commonly accepted notion of the law.
However, we may infer that there is a shift of main focus between what John StuartMill meant by law of demand and supply and what Jevons meant by laws of supply
and demand. By these expressions, Mill mainly meant the equality of demand andsupply (See Yoshii, this volume). In the case of Jevons, he may have implied theequality of supply and demand, but it seems he was more concerned in the form of
how demand and supply changes with the change of the price. There also seems be
a discrepancy between what Jevons understand by demand change and what we
imagine by the same expression. When we think of demand function (or curve), we
normally think a function between the demand and the price. This kind ofconception is very rare in Jevons. Instead, Jevons talks about utility function (orExpressions law / laws of demand and supply do not appear in Jevons (1871). By
contrast, the expression “law of supply and demand” appears twice in chapter 5 (V.47.
V.48) and the expression “laws of supply and demand” appears 18 times dispersed in 17
paragraphs including Prefaces for the 1st and 2nd editions.
24 Jevons cites wrong pages.
23

35

curve). Most of the time when he talks about demand changes, he explains promptlythat the final degree of utility (or derivative of the total utility function) deceases
according as the quantity of the commodity one possesses increases. Although
there is no such expression, I have an impression that Jevons was thinking that thelaws of supply and demand are equivalent to the diminishing law of marginal utility.
Jevons’s account of exchange is a strange one. He emphasize that the total utility
must be maximum after exchange for both two traders. He writes an equation suchas
φ1( a－x ) / ψ1( y ) = y / x = φ2( x ) / ψ2 ( b－y ).

(7-1)“[W]henever two commodities are exchanged with each other, and more or less canbe given or received in infinitely small quantities,” (Jevons’s emphasis) Jevons
explains that the quantities exchanged x and y must satisfy these two equations.
Jevons assumes that the total utility and by consequence the final utility areseparable by each commodity. Functions φ1( s ) and ψ1( t ) signify trader A’s final
utilities when A possesses s units of corn and t units of beef. Functions φ2( u ) andψ2 ( v ) signify trader B’s final utilities when B possesses u units of corn and v unitsof beef. Even if the utility functions are not separable, the equations hold when we
replace φ1( a－x )/ψ1( y) andφ2( x )/ψ2 ( b－y ) by ∂Φ/∂s /∂Φ/∂t and ∂Ψ/∂u /∂ΦΨ/∂v evaluated at (a－x, y) and at (x, b－y) respectively.
If we use Edgeworth box diagram, we can express these relations by Figure 3. The
only difference between Jevons and Edgeworth lies in whether they admit the
middle side y / x is equal to the left- and right-hand sides. Jevons claims that the
middle side is equal to either of both-hand sides. This is a simple consequence ofthe law of indifference. 25 We may argue long on this law, but here is not the rightplace to do. Edgeworth would not admit this law. By consequence, we can say thatthe difference between Jevons and Edgeworth is whether they admit this law or not.
Except this single point, Jevons can be said to be a forerunner of Edgeworth. We
will discuss this point in the next section.

25

Whole of chapter 4 goes into the explanations of this law.
36

B’s consumption of good 2

A’s indifference curve

B’s indifference curve

A’s consumption of good 2

B’s possession of good 2

B’s consumption of good 1yexchange
ratio

x

A’s consumption of good 1

A’s initial possession of good 1

Figure 3
Contrary to well established belief, laws of demand and supply do not need demandand supply functions. We may argue that this implies intermediate character ofJevons’s economics. A common understanding is that Jevons failed to grasp these
crucial concepts. Another strand of understanding is to situate Jevons on a way toa deeper understanding of exchange process (Fonseca and Ussher 2002; Nakano,2009). I am rather inclined to the first understanding and I will explain the reason
soon after.
If we admit the law of indifference, equation (7-1) has a good chance to have aunique solution. The cases of non-existence of solutions are not excluded. Whensolutions exist, they may not be unique, but in general they form separated discrete
set. If we do not ask how we get one of these solutions, Jevons argument must be
estimated quite satisfactory. There is no need to examine exchange process bydemand and supply curves.
Fonseca and Ussher (2002) and Nakano (2009) think that there must be a route
other than the scheme that comprises demand and supply functions. They are rightto believe that demand and supply functions are artifacts that few empirical37

supports and no deep theory basis. I do not enter into this question but those who
doubt this are requested to read Erik Beinhocker (2006), Steeve Keen (2011) andmy papers (Shiozawa, 1999; 2016b). However, I believe that Jevons (1871) has
another aspect that Fonseca and Ussher (2002) and Nakano (2009) do not pay due
attention. This is the point that Aldrich (2000) observes. Aldrich claims that Jevons’s
Theory of Exchange chapter is not a simple theory of (domestic) exchange, but aunified theory of both domestic and international trade.
Aldrich (2000) is right. Jevons introduces in chapter IV on Theory of Exchange aterm “trading body”, which stands for any trader who may be either “a single
individual in one case” or “the whole inhabitants of a continent in another”.(Jevons,
Library IV.19) He justifies this singular terminology because “the principles of
exchange are the same in nature, however wide or narrow may be the market
considered.” (Jevons, Library IV.20) Jevons adds that “our laws of Economics willbe theoretically true in the case of “individuals, and practically true in the case oflarge aggregates; but the general principles will be the same, whatever the extent of
the trading body considered. We shall be justified, then, in using the expression
with the utmost generality.” (Thoery, Library IV.20) Thus, Jevons’s theory of
exchange intends from the start to be a unified theory that is applicable both fordomestic exchange and for international trade. Aldrich emphasizes its possibility inthis way:
As in the aggregative neoclassical analysis of the 1930s, international trade
was conceived as exchange between countries, each with its own preferences
and production possibilities. Jevons developed marginal conditions for
consumption and production and extended the theory of comparativeadvantage in a way that did not become established in the literature until the
1930s. (Aldrich 2000 p.65)
Aldrich (2000) asks himself why Jevonian revolution did not take place ininternational trade theory unlike the case of domestic theory on which Jevons’s
agenda setting, mode of argument, and analytical tools had made a tremendous
impact. In my judgment, this non-existence of a revolution is rather a natural courseof the economics, because Jevons did not make any substantial development ininternational trade theory. Except for mathematical formulations, Jevons and Millare treating the problem in the same framework: pure exchange economy. Moreover,38

he could not treat any topics that are specific in international trade situations. For
example, he could not device any account on the big disparity of real wages
between developed countries and then mostly colonized underdeveloped countries.
He could not explain how the international specialization takes place 26. This wasinevitable, in my opinion, because Jevons did not understand the essential
difference between exchange in a country and exchange between countries andthis is why he thought he could unify exchange within a country and between
counties.
Aldrich (2000) posed an interesting question, but it was ill-posed, or at least it was
shallow. If we go in the depth of the problem, we should ask why Jevons came toconsider his pure exchange economy or an economy where we have two persons
and two commodities. Let me cite Jevons’s own proclamation:
The keystone of the whole Theory of Exchange, and of the principal problemsof Economics, lies in this proposition—The ratio of exchange of any two
commodities will be the reciprocal of the ratio of the final degrees of utility ofthe quantities of commodity available for consumption after the exchange iscompleted. (Italic by Jevons,.Library IV.29)
This is a manifesto of his marginal utility doctrine.
Imagine that there is one trading body possessing only corn, and anotherpossessing only beef. It is certain that, under these circumstances, a portionof the corn may be given in exchange for a portion of the beef with aconsiderable increase of utility. How are we to determine at what point theexchange will cease to be beneficial? (IV.30)
This is an economy with two persons and two commodities. Where does this settingcome from? When we consider exchange, we ordinarily think two-person, two-goodsituation. Do we do because this is the minimal? Please reflect if this kind of setting
In chapter 5 where he explains labor and production, Jevons treats international
trade under the headline of Various Cases of the Theory. He argues correctly when trade(“foreign commerce” in Jevons words) is excluded. It is the case where ω2/ω1 = μ2/μ1 (Jevons’s substitutes to Ricardo’s four magic numbers) but, to study specialization, he
had to analyze the case where the two ratios are not equal. (IV.42) See also the next
footnote (on Turgot).

26

39

was common before Jevons. Did Adam Smith or David Ricardo start to discuss
exchange from this setting? They did not. 27 Present day economists areaccustomed to think with this abstract situation, but this is the very custom that theneoclassical revolution created. Smith, Ricardo and other classical economists
thought of existing economy. Perhaps we may call it industrial capitalism. It is asystem of division of labor where tools and machines play an important role andexchanges are made by means of monetary. An economy of two persons and two
goods may take place when two persons meet by chance in the middle of a desert,
one with water and the other with food. 28 This is the world that Jevons wanted toanalyze. It is a possible situation but not very important for a real life. It is true that
Smith talked the story of a deer and two beavers. This was but a simple illustration,
not a target of analysis. What he wanted to describe and analyze was the emerging
industrial capitalism. That is why he started to talk about pin making.
Jevons set an abstract economy comprised of two traders and two goods. The
traders may have their own utility but no other information nor social institutions.
This is a very simple situation one can imagine and is adapted to a pure analysis.
How did Jevons come to make this setting? As a result of logical deduction? If wethink in an abstract way, exchange must comprise at least two persons and two
different goods. Then, two-person, two-good economy must be the minimal setting
for analysis without any other givens except that persons in trade have theirpreferences and provided that they will not appeal to violence. We are accustomed
to think in this way. However, Jevons himself was not thinking in this way. He wrote
for example “It is also essential that the ratio of exchange between any “twopersons should be known to all the others.” (Jevons, Library IV.16) 29 If this is aminimal requites for a market to work, Jevons was implicitly violating his own
situation setting.
Ricardo (1817) and James Mill (1922) refer to two-country, two-commodity exchange,
but it was not considered as an isolated abstract economy. Reference to Robinson andFriday goes back to Bastia (1848) 6. Property and Plunder, Library 6.63. I owe this to ahint by Giulio Palermo. Economic Sophisms of the same author and the same year
contains three sophisms on the same theme.
28 Turgot in his unfinished paper Value and Money (1769) examined just this kind of
situation. See Turgot (2011, pp.173-178). Murray Rothbard considers that this is thefirst Crusoe economics (ibid, p.xiii). It is not certain if Jevons knew Turgot's Value andMoney. In the Theory, Turgot is only named as a piece of Condorcet in the list of
bibliography. In Jevons (1875) Turgot appears each one time in Chapter IV and VII, butthere are no mentions on the Turgot's theory of exchange.
29 Turgot (1769) is not making such an assumption in the two person exchange case.
2740

My hypothesis is this: John Stuart Mill’s trade theory made many economists toconcentrate in this abstract setting of two-country, two-commodity exchange andthis triggered immergence of the theory of pure exchange economy.
This hypothesis has several circumstantial evidences:(1) Mill’s Principle (1847) was the most influential economics textbook at the 3rdquarter of the 19th century in the United Kingdom.
(2) Mill advocated a reversion from Ricardo’s cost-of-production theory of value tomore fundamental law of demand and supply.
(3) The structure of Mill’s economics is composed of two theories of values, one
domestic and other international and despite of Mill’s claim 30 theory of value was
not sufficiently unified.
(3) It was normal for ambitious economists in 1860’s to want to build a unified
theory of economics (or value theory) and Mill’s example provided almost unique
important case to start their trials. 31(4) International trade was a paramount situation which was too important to betreated as exceptions and required a new value theory.
(5) Despite of his general hostile, contending attitude with respect to John S. Mill,
Jevons is particularly conciliatory to Mill’s trade theory. 32
What is important here is not how Jevons himself thought consciously. Jevons did agreat leap forward in economics. He changed the economics from Plutology
Mill (1848) claimed that “there is nothing in the laws of value which remains ... toclear up” (Library III.1.2). It is a mystery why Mill put this self-betraying proclamation.
31 Mill (1848) cited the “joint cost of production” case as a reason to revert from cost of
production theory to more fundamental law of demand and supply (Mill, 1848, Library
III.16), but this is not comparable to the international trade case by their importance.
32 Jevons praised Mill’s theory of international trade as “ingenious” and “nearly always
true.” (Library IV.100). He also mentioned that he thoroughly concurs with his citationfrom Mill (1848): “Almost every speculation respecting the economical interests of asociety thus constituted, implies some theory of Value” (Library IV.2)30

41

(economics of production) to Catallactics (economics of exchange). His book

Theory of Political Economy proves it. Characteristically, production comes atchapter 5 after chapter 4 which deals with theory of exchange. Chapter 5 is titled
Theory of Labour and there is no chapter with production in the title. In the Preface
to the first edition, he spoke of exchange but no word “production”. Jevons madehis revolution unconsciously. He did not make his catallactic revolution not on thebasis of deep study of economics of production. Even when he talks about
production, it is a production which does not suggests industrial capitalism.
Workers he refers are not employed workers but better interpreted as
self-employed ones.
On the conscious level, Jevons was decisively influenced by two ideas and he knew
it. One was the idea to apply mathematics to society. Another was the idea of utility.
The two were combined to coin a new idea, “final utility” or marginal utility in a more
standard terminology. Some economists praise that this was really revolutionary. I
do not think so. If the idea of “utility function” might be new, the conception thatutility determines the prices of goods was as old as economic thinking. Classicaleconomics immerged from the rejection of this “common sense.” Jevons did notunderstand this crucial point. 33 Except for his adoption of mathematicalformulations, as Marshall (1872) pointed, Jevons’s Theory of Political Economy
contains no substantially new propositions.
Jevons made a revolution, or more exactly, a counter-revolution, but he was notaware of this fact. Then, from where did this change come? If my conjecture iscorrect, he came to know Mill’s international values chapter and he got an idea toconstruct whole economics on the basis of international trade situation. If this is
the case, it is normal that Jevons emphasize that there is no difference of logic
between domestic and international economics, because in his understanding his
new theory was a generalization of international exchange.
Aldrich (2000) had a good insight, but his understanding was totally wrong. Jevons
If Jevons claimed that the final utilities of two newly purchased goods are the same,
he was right, but this does not mean that final utility determines the values of goods. If
goods are produced as much as they are demanded at the price set by producers, it is
this price which determines the actual price. Final utility selects those who estimate it
higher than the final utility of the payable money in exchange of the product. This does
not determine the price but who buys the product at that price.

33

42

did not succeed in constructing a theory of international values. He claimed so, butthat does not mean that he really did. He may have built a theory of pure exchange.
It may be applicable to the long distance trade between different communities but it
is not a theory applicable to an industrial economy. The lack of notions such as
specialization and comparative costs is the evidence of his failure. In opposition to
Aldrich’s expectation, it was inevitable that neoclassical revolution in the theory ofinternational trade did not take place long after Jevons. Aldrich (2000) assumes that
this delayed revolution arrived in 1930’s, but it is no place here to trace theoreticaldevelopment of the “modern theory” of international trade (Chipman, 1969). 34 We
are more concerned with the neoclassical revolution and for this purpose wecannot dispense with two more grand names. One is Edgeworth and the other is
Marshall. In the next section we discuss Edgeworth and in section 10 we discuss
Marshall. Both of them were heavily influenced by Mill’s international value chapter
but in a very different way.

§9. Francis Ysidro Edgeworth
Although the Edgeworth was born and dead about 2 years later than Marshal andthe former expresses intellectual obligation to the latter, I put Edgeworth before
Marshall, because (1) Edgeworth and Marshall stand on opposite extreme and (2)Edgeworth has more common points with Jevons than Marshall.
In the previous section, I produced Figure 3 as an illustration of Jevons’s theory of
exchange. The situations they set are quite similar. Namely, both are two-person,
two-commodity exchange case. Similarity of Figure 3 and Edgeworth’s idea areapparent if once we use later named Edgeworth diagram. 35 Of course, there aresome differences. Most important point is that Edgeworth did not admit that y/x (themiddle side of (7-1)) is equal toφ1( a－x ) / ψ1( y ) = φ2( x ) / ψ2 ( b－y ). In the diagram,
this difference is reflected whether the common tangent line passes through theorigin. Jevons thought that it does and Edgeworth thought not necessarily it does.
This difference reflected two economists’ view on exchange process. Jevons’s
exchange is mediated by prices (but not by money). In other words, when exchange
As for internationa trade theory Tabuchi (2017, in this volume) gives an interestingaccount.
35 Creedy (1992) emphasizes the same point.
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43

takes place, Jevons assumed that two persons change their possession in such a
way that the value one receives is equal to the value one renounces by mutuallyagreed prices. Edgeworth is much more radical thinker of exchange. He wants toanalyze a pure exchange situation before the notion of price is established between
people. Edgeworth assumes an extremely pure exchange economy. Notions such as
prices are something invented by somebody in very old days and institutionalized
after they were repeated experience ofthe people. By rejecting thesepreconceptions, Edgeworth wanted to put his theory of exchange on a firm basis.
I am not sure if he has succeeded in this project. Mathematical Psychics is one of
Edgeworth’s earliest and decidedly his major works. In this book, Edgeworth
defines field of competition as an exchange economy among indefinite number ofindividuals. A field of competition is defined to be perfect when 4 conditions of freecontract are satisfied. In this field of competition, a settlement is “a contract whichcannot be varied with[out?: Shiozawa] the consent of all the parties to it,” a final

settlement is “a settlement which cannot be varied by recontract within the field ofcompetition,” and finally “[c]ontract is indeterminate when there are an indefinite
number of final settlements.” (Edgeworth 1881, p.19). The intent of introducing
these concepts, after him, is to investigate “How far contract is indeterminate.”(ibid. p.20)
To

begin

with,

Edgeworthstartsfromexamining

Jevons’s

two-trader,

two-commodity case. As he does not admit Jevons’s law of indifference, thecommon tangent curve expressed byφ1( a－x ) / ψ1( y ) = φ2( x ) / ψ2 ( b－y ) is notnecessarily equal to y / x.
Lacking the middle side of (7-1), Edgeworth’s condition does not determine an
exchange rate, whereas Jevons’s conditions normally determine a solution. In thelater analysis, Edgeworth goes on to examine the cases of “several persons andseveral variables”(p.26). Jevons could not treat these cases, but the extension was
not difficult for Edgeworth, because he knew how to use Lagrange multipliers.
Edgeworth even introduces the concept of Pareto efficiency by the term “relative
maximum.” (p.23).

Mathematic Psychics is full of sinuous arguments and difficult to grasp his realcontention. It seems, however, that Edeworth was unsatisfied by the treatment of
exchange process by Jevons, Marshall and Walras. I cite only those names that44

Edgeworth named explicitly. These authors assume a price prevailing in a market
and appeal to a concept of aggregate quantity demand. For Edgeworth, such atreatment is not at least general in view of haggling deployed in the market. He
explains the superiority of his method citing that his theory is applicable to thecases of imperfect competition.
Edgeworth’s idea was buried soon after him and “remained dormant until it was
ressureccted by Martin Shubik (1952) as the theory of ‘core’.” (Fonceca, XXX,
Edgeworth’s “Indeterminacy of contract”, 1. Introduction). The literature exploded
in 1960’s and Edgeworth’s three conjectures are proved (Debreu and Scarf 1963).
Edgewoth’s conjectures are now theorems. Citing this fact, many historians of
economic analysis now remark on Edgeorth’ s method. Some scholars like Fonseca
and Ussher (2002), Donzelli (2007; 2009) and Nakano (2009) claims that there wereanother route of development other than that of Marshal and Walras, or economics
based on the concept of demand and supply functions.
I heartily admit this possibility, but I doubt if it can be a realistic economics. The
concept of core assumes that a solution is not blocked by any coalition of the set oftraders in the market. Let it be a set of N traders. Then the number of possible
coalition explodes by the order of 2N. This means an explosion of information andcommunication. Edgeworth’s set of final settlements may shrink to Walrasianequilibrium without checking all coalitions. Suppose that the interventions of a third
party are sufficient for the shrinking. Even in such a case, the information thatshould be communicated between traders is exorbitant. It would not provide an
exchange system that permits to run an economy as big as a small nation. It would
be better to interpret Edgeworth’s idea as an illustration of multi-partite bargaining
process. In this regard, I believe that Marshall’s treatment is much more effective
and realistic, although I do not adhere to any demand and supply cross-point
parable. I will pick up the Marshall case in the next section and discuss problems of
his formula. However, our main concern is not the possible future of the theory. Our
main object is to know where Edgeworth’s idea came from.
In Mathematic Psyhics we find few mentions on Mill (two paragraphs). In a later
long article in Economic Journal, of which Edgeworth was the editor, Edgeworth(1894-85) repeatedly mentions John Stuart Mill and his International Value chapter,
calling it “great chapter” (3 times), “stupendous chapter” (2 times), and “classical45

chapter” (1 time). The reason why Edgeworth did not argue Mill’s international value
chapter is unknown. He may have got his idea from Jevons (1871) or Marshall (1879).
Although his main example was two-trader, two-good case (he repeatedly cited
Robinson and Friday as a case of isolated contract), he knew how to deal with
many-trader, many- good case in an appropriate way. Despite of all these facts, I
think I can claim that Edgeworth was also influenced by Mill’s international value
chapter in a deep level.
First observation is that he thought a pure exchange economy without any
production. Such a situation only exists in the international value chapter in Mill
(1848). Second, when he reflects on The Theory of International Values, Edgewroth(1884-85) considers two-country, three-commodity case. In such a case, he had two
options: (1) complete specialization case (a country produces two commodities andanother country produces the other third commodity, and (2) partially specializedcase where two country have one commonly produced. In the second case, as
Edgeworth discusses himself in Part III, the relative prices of all commodities are
determined through this common good. Why did he give priority to the first option?.
Isn’t this a symptom? Third, Edgeworth’s emphasis on indeterminacy is very uniqueamong economists. If we search such a case in the texts before Edgeworth(1881),
Mill (1844 First question) and Mill (1848, III.18) immerges as probable source ofinspiration.
As I have written above, Edgeworth is doubly influenced by Jevons and Marshall, it
is difficult to detect a direct evidence, but we can at least say that he was not out ofJohn Mill’s field of problem setting. Standing on Mill’s problem setting, Edgeworth
developed a theory of exchange toward an extreme opposite. If we combine thisfact with Marshall’s direct influence from Mill, we may claim that Mill’s proposal torevert to more fundamental and ancillary law compelled the next generation after
him to an economics of a wide variety but within a definite range of directions.

§10. Alfred Marshall
The case of Marshall is much easier than Jevons and Edgeworth, because we haveclear evidence. In fact, he wrote Marshall (1879) which was never officiallypublished in his time but distributed privately by the hand of Sidgwick. The date
1879 stands for the year of this private publishing. This was a part of a two-volume

46

book that was originally planned to be Outline of Political Economy which started tobe composed between 1872 and 1874 (Whitaker 1975, I. 260). Jevons (1871) was
published before this, but if Marshall’s recollection is right, he was not much
impressed by Jevons’ book (Marshall 1925, appendix to review of Jevons (1871)). It
will require a scrupulous study of Marshall’s theoretical development to discern
influences of John Stuart Mill on different themes, but in this paper I concentrate to
the examination of two Pure Theories which were intended to compose a unified
book.
Although he has made some contrivances, Marshall’s Pure Theory of Foreign Tradeis a kind of mathematical annotation of Mill’s international value chapter. Of course,
he is much clear than Mill and successful in providing a proof of uniqueness(Proposition VIII). From a modern mathematical view his explanation does not pay
attention to existence problem, even though a sufficient condition is already given
by John Stuart Mill. As many economists mention it, Marshall started to consider
stability and instability of equilibrium. It can be connected at least to cob-web
theory of the 20th century. It is still questionable if his treatment of stability reallydynamic or not, but our main point of investigation is not here.
Our main interest is how Marshall was influenced by Mill’s treatment and argumentof international trade. The direct influence of Mill’ international value chapter on
Marshall’s Pure Theory is so evident that we have no necessity to prove it. The
question is how Marshall reformulated Mill’s problem. A conspicuous fact is thatMarshall has invented the concept of demand function. Simply speaking, Jevons did
not have a concept of demand function (See section 8 of this chapter). Edgeworth,having read Marshsll’s Pure Theory, criticized that concept. Consequently, Marshallwas the unique person among British founders of neoclassical school, who put thedemand function at the core of economic analysis. 36 More subtle question is why
he did not use the expression “supply curve.” In the case of foreign trade case (inMill’s setting), there is no difference between demand and supply curve. As theycame to be called “offer curve” by later authors, the same relation is called as
demand or supply by the difference of point-of-view. In the case of The Pure Theory
Marshall (1879) contains the term “demand curve” but no “demand function.” But weassume that “demand curve” is employed to express demand function in the case of two
goods case. As he has adopted an exchange between a good and money, any functions
can be called simply “curve”. Yoshii (2017 in this volume) examines Jenkins’
contribution to the formation of demand function concept.

3647

Of (Domestic) Values, the companion volume of the Outline, two expressions
demand curve and supply curve appear almost as frequent as the other. The natural
question is, then, this: did Marshall have a chance to invent demand and supply
curves in other circumstances than he examined Mill’s international value chapter?
We have no direct evidence that prove this. Instead, we have some indirect
evidence that Marshall got the idea of demand and supply function in the course of
studying theory of international values. There are three circumstances for thisthesis, although each of them is closely connected with each other.
The first circumstance is the special composition of the Outline of Political

Economy. As indicated above, this unfinished book contains two major parts: The
Pure theory of Foreign Trade and The Pure Theory of Domestic Values. Contrast
between domestic and international still continues in our days. The particularity of
Outline is that the volume on foreign trade precedes that of domestic values. This isquite strange structure in our days. Normally we first study theory of domestic
economy and then proceeds to foreign economy. Marshall has taken an opposite
composition and we should ask why.
This strange composition seems to reflect Marshall’s process oftheoryconstruction. At the beginning of the Domestic Values, Marshall criticizes Mill’susage of the term “theory of value”. In Marshall’s idea, “theory of value” must be a
generic term which should include both of domestic and international values. He isright but why did he put theory of international values before the theory of domestic
values? Marshal justifies this by saying that “[t]he apparatus of diagrams which wasbest adapted for the investigation of the latter will not be of service here [in theoryof domestic values]”.(p.1) The “apparatus of diagrams” is apparently the diagram inwhich two demand curves (or in the more modern terms two offer curves) cross.
This hints that so-called Marshallian cross came first in his mind when he wasconsidering international values and the domestic version was completed after
that. 37
The second circumstance is the argument and reason that Marshall gives why thetheory of domestic values is more difficult than that of international values. Most of
Sraffa (1926)’s criticism on Marhall’s price theory stats form pointing its
fundamental symmetry. He remarked that this is not an old tradition.

37

48

present-day economists must think in an opposite way, but Marshall thinks
differently. In the theory of international values, the demand curves of one country
is the supply curve for the other country. In the theory of domestic values, Mashallwarns that there is no such symmetry between demand and supply curve. It is
Marshall who has established the logical symmetry of demand and supply curves.
In this particular point, he is right. Marshall’s situation setting in the Pure Theory ofForeign Trade is quite ambiguous, because he contends that he is thinking a case ofmany commodities. But, it is clear that he is thinking a situation where a pattern ofspecialization is already determined. If the bundle of commodities that is produced
in a nation has predetermined proportions, the amount of production of thesebundles is uniquely determined. Then, he is in fact considering a pure exchange
economy. In the theory of domestic values, he adopts money as the commodity to
be exchanged against a commodity to be considered. This presupposes an
economy that Edgeworth would prefer to avoid. Even if Marshall assumescommodity money, the definition of supply curve must have been no easy attempt.
Perhaps we may conjecture that this introduction of supply curve is Marshall’s
major contribution and the second crucial bifurcation point between classical andneoclassical economics. 38 Marshall may have assumed that he had defined supply
curve in a satisfactory way. He may have been dissatisfied by his clumsy and in fact
confused definition of supply curve. We cannot tell firmly which the case was. If it is
the second case, this may have been the reason why he could not complete theOutline. If it is the first case, he was in fact trapped in a logical error. It is also
possible that he wondered between the first and second state of mind.
Marshall’s definition of supply curve is based on what he calls “the great central lawof economic science.” (Domestic Values, p.3, Whitacker p.188) Citing long a part ofan article 39 he has published in 1867, he explains as follows:This law is [1] that “producers, each governed under the sway of freecompetition by calculations of his own interest, will endeavour so to regulate
the amount of any commodity which is produced for a given market during a
The first bifurcation point was, as I have explained above, the Mill’s choice as
standard situation of international trade situation the Mill-Jones point of two-country,
two-commodity economy.
39 “Mill’s Theory of Value” that appeared in Fortnightly Review, April 1876. Reprinted
in Pigou (1925), Part II, Chapter 3, pp.119-133.
38

49

given period, [2] that this amount shall be just capable on the average offinding purchasers during this period at a remunerative price. [3] A
remunerative price is to be interpreted to be a price which shall be just equal
to the sum of the exchange or economic measures of those efforts andsacrifices which are required for the production of the commodity when theamount in question is produced. [4] These economic measures are theexpenses which must be incurred by a person who would purchase theperformance of these efforts and sacrifices.” (Marshall 1925, pp.126-127;
Whitacker 2 p.188. Square brackets are inserted by Shiozawa.)
Recall that the cited part is the Marshall’s summery of what he thinks as the central
truth of the Political Economy. When we put this citation in the original text, we seethat “the central law of economic science” expresses an essence of Mill’s

Principles of Political Economy. Of course, Marshall keeps some reserve such as aproposal to replace “cost of production” by an expression like “expenses of
production,” which is he believes more protected to misunderstanding.
The question we have to examine here is the fact that Marshall uses the term “law”
in singular form. In the citation, many different propositions are in fact told. Is this asingle law? Or, is it a composition of several different laws? Part [3] explains themeaning of the term “remunerable prices”. Part [4] is related to correction or moreexact interpretation of the cost of production. For a long time, cost of production
was commonly interpreted in real terms as “those efforts and sacrifices which arerequired for the production of the commodity when the amount in question is
produced.” Marshall corrects this common interpretation. It should be understoodas the sum of expenses required for the production. 40 However, this central law
comprises at least two different ideas. Part [1] states that producers regulate theamount of their production for a given market during a given period. Part [2] statesthat the produced goods are sold at a remunerable price.
If we understand this law as a law of classical economics, part [2] means that
commodities are sold at a remunerable price in average. The classical theory ofvalue assumes that the value is determined by the cost of production (full cost in
In spite of this remark, the real cost interpretation continues until 1930’s at the timeof Viner. In later part of the 1876 article, Marshall himself was contradicting himself. At
least, he admitted that he had not succeeded in unifying two theories of value, domestic
and international.
40

50

the modern terms). It may fluctuate by the discrepancies of demand and supply, but
comes back to the natural price or value soon or later. Producers assume thequantity of demand that will be sold at this natural price and regulate the quantity of
production. The adjustment process may be complicated but in average the priceof a product moves around the natural price and the production is regulated so as
not to increase the discrepancy between demand and supply too big. This is thecentral truth of the political economy that Marshall interpreted. But, is this the samelaw that Marshall formulated by his demand and supply curves?
John Stuart Mill characterized as “a law of value, anterior to the cost of production,and more fundamental”? (Mill, Library III.16.5)
By the law of demand and supply, many economists will now imagine that a
producer chooses an amount of his/her production for any price that is given in themarket. The above central truth tells no such things. Fundamental assumption isthat prices fluctuate around the natural price. If the market price leaves far fromthe natural price, the producers would not know and cannot calculate the optimalquantity at that market price. They only increase their production if the market
price is higher than the natural price and decrease in the opposite case. This is asimilarprocessthat

Leijonhufvud(1968)

calledcybernetic approach tomacroeconomics. The producer has no definite quantity to produce that is best forhim or her. I will argue this point soon after.
A misinterpretation must have occurred in Marshall, because he induces theexistence of supply curve form this central law 41. The formal definition of supply
curve is given as follows:
The Supply curve SS' for a commodity in a market is such that if any point P2
be taken on it, and P2M2 drawn perpendicular to Ox, P2M2 represents the priceper unit at which a supply of the commodity of which the amount isrepresented by OM2 can be remuneratively produced and brought into themarket in each year (or other given period). (Sidgwick, 1879, p. 5 ; Whitaker
1975, p.192)
In order that this definition is valid, as I will show it soon later, we need an important
41

Yoshii (2017) examines the same point from a different angle.
51

condition: the law of decreasing returns. He may know this fact. Just after giving
the formal definition, Marshall states that “It may be that every increase in theamount supplied involves a more than proportional increase in the expense of
producing it.” However, he also talks about increasing returns to scale case in thesame section. In contrast to a “raw commodity” which we can assume to obey thelaw of decreasing returns, Marshall explains that, in cases of most manufactured
commodities, the law of increasing returns holds. (Sidgwick, 1879, p.6; Whitaker
1975, p.192) How can we define the supply curve in these cases? We cannot.
Let me explain it in more modern terms. It is supposed that producers were to
regulate the amount of their product for a given period of time and at a given pricesystem. This means that they prefer that amount of production in comparison to allother amounts. How can this happen? The only possible situation is that they are
maximizing their profit at an amount of production. The concept of supply curve
implies this. Then, for the profit maximization to hold, the production must be at adecreasing returns to scale point. In fact, let f(x) be the total cost function when an
amount x is produced. The profit is given byp x － f(x)(9-1)

under the assumption that all products are sold at price p. If the profit attains
maximum at point x, expression (9-1) must have the derivative 0. In other words,

p – f’(x) = 0.

(9-2)

If the product has a positive price p, the marginal cost m(x) = f’(x) must be positive.
If the firm is operating with profit, this also means that the return is decreasing toscale. Bt definition decreasing returns to scale means that the average cost isincreasing. This is easy to confirm. In fact, let a(x) be the average cost, that is thetotal expenses divided by the amount of the product and take a derivative offunction a(x), thena’(x) = {f(x}/x)’ = {f’(x)x－f(x)} / x2 = {p－a(x) } / x > 0 ,when the profit is positive and x satisfies (9-2).
The contrapositive of the above observation is the following: when the returns toscale is increasing or constant, supply curve as a function of the product price has
no proper meaning. It is not clear if Marshall was well aware of this fact. In the Pure

Theory of Domestic Values no explicit mention is found. Marshall cites cases ofincreasing returns but makes no warnings.

52

Another symptom that Marshall is confusing is that he often indentifies the supply
curve and the expense curve (or the total cost function). We can define expense
function without any condition, but the expense function and the (inverse functionof the) supply function do not coincide unless the return to scale is decreasing. 42 If
the average cost function or is constant or decreasing, we cannot define thedesired supply level of productions. 43
Marshall passed over the difficulty of defining supply curve. This point remained thesource of trouble through out the Marshall’s life. In the Principles of Economics, heevaded the question by introducing the distinction of internal and external economy.
It was still at the early stage of giant firms. However, with the lapse of time, it
became clear that majority of firms face increasing returns to scale. It was just after
Marshall died that Piero Sraffa (1926) wrote a famous paper On Laws of Returns
and pointed that the production was not limited by the increase of costs but by thelimit of sales. This is simple denial not only of Marshallian cross framework but alsoof the general equilibrium framework. However, at this time, neoclassicaleconomics was too firmly established. No reformulation was made within the
neoclassical economics and it now faces the same difficulty when Sraffa argued
law of returns. 44
We can now understand the real nature of the problem. Marshall wanted to build atheory of domestic values on the same principles as the theory of international
values. In the Pure Theory of Foreign Trade, Marshall successfully reformulated
John Mill’s trade theory to a more formal symmetric theory of reciprocal demand
curves. He knew there was no similar symmetry in the domestic economy and heintroduced the concept of supply curve. It was a natural reaction to the theoreticalsituation that Marshall faced. He did not know the real trouble that the notion of a
supply curve implies. He must have been driven by the charm of re-establishing thesymmetry of supply and demand. When we view from our common knowledge ofthe present, Marshall’s choice may not seem a special decision. If we know,
however, the real trouble of the concept of supply curve, we see how deeplyThis misidentification partly explains why Marshall employed the quantity (insteadof price) as horizontal axe whereas he supposes that prices are given. Expense curve canbe defined for any production quantity, if that production is possible.
43 This is the major reason why neoclassical economics prefer to assume decreasing
returns to scale albeit it is rare to find such an industry or firms. See Shiozawa(1999;
2004; 2016b).
44 For more details, see Shiozawa (2016b), sections 2 and 3.
42

53

Marshall was oriented by the Mill’s thesis on the necessity to revert to the law ofsupply and demand.
The third circumstance is the introduction of the concept of “consumers’ rent”. In

Pure Theory of Domestic Values, the term “consumers’ surplus” is not yet used. If
we read the definition of the term “consumers’ rent” or the mathematical footnote
at the end of section 3 of chapter 2, we can easily know that this is an antecedentof the later “consumers’ surplus.” Why did Marshall feel it necessary to introduce
this concept? A simple answer is: to make in domestic economy a theory that iscomparable to that of the gains from trade. I have no space to argue this point indetail. This must be one of three circumstantial evidences that Marshall was deeply
influenced when he started to build his new theory of economics.
At the end of discussion on Marshall, let us make a brief comparison between
Edgeworth and Marshall. In a word, Edgeworth was more inclined to pure logic of
exchange and Marshall was more realistic. Although Marshall’s concept of supply
curve has a serious defect, his idealization was based on monetary economy.
Edgeworth wanted to exclude it. He was more loyal to the idea of catallactics.
However, he could not really think how the large network of exchanges can actually
be organized. If we think of this point, money and price system (including
price-mediated exchange) are indispensable institution that makes modern
large-scale economy work. As the trouble with neoclassical economics isdeepening, there are some reflective movements in search of alternatives. It is truethat Edgeworth show an extreme opposite to Marshallian paradigm. But the search
for a pure theory of exchange is itself a product of Mill’s misguiding problem setting.
It is necessary to return before the Mill’s solution and his reversion.

§11. Alternative way outs? / Senior, Mangold and Sidgwick
We have traced the history how Mill’s “solution” paved the way to the neoclassicalrevolution. It may seem that the force that led this history was overwhelming andthere were no alternatives to this trend. But we may ask if there was no way out.
Were there no trials in the direction of a new theory? Yes, of course, there were.
McKenzie’s Princeton teacher Frank D. Graham was the most famous dissident to
the mainstream tradition. Even before Marshall and Edgeworth, there were threenotable exceptions: Senior (1830), Mangoldt (1863) and Sidgwick ([1883] 1901).

54

Latter two cases are reported in Edgeworth’s survey (189-95, III).
I do not explain in detail. Edgeworth (1895) has given a good concise account of
two contenders (A.4; B.3). Magoldt (1863) has written in German and his influence
to the English world was limited. He was somewhat forgotten economist even inGerman world (Schneider, 1960). Jevons (1871)’s second edition includes the bookin the list in appendix but no explicit mention on him in the Preface to the Second
edition, where Jevons tried to explore all important precursors in mathematical
economics. Marshall once cited Mangoldt’s name in his Principles, but no mention
appearsinhiscorrespondences(Schneider,1960).

Without

Edgeworth’s

subsection on him, he may have been forgotten almost eternally. Although we have
now English translation of Appendix II (Chipman , 1975), let me pass through him
and introduce Sidgwick’s argument:[L]et us suppose that there is at least one other commodity ---say corn --which is produced both of value, discussed in the preceding chapter, therelative values of cloth and corn in England must be determined by theircomparative costs of production; and, again, the relative values of wine andcorn in Spain must be determined in the same way.

(Sidgwick, 3rd ed[1891],

p.213, Book II. Chapt III., section 2.)
As he suppose that England exports cloth to Spain and Spain exports wine toEngland, this is two-country, many-commodity economy. 45 If there exists a third
commodity that is competitively produced in both countries, the (relative) wages of
two countries are determined by the corn producing industry. Then, through thislink commodity (Graham’s term), the prices of all commodities are determined.
Sidgwick’s contention can be paraphrased as follows. In a two-country,
many-commodity economy, suppose there is a commodity that is produced in two
countries E and S. Let wE and wS be the wage rates of countries E and S. If thetransportation cost is negligible, we can write a price equality condition for thecommon product:(1+πE) wE / cE = (1+πS) wS / cS ,(10-1)In the Sidgwick’s expression, many commodities other than corn may exist. In thissense, he is thinking two-country, many-commodity economy, but we may represent itby two-country, three-commodity economy. See Figure 2.
45

55

HereπE,πS and cE, cS are respectively the standard profit rate and laborproductivity for each country. If we suppose that the profit rates of the twocountries do not much differ, we have approximately

wE / wS = cE / cS.

(10-2)

In other words, wage rates ratio is proportional to the labor productivity ratio. If thewage rate of a country is determined, the prices of all other commodities that are
produced in the country are also determined. As the wage rate ratio is determinedby equation (10-2), the prices of all commodities are determined. The cost of
production theory of value holds.
The difference between John S. Mill and Sidgwick is whether they suppose
commonly produced good. Graham called this common product link commodity. A
simple existence of link commodities thus resurrects the cost of production theoryof value à la Ricardo.
Sidgwick first published his Principles in 1883, a few years after he publishedMarshall’s Pure Theory of Foreign Trade privately. A curious question arises. Did
Sidgwick have this idea when he published Marshall’s Pure Theory? Sidgwick used
the book as text for his lecture in Cambridge. Is it in the course of his teaching Pure

Theory that he got the idea that he exposes in his Principles? A second interestingquestion is how Marshall reacted to Sidgwick’s opinion. We know that he did notcomplete his Outline which comprises two Pure Theory volumes. Is this the reason
that he could not complete it? If so, then, why did he continue to employ the idea of
demand and supply curves at the core center of his theory?
Naturally, the debate that followed Sidgwick (1983) was concerned with theexistence of link commodity. In the third edition (1891, p.213, footnote 1) Sidgwick
cites Bastable who has criticized this point. Bastable’s critique is more apologetic
than analytic, because he appeals to the authority of John S. Mill. Citing Bastable,
Edgeworth (1894-59, III) argues also against Sidgwick but I do not think it ispersuasive enough. In the subsection presenting Mangoldt, Edgeworth questions
the possibility of coincidence that two countries have the same cost of production
for a product. However, he is forgetting the possibility of a mechanism that brings
them coincide, like present day fluctuating exchange rate regime. Of course, all ofthem, including Mill, Mangoldt, Bastable, and Edgeworth, concentrate on terms oftrade and do not analyze how the demand and production may come to equalize.

56

For this analysis, we should know the world production possibility set. If Sidgwick
and Edgeworth knew the shape of the production possibility set, for example if they
had a rough idea of Figure 2, the course of argument may have been very different.
If they knew Figure 2 and the reason why Mill-Jones point does not appear, they
may have trekked a different historical path.
After all, Sidgwick’s contention was a complete refutation of Mill’s “solution” and allother followers. This is in total contradiction with what Edgeworth think thefundamental principle of international trade. This principle, according to him,
implies in its negative form, that the value of articles in international market is notproportioned to the cost.(Edgweorth 1894 I, p.36) and this was the starting point of
all economics of exchange programs. Edgeworth and Marshall were divided in theirorientations but they could not accept Sidgwick, because it implies the fall down of
all of their contributions to economics. The only defense possible for Edgeworth
was to point the implausibility of the existence of such commonly produced
commodity. In face of Sidgwick and Mangoldt, Edgeworth tried obstinately todefend the framework of exchange economy. This was a natural result of arevolution of economics and Edgeworth was too deeply absorbed in this revolution
to convert to a new (or more classical) interpretation.
An interesting question is how Mangoldt and Sidgwick reacted to their own
discoveries. If they think the true significance of their economy, they might have achance to open a path to a totally different economics than that based of demandand supply function.
The case of Nassau W. Senior (1830) is more difficult to interpret, but maybe moreinteresting as an alternative to Mill’s “solution”. He left a series of lectures. They
contain an interesting style of argument. He was more interested in the particularquestion such as how the value of money is determined. Consequently, he did notargue explicitly the theory of international values as it is commonly understood. Nor
he did not write a textbook that explains his system of economics. 46 We have toguess through his explanations on other topics the theory that he might havepossessed in his brain.

Although he talks much about wages and profits, Senior’s Political Economy (1850)
contains few discussions on how the prices are determined.

46

57

His lecture on the value of money is commonly understood as cost-of-production
theory. I cannot tell if it is essentially different from Hume and others’ species-flowmechanisms. Only thing I can say here is that Senior had an image that the samecommodities are produced and exported and these common commodities
contribute to determine the wage rate disparity between countries. Let me cite ashort paragraph:
Or to use a still more concise expression, that labour in England is eight times
as productive of exportable commodities as in Hindostan, and labour in North
America is one-forth more productive of exportable commodities than in
England. (Senior, 1830, On Cost of Obtaining Money, p.12)
Senior points that the price of exported commodities depends on “the amount of
the wages which has been paid, and the time for which they have been advanced”(ibid., p.14). If we combine these propositions, we can make a similar equation like
(10-1) and the wage rate disparity follows from (10-2). If the relative wage rates are
known, it is possible to tell the prices of all other commodities, because they pay
the same wage rate in the same country.
By his explicit reference to labor productivity and wage rate and his firm frameworkof const-of-production theory of value, Senior had a chance to develop totallydifferent theory of international values. 47 In fact, in view of the new theory ofinternational values presented in chapter XX, almost of all Senior‘s arguments canbe translated into the new theory.
Senior was 18 yeas junior to Ricardo and 15 years senior to John Stuart Mill.
Senior’s lectures in Oxford were delivered in 1820’s and some of them was
published between 1828 and 1830. John Mill had a chance know the Senior’s
cost-of-production theory of international values before Mill published Mill (1844)
and Mill (1848). Indeed, as Bowley (1937) put it, Senior, Torrens and J.S. Mill
Bowley (1937, chapter 6, p.201) points the possibility of two different ways of treatinginternational trade: one that investigates comparative physical costs and the other thatanalyzes in money terms. Bowley places Ricardo, J.S. Mill, Taussig, Marshall and
Haberler in the first group and Senior and Ohlin in the second group. My
understanding is 90 degree different from her classification. By their theories of value,
Senior, Mangoldt and Sidgwick are much closer to Ricardo, because they all thoughtthat cost of production theory of value (or classical theory of value) is valid ininternational trade as well as in domestic exchange.

47

58

exchanged their opinions on the terms of trade:
The famous controversy between Senior and Torrens on the terms of trade,which was take up again by J.S. Mill, turned exactly on this question of therelevance of an analysis confined to two commodities and two countries.
(Bowley, 1937, p.225)
If John Stuart Mill reflected more closely on his “solution” and study Senior, he may
not have advanced that famous thesis that appealed the reversion to the more
fundamental law of demand and supply.

§12. What was the neoclassical revolution? Implications for Future
Research
This paper has shown an origin of the neoclassical revolution. It goes back to young
John Stuart Mill, when he tried to solve an unsettled problem. It was a question left
by Ricardo in the filed of international trade.
What Mill posed to himself was how the advantage of trade is divided among
trading nations. He intended to solve this problem by providing a theory ofinternational values. The simplest situation setting was two-country, two-commodity
case. Nobody doubted there was a deep trap in this situation setting. Mill simply
excluded the situations where one country cannot enjoy gains from trade. By thispure inference, he was lead to examine a pure exchange economy. As a result of his
examination, a conclusion came to his mind. It was his famous thesis: “we mustrevert to a principle anterior to that of cost of production, and from which this lastflows as a consequence,—namely, the principle of demand and supply.” (Mill, 1844,
I.19)
This thesis made a long strong influence on the research programs of economics. In
the UK, three founding fathers were deeply influenced by the thesis and by thesetting. They worked different ways and constructed their own economics. Amongthe three, it was Alfred Marshall with his demand and supply functions that paved
the way to today’s mainstream economics.

59

The neoclassical revolution in the UK was a turn from economics of production tothat of exchange. Nearly 150 years after, we have trouble with economics. Many
economists and non-economists now recognize that economics needs a change.
What will be the remedy for that? A series of modifications will not be helpful. A
fundamental re-building is required. History of the neoclassical revolution is
illustrative. Neoclassical economics is a kind of Ptolemaic geocentric system. It had
developed much and explains many, but it is basically wrong. It needs a Copernican
revolution.
This chapter described a story. A question which was not hitherto referred to is this:why wasn’t the story conceived in the past? One of possible answers seems to lie ina Takashi Negishi’s postcard to the author 48 It reads:
In our country international economists are not interested in the history of
economic doctrines and historians of economic thought know little about theinternational economics. (Postcard dated July 8, 2011. Translated fromJapanese by the author)
Professor Negishi talks about intellectual situation in Japan, but similar situation isobserved in many other countries. If a tipping point of economics was in theinternational trade theory, a coincidence of history and theory was necessary. I am
rather a theoretician and not a historian. It was Yasuaki Tsukamoto who taught methat history is a strong tool to persuade people to a new theory. He made me
consider the meaning of the John Stuart Mill’s “solution” in a historical perspective.
He thus helped me to spot the point where the classical economics turned toneoclassical economics.

Acknowledgment
An earlier version of this paper was first read at a conference jointly organized by
the South-West branch of the Japanese Society for the History of Economic
Thought and the Kyushu branch of Japan Association for Evolutionary Economics
held on June 21, 2014.
The original English version with the title On Ricardo’s Two Rectification Problems
I reproduce this sentence on Negishi’s permission (post card dated at December 19,2014).
48

60

was completed in September of the same year. It was then divided into two parts.
The first half is to be published with the same title as Shiozawa (2017). The second
half of the original version became independent and formed the first draft of thischapter. The idea of this chapter was reported with the title Why did John Millretreat? / An Internalist View on an Origin of the Neoclassical Revolution as a partof a special session in the annual conference of the Japanese Society for theHistory of Economic Thought held in Hikone, Shiga Prefecture on May 31, 2015. The
original version was completely revised owing much to the preparatory discussions
for the special session organized by Satoko Nakano. I thank Masashi Izumo, Akinori
Isogai, Satoko Nakano for giving me the chance of reporting. I give my special
thanks to Satoshi Yoshii who charged me a difficult task to respond by hiscomments and advices on this paper. I also owe much to members of the ResearchGroup for International Value Theory for their valuable comments and discussions.
Robin Edward Jarvis encouraged me by his short review with deep understandingon the first version of this paper.

61

References
Aldrich, J. (2000) The Jevonian Revolution in International Trade Theory. Journal of

History of Economic Thought 22(1): 65-84.
Bastia, F. (1845) Selected Essays on Political Economy. Library.
Beinhocker, E. D. (2006: Paperback Ed. 2007) The Origin of Wealth.; Evolution andComplexity and the Radical Remaking of Economics, (Paperback Edition Subtitle:
The Radical Remaking of Economics and What it Means for Business and Society),
Harvard Business Review Press.
Blaug, M. (2001) No History of Ideas, Please, We're Economists. Journal of

Economics Perspective 15(1): 145-164.
Boyer R., H. Uemura and A. Isogai (2012) Conclusion in Boyer R., H. Uemura and A.
Isogai Eds. (2012) Diversity and Transformation of Asian Capitalisms, Routledge.
Bowley, M. (1937: Paperback 2010) Nassau Senior and Classical Economics,
Routledge.
Chipman, J.S. (1965) A Survey of the Theory of International Trade: Part 1, The
Classical Theory. Econometrica 33(3): 477-519.
Chipamn, J.S. (1975) On the Equation of International Demand, Hans von Mangoldt,
with Introductory Note. Journal of International Economics 5: 55-97.
Creedy, J. (1992) Jevons's Complex Cases in the Theory of Exchange. Journal of theHistory of Economic Thought 14(1): 55-69.
Debreu, G. and H. Scarf (1963) A Limit Theorem on the Core of an Economy.

International Economic Review 4(3): 235-246.
Dobb, M. 1973 Theories of Value and Distribution since Adam Smith, Cambridge
University Press.
Donzelli, F. (2007) Jevons, Jenkin, and Walras on demand-and-supply analysis in thetheory of exchange, Working paper, Dipartimento do scienze economia aziendalee statistiche, University of Milano.
Donzelli, F. (2009) Edgeworth vs. Walras on Equilibrium and Disequilibrium. Working
Paper no.2008.47, Departimento di of Economy

and Statistics, State Universityof Milano..
Dorobăț, C. E. (2015)
Edgeworth, F. Y. (1881) Mathematical Psychics: an Essay on the Application of

Mathematics to the Moral Sciences. Reprinted, Augustus M. Kelly, 1967.
Edgeworth, F. Y, (1894-95) The Theory of International Trade (in three Parts)

Economic Journal 4: 35-50, 4: 425-443, 4: 606-638.
Faccarello, G., 2014 'Nous marchons sus un autre terrain.' The Reception of62

Ricardo in the French Language: Episodes from a Complex History, in Faccarello
and Izumo (Eds.) The Reception of David Ricardo in Contemporary Europe andJapan, London: Routledge, 2014, 10-75.
Fonseca, G.L. (????) Edgeworth’s “Indeterminacy of Contract” in History of
Economic Thought Website.
Fonseca, G.L., and L.J. Ussher (2002) Microfoundation and the Marginalist
Revolution. Paper pesented at the History of Economic Society Conference,
University of California, Davis, July 6, 2002.
Fujimoto, T. and Y. Shiozawa (2011-12) Inter and Intra Company Competition in theAge of Global Competition, Evolutionary and Institutional Economics Review
8(1):1-37, 8(2):193-231.
Gehrke, Ch. (2014) The reception and further elaboration of Ricardo’s theory ofvalue and distribution. In Faccarello and Izumo (Eds.) The Reception of David

Ricardo in Continental Europe and Japan. Routledge, London. Chapt.2,
pp..XXX-XXX.
Gehrke, Ch., and H. Kurz (2006) Sraffa on von Bortkiewicz: Reconstructing theClassical Theory of Value and Distribution. History of Political Economy 38(1):91-149.
Hawkins, T. (1974) The Theory of Matrixes in the 19th Century. Proceedings of theInternational Congress of Mathematics, Vancouver, 1974.
Hicks, J.R. (1974) The Scope and Status of Welfare Economics, Oxford Economic
Papers (New Series) 27(3): 307-326.
Hick, J. R. (1976) Revolution in economics, in Latsis (Ed.) Method and Appraisal in

Economics, Cambridge University Press, 1976, pp. 207-218.
Hollander, S. (1979) Economics and Ideology: Aspects of the Post-Ricardian
Literature. Literature of Liberty 2(3): 5-35. Available at
http://www.econlib.org/library/Essays/LtrLbrty/hlnPRL.html
Humphrey, T. M. (1995) When Geometry Emmerged: Some Neglected Early
Contributions Offer-Demand Curve Analysis. Federal Reserve Bank of RichmondEconomics Quarterly 81(2): 39-73.
Humphrey, T. M. (1996) The Early History of the Box Diagram. Federal Reserve Bankof Richmond Economics Quarterly 82(1): 37-75.
Koopmans, T.C. (Ed.) (1951) Activity Analysis of Production and Allocation, New
York, NY: John Wiley and Sons.
Kuhn, T. (1962) the Structure of Scientific Revolutions. University of Chicago Press,
Chicago.

63

Inoue, T. (2005) W.S. Jevons / Is Jevons’s economics a microeconomics? (inJapanese) in Ohmori (Ed.) The World of Economic Classics 2, Nihon Keizai
Hyoronsha, Chapter 1, pp.3-47..
Jevons, W.S. (1865; 1986) The Coal Question, Macmillan and Co.
Jevons, W.S. (1866) Brief Account of a General Mathematical Theory of Political
Economy. The Journal of the Royal Statistical Society, Section F, 29: 282-87.
Availableathttps://www.marxists.org/reference/subject/economics/jevons/mathem.htm
Jevons, W.S. (1871; 1879, 1888) The Theory of Political Economy (1st Ed. 1871, 2nd
Ed. 1879, 3rd Ed. 1888) Available at Library of Economics and Liberty.
Jevons, W.S. (1875; 1876) Money and the Mechanism of Exchange. Available at
Library of Economics and Liberty.
Jones, R. (1961) Comparative Advantage and the Theory of Tariffs: A Multi-country,
Multi-commodity Model. Review of Economics Studies 28(3): 161-175.
Keen, S. (2011) Debunking Economics, Zed books.
Knight, F. (1935) Ricardian Theory of Value and Distribution. Canadian Journal of
Economics and Political Science 1(1): 3-25; 1(2): 171-195; 1(3):Lardner, D. (1950) Railway Economy; a Treatise of the New Art of Transport. New
York; Harrer and Brothers.
Leijonhufvud, A (1968) On Keynesian economics and the economics of Keynes: astudy in monetary theory, Oxford University Press.
MacLeod, Ch. (1983) Henry Martin and the authorship of ’Considerations upon the
East India Trade’. Historical Research 56(134): 222–229.
Maneschi, A. (2002) The Tercentenary of Henry Martyn’s Considerations upon the
East India Trade. Journal of the History of Economic Thought 24(2): 233-249.
Maneschi, A. (2004)
Mangoldt, Hans von (1863: 1963) Grundriss der Volkswirthschaftslehre. English
translation of Appendix II in Chipman (1975).
Marshall, A. (1879) The Pure Theory of Foreign Trade: The Pure Theory of Domestic

Values.
Marshall, A. (1923) Money, Credit and Commerce.
Marsahll, A. (1925) Memorials of Alfred Marshall, Edited by A. C. Pigou, London;
Macmillan.
Martyn, H. (1701: 1720) Considerations upon the East India Trade, anonymous
pamphlet. Reprinted with the title in 1720. McLock (1856) included the pamphlet
in his64

McCulloch, John R., ed. 1856. Early English Tracts on Commerce. Reprinted byCambridge University Press, Cambridge, 1954.
McKenzie, L (1954a) On Equilibrium in Graham’s Model of World Trade and other
Competitive Systems. Econometrica 22(2):148-161,
McKenzie, L (1954b) Specialization and Efficiency in world Production, Review of

Economic Studies 21(3): 165-180.
McKenzie, L (1955) Specialization in Production and the production Possibility
Locus, Review of Economic Studies 23: 56-64.
Mill, James (1822) Elements of Political Economy.
Mill, J.S. (1844) On Laws of Interchange between Nations. First essay in J.S. Mill,

Essays on Some Unsettled Questions of Political Economy, 1844.
Mill, J.S. (1848) Principles of Political Economy.
Mirowsky, Ph. (1989; 1991) More Heat than Light, Economics as Social Physics,
Physics as Natures’s Economics, Cambridge University Press. Paperback1991.
Morishima, M. (1989) Ricardo’s Economics: A general equilibrium theory of
distribution and growth. Cambridge University Press.
Nakano, S. (2009) Jevons's Market View through the Dynamic Trajectories of
Bilateral Exchanges. Chapter 10, pp.169-201. In A. Ikeo and H. Kurz (Eds.) A
History of Economic Theory / Essays in honour of Takashi Negishi, London:
Routledge, 2009.
O’Connor, J.J., and E.F. Roberson (2005) The function concept.
http://www-history.mcs.st-and.ac.uk/HistTopics/Functions.html
Ohlin, B. (1933) Interregional and International Trade.
Ricardo (1817:1821) On the Principles of Political Economy and Taxation, Edited by
Sraffa, Volume I of The Works and Correspondences of David Ricardo,
Cambridge University Press, 1951. Cited as “Sraffa 1951”. “Library” stands fortexts and paragraph numbers in the Library of Economics and Liberty.
Rowthorn, R. (2013) The Impact of China and India. In N. Yokokawa, J. Gosh and R.
Rowthorn (Eds.) Industrialization of China and India: Their Impacts on the World

Economy. Routledge. 2013. Chap. 1.
Savosnick, K. M. (1958) The Box Diagram and the Production Possibility Curve.
Ekonomisk Tidskrift, 60(3): 183-197.
Schneider, E. (1960) Hans von Mangoldt on Price Theory: A Contribution to theHistory of Mathematical Economics. Enonometrica 28(2): 380-392.
Schumpeter, J.A. (1954; 2006) History of Economic Analysis, Allen and Unwin.
Talyor and Francis e-Library, 2006.

65

Senior, N.W. (1830) Three Lectures on the Cost of Obtaining Money. Available athttps://archive.org/stream/threelecturesont033052mbp#page/n0/mode/2up
Shiozawa, Y. (1975) Durable Capital Gods and their Valuation, KIER Discussion
Paper No.8, Institute of Economic Research, Kyoto University. Uploaded in
ResearchGate.
Shiozawa, Y.

(1999) Economics

and Accounting:a comparison between

philosophical backgrounds of the two disciplines in view of complexity theory,
Accounting, Auditing and Accountability Journal 12(1): 19-38.
Shiozawa, Y. (2004) Evolutional Economics the 21st Century. Evolutionary andInstitutional Economics Review, 1(1): 5-47.
Shiozawa, Y. (2007) A New Construction of Ricardian Trade Theory: A many-country,
many-commodity case with intermediate goods and choice of techniques,

Evolutionary and Institutional Economics Review 3(2): 141-187
Shiozawa, Y. (2011) Subtropical Convex Geometry as Ricardian Theory ofInternational Trade. A draft paper is available at my ResearchGate.
.Shiozawa, Y. (2014) The Final Solution of Ricardian Problem on International Trade.
( in Japanese: Ricardo Boeki Mondai no Saishu Kaiketsu), Iwanami Shoten.
Shiozawam Y. (2015) International Trade Theory and Exotic Algebra. Evolutionary

and Institutional Economics Review 12(1): 177-212.
Shiozawa, Y. (2016) The Revival of Classical Theory of Values, Yokokawa et als.
(Eds.) The Rejuvenation of Political Economy, 2016, Oxon and New York:
Routledge, Chapter 8, pp.151-172.
Shiozawa, Y. (2016b) A Guided Tour of the Backside of Agent-Based Simulation
pp.3-50, in Hajime Kita, Kazuhisa Taniguchi, and Yoshihiro Nakajima (Eds.)

Realistic Simulation of Financial Markets / Analyzing Market Behavior by the Third
Mode of Science, Springer Japan.
Shiozawa, Y. (20176, to appear) On Ricardo’s Two Rectification Problems. Chapter
10 in Senga, Izumo and Tabuchi (eds.) Ricardo andSidgwick, H. (1883; 1901) Principles of Political Economy. London: McMillan.
Available at http://ebook.lib.hku.hk/CADAL/B3139033X/
Smith, A. (1896) Lectures on Justice, Police, Revenue and Arms, delivered in the
University of Glasgow by Adam Smith. Reported by a student in 1763, and editedwith an Introduction and Notes by Edwin Cannan.
Sraffa (1960) Production of Commodities by means of Commodities. Cambridge
University Press.
Stigler, G. (1952) The Ricardian Theory of Value and Distribution. Journal of66Political Economy 60(3): 187-207.
Tabuchi, T. 2017 Comparative Advantage in the Light of the Old Value Theories.
Chapter ## in this volume.
Takenaga, S. 2016? Structure of the theory of value of David Ricardo, uploaded inReserachGate. DOI: 10.13140/RG.2.1.5068.2646.
Turgot, A.R.J. (2011) The Turgot Collection: Writings, Speeches, and Letters ofAnne Robert Jacques Turgot, Baron de Laune. Edited by David Gordon, Ludwig
von Mises Institute. Value and Money appears as Chapter 8, pp.163-182.
Wald, A. (1934) Uber die Produktionsgleichungen der o“konomischen Wertlehre,
Ergebnisse eines mathematischen Kolloquiums.
Weintraub, E. Roy (1985) General Equilibrium Analysis: Studies in Appraisal,
University of Michigan Press.
Whitaker, J. K. (Ed.) (1975) The Early Economic Writings of Alfred Marshall,
1867-1890. Two volumes. London; McMillan for the Royal Economic Society.
Yoshii, S.(2014) Conversion to a Simultaneous Determination System of Prices andQuantities, (in Japanese) Shiozawa and Aruka, Reconstruct Economics, Chuo
University Press. Chap.5, pp.269-349.
Yoshii, S. (2017) An extinction of adjustment time and an introduction of stability
condition in economics through misunderstandings to J.S. Mill's law of supply anddemand and international value theory, Chapter XX, in this volume.
Yukizawa, K. (1974) Original Meaning and Deformed Interpretation in Ricardo’s‘Comparative Advantage Theory.’ Shogaku Ronsan (Chuo University) 15(6): 25-21.
English translation by Takenaga is available.
White, M.V. (1989) Why are there no supply and demand curves in Jevons? Historyof political economy 21(3): 425-456

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