Franco Donzelli
Topics in the History of Equilibrium Analysis
Lesson 4
Jevons, Jenkin, and Walras on
demand-and-supply analysis in
the theory of exchange
Ph.D. Program in Economics
University of York
February-March 2008
Introduction 1

W. Stanley Jevons develops his “theory of exchange” in:




In spite of Jevons’s insistence on the fundamental role of the socalled “laws of supply and demand”, no formal demand-and-supply
analysis:



“Brief Account” (1866)
Chapter 4 of The Theory of Political Economy (TPE), first edition
(1871)
Chapter 4 of The Theory of Political Economy (TPE), second
edition (1879)
is actually employed by Jevons in the derivation of the theory;
can be actually deduced from the formal statement of the theory.
This is a mystery which has attracted some attention in the literature,
but has not been adequately solved on theoretical grounds (White)
Franco Donzelli
Lesson 4 - Jevons, Jenkin, and Walras
2
Introduction 2

A comparison with the theory of exchange put forward by two
economists contemporary with Jevons, Léon Walras and Fleming
Jenkin, can help unraveling this issue.

Léon Walras develops his theory of exchange in:


his first two mémoires: “Principe d’une théorie mathématique de
l’échange” (1874) and “Equations de l’échange” (1877);
Section II of the first edition of the Eléments d’économie politique
pure (Eléments)(1874).

Walras’s solution of the exchange problem rests on a fully-fledged
demand-and supply analysis of the traders’ choices and behavior.

Since 1874, Walras repeatedly criticizes (in private correspondence
and public contributions) Jevons’s approach to the theory of exchange,
in particular the lack in it of a true and proper demand-and-supply
analysis.
Franco Donzelli
Lesson 4 - Jevons, Jenkin, and Walras
3
Introduction 3

Jevons does not react to Walras’s critical remarks: in particular he
does not try to incorporate Walras’s implicit and explicit suggestions
into the second edition of TPE.

Why? Perhaps because Walras’s remarks are made at a time when
Jevons’s ideas have already taken a final shape, which cannot be
easily modified.

But then why Jevons does not react to Jenkin’s remarks, that are
advanced at a much earlier time (1868), when Jevons had not yet
started writing TPE (1870)?

Fleeming Jenkin, an engineer-economist very active in the economic
debates of the late 1860s and early 1870s, develops an almost
complete microfounded demand-and-supply analysis and graphically
solves the problem of equilibrium determination in an exchange
economy in a series of two (or three) letters mailed to Jevons in
1868.
Franco Donzelli
Lesson 4 - Jevons, Jenkin, and Walras
4
Jevons’s theory of exchange: the conceptual apparatus 1

In the first thirteen Sections of TPE Jevons discusses a two-trader,
two-commodity, pure-exchange economy, that is an Edgeworth Box
economy ℰJ2x2 = {(ℝ2+, ui(‧), ωi)i=12} satisfying a few further specific
assumptions concerning the traders’ endowments and utility
functions:
 the traders are “cornered”, with: ω1 = (ω̅1, 0), ω2 = (0, ω̅2)
 each trader is characterized by a cardinal, additively separable
utility function:
ui 
x i v 1i 
x 1i v 2i 
x 2i 
,
x i  X i , i 1, 2
satisfying the following restrictions on the signs of the first and
second-order pure partial derivatives:
Franco Donzelli
Lesson 4 - Jevons, Jenkin, and Walras
5
Jevons’s theory of exchange: the conceptual apparatus 2
u i 
x i 

u i
xi  
u i
xi 
,

x 1i

x 2i
2
2

u i
xi  
u i
xi 

x 21i

,

x 22i

v
x 1i 
,v
x 2i 
 0, 
x i  X i , i 1, 2
1i 
2i 



v
x 1i 
,v
x 2i 
 0, 
x i  X i , i 1, 2
1i 
2i 
Even if Jevons does not explicitly define the concept of Marginal
Rate of Substitution, he implicitly uses it:
2i
MRS i21 
x i  dx
dx 1i

u i
x i
dx i 
u i 
x i


u i
xi

x 1i

u i
xi

x 2i

v
x 1i 
1i 
, i 1, 2
v
x 2i 
2i 
Even if Jevons’s model unambiguously refers to an Edgeworth Box
economy, his verbal interpretation of the model is not free of major
ambiguities.
Franco Donzelli
Lesson 4 - Jevons, Jenkin, and Walras
6
Jevons’s theory of exchange: the conceptual apparatus 3

The first ambiguity has to do with Jevons's peculiar concept of "trading
bodies", that are alternatively viewed as either individual traders, or
representative agents, or "fictitious means".

The second ambiguity arises from Jevons's interpretation and use of
the concepts of statics, dynamics and equilibrium:

after sharply distinguishing between statics and dynamics, and
contending that the exchange problem ought be tackled from a
purely statical point of view, Jevons is apparently willing to
concede that the study of the equilibration process is not
inconsistent with statics;

yet, after recognizing that a truly dynamic analysis would require
integrating suitable differential equations describing the trading
process over time, he ends up with endorsing a strictly
“instantaneous” interpretation of the equilibrium concept.
Franco Donzelli
Lesson 4 - Jevons, Jenkin, and Walras
7
Jevons’s theory of exchange: the conceptual apparatus 4

The third ambiguity is that surrounding the so-called “law of
indifference”, which is initially viewed as the outcome of a market
equilibration process taking place under stringent assumptions about
the traders’ knowledge and information, but then reduced to an
almost trivial truism in the only relevant application.

“Thus, from the self-evident principle, stated on p. 137, that there
cannot, in the same market, at the same moment, be two different
prices for the same uniform commodity, it follows that the last
increments in an act of exchange must be exchanged in the same
ratio as the whole quantities exchanged. [...] This result we may
express by stating that the increments concerned in the process of
exchange must obey the equation:
dx 2
dx 1
Franco Donzelli
 xx 21

1
Lesson 4 - Jevons, Jenkin, and Walras
8
Jevons’s theory of exchange: the conceptual apparatus 5

The “law of indifference” is supposed to apply to an “act of exchange”,
where “two commodities are bartered in the ratio of x₁ for x₂”.

Then the result is simply obtained by observing that "every mth part of
x₁ is given for the mth part of x₂, [...] so that, at the limit, even an
infinitely small part of x₁ must be exchanged for an infinitely small part
of x₂, in the same ratio of the whole quantities", which is indeed a
platitude.

An “act of exchange” involves two traders only.

The “law” holds “at one moment” and an “act of exchange” is
“instantaneous” as well: Jevons should not speak of “the increments
concerned in the process of exchange”.
Franco Donzelli
Lesson 4 - Jevons, Jenkin, and Walras
9
Jevons’s theory of exchange: a formal statement 1

Jevons starts by assuming, “for a moment”, that the “[finite] ratio of
exchange” between two commodities be “established” at a given
level.

Under that provisional assumption, Jevons verbally arrives at the
conclusion that the benefits from exchange for either trader cease
when the ratio of each trader’s “degrees of utility” is equal to the
inverse of the ‘differential’ “ratio of exchange” of the two
commodities, which in turn is assumed to be equal to “the
established [finite] ratio of exchange”.

The “point” so determined is called the “point of equilibrium” by
Jevons.

First surprising omission: since the provisionally “established ratio of
exchange” is generally not what would currently be called a
competitive equilibrium “ratio”, the quantities of commodities that the
traders want to exchange at Jevons’s “point of equilibrium” cannot
generally be exchanged.
Franco Donzelli
Lesson 4 - Jevons, Jenkin, and Walras
10
Figure 1
Fig 1
Franco Donzelli
Lesson 4 - Jevons, Jenkin, and Walras
11
Jevons’s theory of exchange: a formal statement 2

But not a single word is uttered by Jevons about this eventuality and
its possible consequences.

Similarly surprising is the diagram (Figure 5 of TPE) used to
illustrate the verbal argument: one trader only; two superposed
marginal utility curves, drawn under the assumption that “the ratio of
exchange [...] be that of unit for unit, or 1 to 1”.

But, once again, nothing is said about the reason for selecting
precisely that “ratio of exchange” or about the consequences of that
selection, in the likely case the “1 to 1 ratio” were not what would
currently be referred to as the competitive equilibrium “ratio”.

Then, taking for granted that equation (1) holds, Jevons eventually
proceeds to determine the equilibrium conditions for his Edgeworth
Box economy
2
E2J 2  
 2, u i 

, i 
i1
Franco Donzelli
Lesson 4 - Jevons, Jenkin, and Walras
12
Exchange equilibrium in Jevons
d*12
x*12
O2
tg α*= x*2/x*1=
d*21/s*11 =
s*22/d*12 =
x*21/(ω̅1-x*11)=
(ω̅2-x*22)/x*12
x*21
x*22
α*
d*21
s*22
α*
O1
Franco Donzelli
ω
x*11
Lesson 4 - Jevons, Jenkin, and Walras
s*11
13
Jevons’s theory of exchange: a formal statement 3

Jevons makes it clear that the subsequent discussion will concern
what is supposed to hold in a “state of equilibrium”.

But the equilibrium concept is here used in a much stricter sense
than before: he is actually referring to what would be termed
nowadays a ‘competitive equilibrium’.

Letting x1* and x2∗ be the quantities of the two commodities traded in
such a ‘competitive equilibrium’ state, x2∗/x1∗ turns out to be the
competitive equilibrium ‘finite’ “ratio of exchange”.

Given the assumptions on the traders’ characteristics, one obviously
has:
x1*= s11*=d12* and x2* = d21* = s22*, where s11* = ω̅1 – x11* and
d12* = x12∗ are the ‘competitive equilibrium’ quantities of commodity 1
respectively supplied by 1 and demanded by 2, while d21∗ = x21∗ and
s22∗ = ω̅2 – x22∗ are the ‘competitive equilibrium’ quantities of
commodity 2 respectively demanded by 1 and supplied by 2.
Franco Donzelli
Lesson 4 - Jevons, Jenkin, and Walras
14
Jevons’s theory of exchange: a formal statement 4

Then, for any pair of differentials dx1∗ and dx2∗ such that
dx2∗/dx1∗ = x2∗/x1∗, for trader 1 one has:

v

dx 1 v 
x 2 
dx 2 ,

1 x 1 
11 
21 
or
v

x

1
11 
1
v
x
21 
2

dx 
2
dx 
1
.

2
A similar condition holds for trader 2:
v
x
12 
1

v


2 x 2 
22 
Franco Donzelli
dx 
2
 dx  .

3
1
Lesson 4 - Jevons, Jenkin, and Walras
15
Jevons’s theory of exchange: a formal statement 5

Hence, by substituting (1) into both (2) and (3), one gets:

v


1 x 1 
11 
v
x
21 
2

x
2
x
1

v
x
12 
1
,

v


2 x 2 
22 

4
which are Jevons’s “equations of exchange”, representing his
fundamental result in the “theory of exchange”.

The way in which such “equations” are first obtained and then
interpreted by Jevons prompts the following remarks.

In the first place, in deriving the “equations of exchange”, Jevons
makes explicit use of the “law of indifference”, which holds only at a
specified time instant.

Hence Jevons’s equilibrium concept must be given an
“instantaneous” interpretation as well.
Franco Donzelli
Lesson 4 - Jevons, Jenkin, and Walras
16
Jevons’s theory of exchange: a formal statement 6

In the second place, it should be stressed that Jevons’s argument is
entirely couched in terms of the ‘competitive equilibrium’ values of
the traded quantities of the two commodities, x₁∗ and x₂∗, from which
Jevons directly derives the ‘finite’, ‘competitive equilibrium’ “ratio of
exchange”, x₂∗/x₁∗, and indirectly also the ‘differential’ one, dx₂∗/dx₁∗,
since the two “ratios” are assumed equal by virtue of the “law of
indifference”.

Quantities or “ratios” different from the ‘competitive equilibrium’ ones
are nowhere mentioned or even alluded to by Jevons in the
development of his formal argument.

This explains why Jevons nowhere introduces, let alone discusses,
an equation like:
v


1 x 1 
11 
v
x 2
21 

dx 2
dx 1

v
x 1
12 
,
v


2 x 2 
22 

5
defining Edgeworth’s “contract curve”.
Franco Donzelli
Lesson 4 - Jevons, Jenkin, and Walras
17
Jevons’s theory of exchange: a formal statement 7

In the third place, it remains to discuss what relationship, if any, can
be established between Jevons's “theory of exchange”, as
expressed by his “equations of exchange” (equations (4) above),
and the so-called “laws of supply and demand”.

According to Jevons (1970, p. 143), his “theory is perfectly
consistent with the laws of supply and demand”.

Yet such consistency boils down to a platitude:
“We may regard x1 as the quantity demanded on one side and
supplied on the other; similarly, x2 is the quantity supplied on the
one side and demanded on the other. Now, when we hold the two
equations to be simultaneously true, we assume that the x1 and x2
of one equation equal those of the other. The laws of supply and
demand are thus a result of what seems to me the true theory of
value or exchange.” (Jevons, 1970, pp. 143-4)
Franco Donzelli
Lesson 4 - Jevons, Jenkin, and Walras
18
Exchange equilibrium in Jevons
d*12
x*12
O2
tg α*= x*2/x*1=
d*21/s*11 =
s*22/d*12 =
x*21/(ω̅1-x*11)=
(ω̅2-x*22)/x*12
x*21
x*22
α*
d*21
s*22
α*
O1
Franco Donzelli
ω
x*11
Lesson 4 - Jevons, Jenkin, and Walras
s*11
19
Jevons’s theory of exchange: a formal statement 8

Once the formal statement of the two-trader, two-commodity model
is completed, Jevons tries to generalize his “equations of exchange”
to economies with more than two traders and/or more than two
commodities.

All his attempts rest on the assumption that:
“the exchanges in the most complicated case may [...] always be
decomposed into simple exchanges, and every exchange will give
rise to two equations sufficient to determine the quantities involved.”
(Jevons, 1970, p. 154)

Unfortunately, however, this assumption is unfounded. Hence,
Jevons’s reductionist strategy ends up in a failure.

In spite of what he seems to suggest (1970, p. 154), Jevons is really
unable to deal with traders who are not “cornered”.
Franco Donzelli
Lesson 4 - Jevons, Jenkin, and Walras
20
Jevons’s theory of exchange: a formal statement 9

When he tries to put forward a theory of multilateral commodity
exchanges, involving L > 2 commodities, he ends up with a set of
L(L-1)/2 bilateral exchanges, each involving a pair of commodities
and each viewed as independent of the others, so that the L(L-1)/2
“ratios of exchange”, obtained by applying the simple “equations of
exchange” of Jevons’s simple two-commodity model, do not satisfy
the Cournot-Walras arbitrage conditions.

Three main gaps in Jevons’s “theory of exchange”:



the price concept is almost entirely neglected and no serious
demand-and-supply analysis is developed;
the equation of Edgeworth's “contract curve” is missing
no possible extension beyond the narrow boundaries of the twotrader, two-commodity model.
Franco Donzelli
Lesson 4 - Jevons, Jenkin, and Walras
21
Walras’s pure-exchange, two-commodity model 1

Walras discusses a pure-exchange, two-commodity economy
ℰW2xI = {(ℝ2+, ui(‧), ωi)i=1I}, with I ≥ 2, satisfying a few further specific
assumptions concerning the traders’ endowments and utility functions:

the traders are “cornered”, with:
ωi = (ω1i, 0), with ω1i > 0, for i = 1, …, I’, with I’ ≥ 1,
and ωi = (0, ω2i), with ω2i > 0, for i = I’+1, …, I, with I > I’;

each trader is characterized by a cardinal, additively separable
utility function, satisfying restrictions on the signs of the first and
second-order pure partial derivatives similar to those assumed by
Jevons.

Let p = (p12 ,1) ∈ ℝ2++ be the price system, expressed in terms of
commodity 2 taken as the numeraire.

For all p = (p12 ,1) ∈ ℝ2++, the optimization problem to be solved by
trader i can be written as:
Franco Donzelli
Lesson 4 - Jevons, Jenkin, and Walras
22
Walras’s pure-exchange, two-commodity model 2
v

x 1i 
i
MRS 21 
x 1i , x 2i  1i
p 12
v 
x 
2i
2i
px i pi ,


6

7
By solving this system, one obtains the individual demand and supply
functions for the two commodities for each trader:
s 1i 
p 12 
p 12 

1i x 1i 
d 2i 
p 12 x 2i 
p 12 
for i = 1, …, I’, and
d 1i 
p 12 x 1i 
p 12 
s 2i 
p 12 
p 12 

2i x 2i 
for i = I’ + 1, …I.
Franco Donzelli
Lesson 4 - Jevons, Jenkin, and Walras
23
Walras’s pure-exchange, two-commodity model 3

Then, by aggregating over the traders, one obtains the aggregate
demand and supply functions for both commodities, from which one
can get the excess demand functions:

z1 
p 12 d 1 
p 12 s 1 
p 12 IiI 1 x 1i 
p 12 
Ii1 x 1i 
p 12 

1 
Ii1 x 1i 
p 12 
p 12 


1 x 1 
1,

z2 
p 12 d 2 
p 12 s 2 
p 12 Ii1 x 2i 
p 12 
IiI 1 x 2i 
p 12 

2 
Ii1 x 2i 
p 12 
p 12 


2 x 2 
2.

By equating to zero the excess demand functions, one obtains the
market clearing equations, one for each commodity:
zl 
pW
pW

1 0,
12 x l 
12 

l 1, 2.

8
Finally, by solving either equation, one obtains the Walrasian
competitive equilibrium relative price, p12W.
Franco Donzelli
Lesson 4 - Jevons, Jenkin, and Walras
24
Walras’s pure-exchange, two-commodity model 4

The solution thus arrived at is for Walras the “mathematical” (either
“analytical” or “geometrical”) solution.

But, according to Walras, such solution is also concretely determined
“on the market”, by means of the well-known tâtonnement process.

In the present case, the process will consist in the adjustment of the
only one independent relative price, p12: p12 increases or decreases,
according to whether z1(p12) is greater or less than zero, and the
process goes on until the equilibrium price, p12W, is eventually reached.

With his model of a pure-exchange two-commodity economy, Walras
arrives at results partially similar to those arrived at by Jevons a few
years before with his “theory of exchange”.

This partial similarity, on the other hand, is explicitly recognized by
both of them - with many a qualification on Walras's side - in the wellknown exchange of correspondence taking place in May 1874.
Franco Donzelli
Lesson 4 - Jevons, Jenkin, and Walras
25
Exchange equilibrium in Walras
x’12
d’12
x*12
O2
tg α’ = p’12=
α*
= d’21/s’11 =
= s’22 /d’12
<
tg α* = p*12
x*21
d’21
x’21
O1
Franco Donzelli
x*22
x’22
α’
x*11
Lesson 4 - Jevons, Jenkin, and Walras
s’22
α*
ω
x’11
s’11
26
Walras’s critique of Jevons’s theory of exchange 1

Yet, in spite of the similarities in some of the results eventually
obtained, not only does Walras’s overall approach significantly differ
from Jevons’s, but the former’s exchange models also prove to be a
potentially much richer theory than the latter's “theory of exchange”.

The fundamental difference between the two approaches lies in the
different interpretation of the perfectly competitive hypothesis: the
‘Perfect Competition Assumption’ means for Walras, but not for
Jevons, that the traders make their optimizing choices by taking prices
as given parameters.

As Walras himself clearly points out (1988, p. 253, 2-5), in his
exchange models Walras takes the “prix”, instead of Jevons’s
“quantitités éxchangées”, “comme inconnues du problème”.

Thereby, he is able to extensively generalize the version of Jevons's
“law of indifference” which is effectively employed by the latter in his
“theory of exchange”, and which, as has been shown above, is really
nothing more than a truism.
Franco Donzelli
Lesson 4 - Jevons, Jenkin, and Walras
27
Walras’s critique of Jevons’s theory of exchange 2

What Walras actually resorts to in building his exchange models is a
much more general “law”, that might be called the “Law of One Price”:
at any given instant, one and the same price system is simultaneously
announced to all traders, both at equilibrium and out of equilibrium.

Yet, out of equilibrium not all the chosen trading plans can be actually
carried out. But this implies that some mentalistic concepts for which
no observable counterpart can be found, such as the trading plans
chosen by at least some traders when the economy is out of
equilibrium, necessarily enter Walras’s exchange models.

Nothing similar can instead be found in Jevons’s “theory of exchange”:
for, in this case, prices are never announced to traders, nor
disequilibrium trading plans are ever explicitly taken into account.
Franco Donzelli
Lesson 4 - Jevons, Jenkin, and Walras
28
Walras’s critique of Jevons’s theory of exchange 3

No prices and no trades other than the ‘competitive equilibrium’ ones,
which are all observable magnitudes, appear in Jevons’s “equations”,
which, as we have seen, are derived under the assumption that the
economy already is “in an equilibrium state”.

Walras can immediately aggregate the traders’ optimal trading plans,
irrespective of their number, and can consequently define the
aggregate demand and supply functions for each commodity without
any difficulty.

As Walras rightly points out (1993, p. 50), such functions cannot
instead be obtained in Jevons’s case, due to the latter’s inability to
take prices as the “inconnues du problème” and his related refusal to
deal with unobservables.
Franco Donzelli
Lesson 4 - Jevons, Jenkin, and Walras
29
Walras’s critique of Jevons’s theory of exchange 4

Walras, unlike Jevons, can extend his two-commodity model with
“cornered” traders to a multi-commodity model with traders
characterized by arbitrary endowments.

Finally, with his theory of the tâtonnement, Walras is apparently able to
provide an answer to the issue of equilibrium attainment, an issue that
had been left by Jevons in a state of ambiguity and confusion.

Yet Walras’s approach is far from unobjectionable: after Bertrand’s
critique (1883), Walras is led to explicitly introduce a ‘No-Trade-Out-OfEquilibrium Assumption’, which turns the tâtonnement process in the
exchange models into a purely virtual process in ‘logical’ time, over
which nothing observable is allowed to take place.
Franco Donzelli
Lesson 4 - Jevons, Jenkin, and Walras
30
Walras’s critique of Jevons’s theory of exchange 5

Walras’s criticism of Jevons’s alleged shortcomings is quite explicit:
“Je ne vois pas non plus que vous [...] fondiez [l'équation d'échange]
sur la considération de satisfaction maximum, qui est pourtant si
simple et si claire. Je ne vois pas non plus que vous en tiriez l'équation
de la demand effective en fonction du prix, qui s'en déduit si aisément,
et qui est si essentielle à la solution du problème de la détermination
des prix d'équilibre.” (Walras, 1993, p. 50)

Yet, Jevons does not react to Walras’s critique.

One possible explanation is that it comes too late.

Yet, this is not a satisfactory explanation of Jevons’s silence: for
Jevons had not apparently reacted to the critical remarks made by
Jenkin in 1868 against the summary of Jevons’s theory put forward in
the “Brief Account”.
Franco Donzelli
Lesson 4 - Jevons, Jenkin, and Walras
31
Jenkin on demand-and-supply analysis 1

Jenkin's contribution essentially consists in an almost complete theory
of both the derivation of the traders’ individual demand and supply
curves from their marginal utility curves, and the graphical
determination of a competitive equilibrium along quasi-Walrasian lines.

Not a single piece of the notable demand-and-supply apparatus put
forward by Jenkin in his correspondence with Jevons finds its way into
the latter’s later writings, including the two editions of TPE published
during Jevons's lifetime.

Jenkin might have played with respect to Jevons a role similar to that
played by Paul Piccard with respect to Walras.

But, while Walras is eager to exploit the new conceptual and analytical
tools made available by Piccard in order to erect upon them his whole
theoretical system, Jevons, instead, is not prepared to accept Jenkin's
gift, also because that gift, unlike Piccard's, is partly poisonous.
Franco Donzelli
Lesson 4 - Jevons, Jenkin, and Walras
32
Figures 1, 2
Fig. 1
Fig. 2
Franco Donzelli
Lesson 4 - Jevons, Jenkin, and Walras
33
Figures 3, 4
Fig. 3
Fig. 4
Franco Donzelli
Lesson 4 - Jevons, Jenkin, and Walras
34
Figures 5, 6, 7
Fig. 5
Fig. 6
Franco Donzelli
Fig. 7
Lesson 4 - Jevons, Jenkin, and Walras
35
Jenkin on demand-and-supply analysis 2

The fact is that neither Jenkin, nor, to an even greater degree, Jevons
himself are willing to bear the logical consequences of adopting an
approach to the solution of the equilibrium determination problem in a
pure-exchange economy that will later come to be known as the
Walrasian demand-and-supply, or excess-demand, approach.

When in a pure-exchange, two-commodity model the traders are
assumed to behave as competitive utility maximizers, three
consequences necessarily follow:
1) at a given 'relative price' (or "ratio of exchange", or "rate of
exchange"), the traders choose unobservable trade plans, typically
unexecutable, which can be turned into observable, executable
trades only at equilibrium;
Franco Donzelli
Lesson 4 - Jevons, Jenkin, and Walras
36
Jenkin on demand-and-supply analysis 3
2) the adjustment process towards equilibrium is brought about by
progressively changing the ‘relative price’ in conformity to the usual
price adjustment rule, according to which the change in the ‘relative
price’ is a sign-preserving function of the aggregate excess-demand
for the corresponding commodity;
3) the price change cannot itself be the product of the individual
traders’ choices, but can only be effected by an objective mechanism,
pursuing a superindividual aim.

Walras, after some uncertainties and oscillations, eventually accepts
the rules of the competitive game.

As to the first rule, Jenkin’s stance is peculiar:
for he accepts the competitive idea that the traders make their
choices by taking the ‘relative price’ as a fixed parameter, but he does
not accept the consequent requirement that no trades be carried out
at disequilibrium ‘prices’.
Franco Donzelli
Lesson 4 - Jevons, Jenkin, and Walras
37
Jenkin on demand-and-supply analysis 4
On the contrary, according to Jenkin, plans must always be carried
out, even out of equilibrium.
But then he is forced to concoct an explanation for disequilibrium
behavior, which explains his adoption of the “short-side rule”.

As to the adjustment process, Jenkin never accepts the idea that
there exists an objective mechanism, moreover of a virtual type,
which is at work in the economy.
For him, the driving force of the adjustment process must lie in the
subjective motivations of the individual members of the economy.
But no such set of concurrent subjective motivations can possibly
exist in an Edgeworth Box economy which is such as to lead the
traders to jointly change the ‘relative price’ in a definite direction.
Franco Donzelli
Lesson 4 - Jevons, Jenkin, and Walras
38
Jevons on demand-and-supply analysis 1




Given Jenkin’s negative conclusions about the possibility of
buttressing Jevons’s “exchange equations” with a demand-andsupply analysis of the Walrasian type, it is not surprising that Jevons
should not feel encouraged to exploit to his advantage the tools
provided by his correspondent.
But the reasons underlying Jevons’s refusal to adopt a Walrasian or
quasi-Walrasian approach to equilibrium determination in the theory
of exchange are probably even more basic than those leading Jenkin
to doubt of the usefulness of that approach.
For Jevons, in fact, the very distinction between a trade plan and an
“act of trade” is unconceivable.
All trades of which one can legitimately speak are the observable
outcome of bilateral bargains involving two traders at a time: there is
no such thing as a trade plan, disconnected from an “act of trade”,
which can in principle be carried out.
Franco Donzelli
Lesson 4 - Jevons, Jenkin, and Walras
39
Jevons on demand-and-supply analysis 2

In short, no unobservable counterfactuals are allowed for in Jevons’s
theory of exchange.

This has to do with the physicalist standpoint endorsed by Jevons: as
in mechanics the motion of a material point in ordinary space can be
obtained by integrating its velocity function w.r.t. time, so in an
Edgeworth box economy the ‘trajectory’ described in the space of
allocations by the commodity holdings of two traders can (or at least
should) be obtained by integrating the ‘differential’ “ratio of exchange”
between the two commodities.

The mechanical analogy is grossly misleading, yet it reveals the
source of Jevons’s hostility towards unobservable counterfactuals.

But the distinction between trade plans and “acts of trade” as well as
the use of unobservables and counterfactuals are crucial for the
Walrasian type of demand-and-supply analysis, which is therefore
precluded to Jevons.
Franco Donzelli
Lesson 4 - Jevons, Jenkin, and Walras
40
Figures 1
Fig 1
Fig. 2
Franco Donzelli
Lesson 4 - Jevons, Jenkin, and Walras
41
Figures 2
Fig 3
Fig. 4
Franco Donzelli
Lesson 4 - Jevons, Jenkin, and Walras
42
Figures 3
Fig 5
Fig. 6
Franco Donzelli
Fig. 7
Lesson 4 - Jevons, Jenkin, and Walras
43
Exchange equilibrium in Jevons
d*12
x*12
O2
tg α*= x*2/x*1=
d*21/s*11 =
s*22/d*12 =
x*21/(ω̅1-x*11)=
(ω̅2-x*22)/x*12
x*21
x*22
α*
d*21
s*22
α*
O1
Franco Donzelli
ω
x*11
Lesson 4 - Jevons, Jenkin, and Walras
s*11
44
Exchange equilibrium in Walras
d’12
x’12
x*12
O2
tg α’ = p’12=
α*
= d’21/s’11 =
= s’22 /d’12
<
tg α* = p*12
x*21
d’21
x’21
O1
Franco Donzelli
x*22
x’22
α’
x*11
Lesson 4 - Jevons, Jenkin, and Walras
s’22
α*
ω
x’11
s’11
45