EDGEWORTH'S CONTRIBUTION TO THE THEORY OF EXCHANGE
| DOI | http://doi.org/10.1111/j.1467-9485.1979.tb00541.x |
| Published date | 01 June 1979 |
| Date | 01 June 1979 |
| Author | John Creedy |
Scottish
Journal
of
Political Economy,
Vol.
26,
No.
2,
June
1979
EDGEWORTH’S CONTRIBUTION TO THE
THEORY OF EXCHANGE
JOHN
CREEDY
University
of
Durham
It will be interesting to watch the development
of
his theory
[Marshall (1881, reprinted in 1975, p. 267)]
I
INTRODUCTION
It is now almost
100
years since the publication
of
Edgeworth’s
Mathematical
Psychics.
In an article published 76 years later Stigler was still able to write,
“His exposition deserves the closest scrutiny in spite
of
the fact that few
economists of his time or ours have attempted to disentangle and uncover
the theorems and conjectures of the
Mathematical Psychics,
probably the
most elusively written book of importance in the history of economics’’
(1957, reprinted in 1965, p. 246).l
A
further two years later Shubik then
published his seminal paper on “Edgeworth market games”, which used the
recent results from the theory of games to elucidate Edgeworth‘s analysis of
the number of “recontracting” competitors and the formation
of
prices.
As
a
result of considerable activity during the last twenty years the modern judge
is now (usually) much more benign. Thus Samuelson states, “what is now
seen to
be
magnificent about Edgeworth’s
Mathematical Psychics
is his
40 pages of discussion on indifference contours, exchange, recontracting,
supply and demand, contract curves and (deepest of all) the core” (1974,
p. 1279).’
It therefore seems an appropriate time to review Edgeworth‘s contribution
to the pure theory
of
exchange. Just as Edgeworth’s work is of crucial
importance to the development of economic analysis, an appreciation of his
thought on exchange is crucial in considering the rest of his life’s work. Many
of his views
on
taxation, monopoly and international trade are directly in-
fluenced by his earliest work in economics. This paper concentrates, however,
on his direct contribution to exchange and competition
the or^.^
In order to
Ironically Stigler later stated, “The proof of the need for indefinite numbers has serious
weaknesses”
(1965,
p.
248).
When
MathematicalPsychics
was reprinted, Schneider remarked,
“For about fifty years economic theory has neglected this contribution. How many detours
and mistakes would have been avoided if this masterpiece had formed the basis for con-
tinuous development”
(1935.
p.
236).
This praise is not of
course
unanimous.
The criticisms of Walker
(1973).
JaE6
et
al.
(1974)
have
been
considered elsewhere, in Creedy
(1978).
The remark by Hutchison
(1953,
p.
114)
that,
“In
the light of.
. .
(Edgeworth’s)
. . .
warnings and distinctions it would not appear that he could have attached any wide
significance to his own dynamic model
of
recontracting”,
can
surely not be taken seriously.
Date of receipt of final manuscript: 7th August
1978.
163
164
J.
CREEDY
appreciate the originality of this contribution it is first necessary to consider
the state of the theory before
1881.4
The works
of
Jevons
(1871)
and Walras
(1874)
were well
known
to Edge-
worth, although Jevons was by far the greatest infl~ence.~ Following the
“high period” of utilitariarism in England, total utility was assumed to
be
a
sum of the separate utilities of each good available after exchange, with
positive but decreasing marginal utility.6 The marginal utility theory could
then be summarised by Jevons’ famous “equations of exchange”, whereby,
“the degrees of utility
of
commodities will be in the inverse proportion of the
magnitudes of the increments exchanged”
(1970,
p.
143).’
The conditions on
the utility function guaranteed, furthermore, that demand curves sloped
downwards, that an increase in income produced an increase in the con-
sumption of
all
goods (that is, no inferior goods), and also ruled out any
complementarity.
Although Jevons and Walras had clearly indicated how the quantities
demanded could be obtained as the solution to a set
of
simultaneous equations
with prices
taken
as
given
(parametric), it is important to stress that
no
theory
of
price formation as such existed. In particular, Jevons’ famous “law of
indifference” that, “there can only
be
one ratio of exchange of one uniform
commodity at any moment”
(1970,
p.
132)9
was part of the definition of a
perfect market. Thus price taking was axiomatic, “higgling” between buyers
and sellers was not necessary. Jevons also explicitly stated that his theocy was
limited to the static equilibrium conditions, “It is a far more easy task to lay
down the conditions under which trade is completed and interchange ceases,
than to attempt to ascertain at what rate trade will go on when equilibrium
is not attained”
(1970,
p. 138).
Edgeworth’s approach in
Mathematical Psychics
was, however, from a
It is,
of
course, difficult to know the direct influences.
In
(1881,
p.
34)
he states that some
proofs
in
his early
Mind
paper
(1879,
July) “were offered.
.
.
without acknowledgement,
because without knowledge, of the cumulative proofs already adduced by Prof. Jevons”.
In
the
Memorials
(1925)
he
says
that,
‘‘.
. .
Jevons highly praised the then recently published
Economics ofZndustry”
(1925,
p.
66).
In
Memorials
(1925,
p.
371)
a letter from Marshall
to
Jevons (dated
30
June,
1979)
says that the
Economics
of
Industry
is
“nearly hished” and
“one
of
the
first
bound
copies will find its way
to
Hampstead”. This suggests that the two
near neighbow did not meet until late in
1879.
Edgeworth did not know
of
Marshall until
Jevons recommended
him.
Edgeworth also refers to Gossen and Cournot, but strangely not to Menger
(1871).
Blaug argues
(1968,
p.
299),
“Here was a revolution that was not generally admitted to have
taken place until more than a generation after the event”.
See
also
Black
et
af.
(1972).
Thus the cardinal utility function was additively separable, with positive first, and
negative second, derivatives.
The simultaneitv of the eauations for the two goods was made clear bv Jevons. See
-
(1970,
p.
143).
The assumotion that
all
goods were substitutes led to many mechanical analogies which
would not be appropriate with complementarity.
(See
also E6geworth
(1925,
IIK p.
38.))
Jevons noted, “In this principle we have one of the central pivots
of
the theory”
(1970,
p.
137).
He also explicitly ruled out the possibility
of
consumer’s surplus being extracted,
“the last increments in an act of exchange must
be
exchanged
in the same ratio
as
the whole
quantities exchanged”
(1970,
p.
139).
Again perfect knowledge was explicitly assumed,
“A market, then, is theoretically perfect only when all traders have perfect knowledge
of
the conditions of supply and demand”
(1970,
p.
134).
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