# [OPE-L:7012] [OPE-L:504] Law of one price and equilibrium WAS Postscript on

Alan Freeman (a.freeman@greenwich.ac.uk)
Thu, 25 Feb 1999 12:19:50 +0000

In response to Gil's [OPE-472] on equilibrium and the law of one price.
This also deals with aspects of other contributions on the same issue such
as Brendan and Steve, but I'll address Gill because his formulation is the
clearest and illustrates the issue in its clearest form.

Gil writes:

> Second, the "law of one price" is a condition which only makes sense in the
> context of market equilibrium, and not just any old equilibrium, but as
> indicated above, a special animal known as *perfectly (or purely)
> competitive equilibrium*.

Sorry Gil, no.

Let's suppose an economy with three goods, corn, wine and sweaters. Suppose
A produces corn, B produces wine, and C produces sweaters. Suppose that 1
corn exchanges for 2 wine, 1 wine exchanges for 2 sweaters, and 4 sweaters
for 1 corn. That is, the law of one price.

Now suppose A, B and C make 10 corn, 10 wine, and 10 sweaters, and
respectively demand 9 wine, 11 sweaters and 10 corn. There's no system of
exchanges that realises these demands at these prices or indeed any prices.
The economy cannot be in equilibrium. But there is a uniform price for all
products.

Even if the economy produces in proportions that permit market clearing,
nothing establishes that a uniform price in all products must effect this
clearing. If the economy demands 10 wine, 10 sweaters and 10 corn, this
still can't be effected at the given prices.

Uniform prices are independent of whether the economy is in equilibrium.
Equilibrium supposes that everything that's produced is also consumed, that
is, supply equals demand. This ain't just me that says it: here's Lionel
McKenzie's lead article from the New Palgrave volume on General Equilibrium
(p2): "Equilibrium of the market occurs at a price for which the sum of
demands,including offers as negative demands, is equal to zero for each
good." It's a standard definition, and quite close to the one in Marx's
gunsights, for good
measure:

"Nothing can be more childish than the dogma, that because every sale is a
purchase, and every sale a purchase, therefore the circulation of
commodities necessarily implies an equilibrium of sales and purchases"
(Volume I:113, Lawrence and Wishart edn)

Not only is there is no logical basis to assert that the formation of
uniform prices must lead to market clearing, there are many schools, not
just TSS-Marxist, who study non-market-clearing at uniform prices, for
example the whole non-Walrasian equilibrium school of Benassy, etc. See the
New Palgrave on Equilibrium, p253, (subtitle 'functioning of a non-clearing
market') for copious references.

Market equilibrium, whether animally specialised, pure, perfect or just
plain 'childish dogma', is more restrictive than the law of one price.

The only reason for thinking differently is if you suppose that *by
definition*, a uniform price is a market-clearing price.

In that case your assertion above is, I think, what is commonly known as a
tautology.

Alan