Thanks to Richard Lipsey. I read the second edition of his book in
undergraduate days and I am grateful for awakening a suspicion that there
was something behind the eternal confusion with the reversal of axis. I have
wrestled with this confusion for thirty plus years.
1. Marshall did not merely reverse the axis. It is a simple matter of
convention whether one puts the independent variable on one or the other
axis, and as such should not confuse anyone. Behind this axis reversal,
Marshall seemingly killed economic science by aborting causation in two
fundamental ways: by sabotaging epistemology and by perverting
methodology.
2. In epistemology, the goal of science is to discover and articulate the
causation, and Marshall did not pursue the study of causation. How could
anybody ever even define demand without taking price as predetermined,
far less let demand determine price? Can there be demand if the buyer
has no idea what the price is? To suppose that demand determines price
is a sabotage of epistemology. Price can never be set by one party: it
must without exception be set by agreement between the buyer and the
seller. One cannot represent the buyer with a demand curve and a seller
with a supply curve at all: one must show the buyer with income and
preference, and the seller with technology and endowments. Equality of
demand and supply determines only the quantity, and cannot possibly
determine the price. The price of x is the quantity of y that pays for x
(per unit), and the equality of demand for and supply of x surely can in
no way determine the quantity of y that pays for x. In short, the change
in price is causally based on income from the buyers side and cost from
the sellers side, and Marshall avoids both. Marshall presents a
self-contradiction: price determines demand and supply, and then demand
and supply determine price. His pupil Keynes was brighter, and got the
idea that (aggregate) demand and (aggregate) supply determine output not
price, and yet nobody noticed the reversal of Marshall by his pupil.
3. In methodology, Marshall violated the very old idea enshrined by the
Buddha in the parable of six blind men trying to study an elephant.
Partial equilibrium is bound to distort causality because it permits one
to contradict the omitted but causally linked parts. The buyer must be a
seller of something to earn the income with which he proposes to buy
something, and that must not be left out as an exogenous variable,
because that is very much an endogenous one. One can learn about neither
price nor quantity unless one brings the production and consumption by
each individual together in one full model: a partial model will never
do. Thus Marshall is surely mistaken to suppose that an increase in
demand can lead to an increase in price. It cannot. An increase in
income can allow an increase in demand at a given price, or an increase
in price for a given quantity, or a combination of both. If income is
fixed, an increase is demand is possible only with a decrease in price.
In consumer equilibrium, the price must be equal to lambda times the
marginal utility of the good and the lambda is based on income. Without
a change in income, no change in price is possible unless Marshall
violates the equilibrium condition just mentioned: price must be equal
to lambda times marginal utility. Just as the blind man who said the
elephant was a curved and bony stick (after partially touching the tusk
and ignoring the rest of the elephant), the partial model is necessarily
distorted.
Walras did it right with a general equilibrium model. The key culprit behind
the Marshallian confusion is the very method of isolating the issue of
determining variables, for leaving the casual variables out. An increase in
demand cannot increase price: an increase in income can.
Marshalls diagram of demand and supply of one good is a
methodological absurdity: it is impossible for a single good to be bought
and sold, because there must be at least two goods to pay for each other.
Thus the demand for x must be made with an offer of supply of y and
vice-versa in barter. Marshall got it wrong, and Walras got it right.
With one good, there can be at most a numeraire to convert the
quantity into value. The numeraire factor is not price. A single goods
demand-supply intersection can at most determine its numeraire unit, not its
price. The price must be a ratio. The so-called nominal price is a mistaken
term to denote the numeraire value: it should not be called price.
2. Walras did it right to set up a general equilibrium model in which
quantities are the dependent variables under predetermined or independent
prices. Walras does not have a theory of price. He shows how the quantities
are determined by equating the production and consumption for each good.
His aim is to show that a unique set of prices would ensure that all
quantities reached equilibrium, but he did not show how those prices would
be reached. He left the work for us, and we failed mightily. The auction
idea is meaningless in causal sense: the job is to describe the auction
process.
3. Walras provides a valid starting point for a theory of price, but
Marshall does not. To make any progress towards developing a theory of
price, the first need is to throw away Marshall's mistake and
self-contradiction. Here are the steps. First, take an autarkic individual
who produces n different goods. There is no market and hence no market
price. But optimization means that the subsistence producer must equalize
the production of each good with its consumption, and that the marginal rate
of substitution in production must be equal to the marginal rate of
substitution in consumption for any pair of goods. The common rate of
substitution in both production and consumption provides the equilibrium
rate of substitution under autarky, and may be regarded as shadow price
ratios. These are not market price ratios.
3. To get at market price (as a ratio), one must introduce entrepreneurship
for profit. An optimizer does not seek profit, but merely allocates what he
already has. An entrepreneur seeks profit and creates new value that did not
exist before. He can do this by exchange such that the buyer offers a price
higher than the marginal cost of the producer but lower than the marginal
opportunity cost of the same good if the buyer were to produce the good. To
formalize this, one must add another set of equations to the Walrasian
model. Those equations must show that in each transaction, the value of the
first good which is paid for by the second good is equal to the value of the
second good. The price of the first good in the market then is the quantity
of the second good per unit of the first good. For the seller of the first
good, the quantity of the second good received in payment must be higher
than the quantity of the second good he could produce in substitution of the
first; for the buyer of the first good, the quantity of the second good he
pays out must be lower than the quantity of the second good he could produce
in substitution if he produced the second good instead of the first. The
price then must be settled by bargaining between the buyer and the seller.
It must be higher than the sellers production cost and lower than the buyers
production cost, both measured in terms of the other good. The same argument
can be repeated with marginal utility in place of marginal cost.
4. To put it in gist, the optimizer is a price taker who chooses only the
quantities and not the price, while the entrepreneur is someone who does
not choose quantities, but prices. It is as if producers presume some
expected price, say from their sense of immediate past, and choose
quantities optimally. Then they go to the market and become
entrepreneurs. They already have the quantities, and now they must
choose prices to set their values such that the goods that pay for each
other become equal in value, namely, such that a certain quantity of the
second good pays fully and fairly for a unit of the first good. Walras
can be and must be retained, but Marshall, NAUGHT. Price theory must
presume that the quantities have already been chosen and have arrived in
the market. A dynamic model will of course show what happens in the next
round of quantity choices after the change in price by todays market
clearing.
5. The foundation of price theory is the idea of equivalence, namely that
the two goods that pay for each other must have equal value. Price is
the ratio to establish this equivalence. One must go beyond Walras to
show the equivalence. One can see the essential validity of classical
price theory if one thinks of value as the weight of demand and supply.
Thus suppose that at the price of previous day, the value of todays
demand is larger than the value of supply. We can visualize a scale in
which one side takes the demand and the other side takes the supply and
the scale must come to a balance. Now, if the previous days price makes
demand heavier than supply, the rise in price will increase the weight
(value) of supply (and with some reduction in quantity from the demand
side) will reduce the weight of demand until balance is established. In
the abstract, this mechanical process seems to tell the story right.
However, we must tell the human story of the buyers and sellers as
entrepreneurs. This means that instead of a machine automatically
balancing demands with supplies in terms of value by adjusting prices,
we must show the human process of bargaining. Of course one kind of
bargain may appear like auction, but an auction as such does not fully
reflect the price-setting process. We must have the arbitrageur here.
How come we have too much of Marshall and too little of Walras?
Mohammad Gani
|
