And if Gerard thinks so, who am I, as a lowly "hagiographer", to dispute one
of the foremost theoreticians of modern economics. - Warren Young
I beg your pardon to point out that the above sentiment shows the highly
admirable qualities of loyalty and respect to seniors, but also constitutes
the fallacy of authority. Being one of the foremost theoreticians gives no
guarantee that one is able to deliver the error-free truth.
In my reading of Debreu's 1991 paper (the AEA presidential address) [1] I see
a remarkable confession that also should be seen in association with Arrow's
impossibility theorem [2] published forty years earlier. The confession is
that the most ambitious enterprise of neoclassical economics to build a
general equilibrium model failed. In Arrows eyes, there is no way to
incorporate social choice in it. The essentially same theme is presented in
Debreu's paper that the construction of a grand unified theory of the economy
is out of reach. Unifying economics is pretty simple [3], and Debreu is
mistaken to say that it is out of reach. Likewise, his partner Arrow is
mistaken to suppose that social choice is impossible. It is extremely easy
to show that social choice is possible. [4]
Arrow and Debreu together of course have done the most advanced theoretical
work in economics, and have both been rightfully honored. The aim of the
general equilibrium model is to describe the entire economy and capture all
its essential elements in a compact unified model. The failure of Arrow and
Debreu to deliver such a model perpetuates the old problem created by Walras
and made unworkable by Pareto.
Walras thought that he described the entire economy with his general
equilibrium model, but he actually presented the model of economic behavior
of a single isolated person who produces n different goods. If there is a
single isolated individual who produces and consumes n different kinds of
goods, he must equate the production (supply) and consumption (demand) for
each good. If one adds matters of risk and uncertainty and considers several
periods, the essential nature of the model is still that it is one of
autarky by a single individual. It does not describe the economy consisting
of more than one person engaged in trade.
To model trade, one must necessarily connect two real goods that directly or
indirectly pay for each other in a transaction. A basic equilibrium
condition in exchange is that in each individual transaction of one good
against another, the values must be equal so that one pays for the other.
Walras does not impose this condition and hence his model cannot be one of
exchange at all. On must also add a budget balance in real values for each
person, and further set up the equality of lending and borrowing in each
period. All told, four equalities are requires to describe an entire economy
with exchange, but Walras mentions only one.
Pareto actually abolishes the possibility of exchange altogether by
requiring that marginal rates of substitution in both production and
consumption be the same for two different people, as both must equate the
substitution rates to the ratio of prices. This is fundamentally mistaken.
The very existence of gainful trade requires that the substitution rates
between any two goods must differ between buyers and sellers to allow for
gainful trade, either in production (reflecting differences in costs) or in
consumption (reflecting differences in marginal benefits or relative
utilities) or both. For the same reason, the idea of representative
individual is void ab intio: there is just no way for a seller to represent
a buyer, and no exchange can be described without showing both the buyer and
the seller with their preferences technologies and endowments. If people are
all alike, they cannot possibly trade and they cannot possibly have a market
at all.
Arrow and Debreu could not detect the basic flaw in Walras and Pareto.
Arrows formulation of social choice fails to set up the problem correctly
owing to this oversight. No society ever faces a problem of many different
people choosing one common good. In politics, when different voting blocks
prefer different candidates, the solution is a parliament with different
members, not the election of one member for all. If the national candidates
fail to command the majority, the solution for them is to articulate the
majority aspiration and retry the vote, and not to give up the election as
an impossible feat.
But in economics, there is never a need for all consumers or producers to
make a single choice. Arrow did not think about allocation. If he did, he
would specify the budget of each party and see that social choice is very
simple: all different people buy all different goods according to budget and
preferences. If he could set up an exchange problem, he would see that
exchange can occur if and only if over any given pair of goods to be
exchanged against each other, the preference orders must necessarily be
opposite. Thus if one is to sell x and buy y, one must prefer y to x; but
then the buyer of x must prefer x to y. Arrows impossibility theorem implies
that exchange is impossible, which clearly is not true. In short, Arrow
enlarges the mistake of Pareto. The Arrow-Debreu model is a failure.
We must have the courage to raise questions, and to propose solutions. Of
course other economists are to be persuaded by the force of argument and the
factual evidence. We cannot give up merely because there are famous people
who made mistakes.
Mohammad Gani
[1]. Gerard Debreu (1991): The mathematization of economic theory. American
Economic Review, Volume 81, No 1.
[2]. Kenneth Arrow (1951): Social Choice and Individual Values. New York:
Wiley & Sons
[3]. Mohammad Gani (2003): Foundations of Economic Science, Scarborough,
Ontario: Scholars.
[4] Mohammad Gani (2004): "Though Arrow Says Its Impossible, It Happens
Everyday," downloadable at http://ideas.repec.org/p/wpa/wuwpmi/0405008.html
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