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Alejandro Nadal

Economic theory has a serious and embarrassing problem: it does not appear to have a rigorous and well-defined concept of money. This is why orthodox textbooks, when introducing money have to resort to a descriptive sleight of hand and state that “money is what money does”. They typically go on to say that it is the unit of account, the means of exchange and a reserve of value. But they fail to add that these functions are not exclusive of money.

That money poses a serious problem for mainstream economic theory is best exemplified by the fact that the most sophisticated account of interdependent markets (general equilibrium theory) does not tolerate the introduction of money (Hahn 1982). That’s an amazing headline story, one that should be taught in Economics 101.

Where does this problem come from? It’s a long and multi-faceted story, and it has to do with the orthodox narrative about the origin of money. This story, repeated from Adam Smith to Samuelson, states that in the beginning there was a barter economy and that because transaction costs were so high, men invented money. In the words of Mill (1965), “money is a machine for doing quickly and commodiously what could be done without it”. And Mill added that “the introduction of money does not interfere with the laws of value,”  something Frank Hahn would dispute.

As a transactions technology, money is accessory and the price formation and trading processes can be analyzed in a moneyless world. Thus, the key assumption of orthodox theory is that trading can take place in the absence of money.

What if somebody showed that pair wise trading is impossible in a moneyless world? Consider the following economy comprising three agents and three commodities (Veendorp 1970). To simplify matters, assume the economy has already reached an equilibrium price vector in which all prices are equal to one (p* = 1, 1, 1). Because this is a theory of a decentralized economy, exchanges are organized through bilateral or pair wise markets (see Lesson 11 in Walras (1954:158): if n is the number of commodities, there are n(n – 1)/2 bilateral markets of the type A:B. In this example the matrix of excess demands is as follows (agents in lines and goods in columns, a negative sign denotes an offer to sell, zero denotes goods that are of no interest to an agent).


Agents A       B       C

I              1       0      -1

II           -1       1       0

III           0      -1       1

This economy is in equilibrium (and agents are bound by their budget constraints). And yet, lo and behold, trade at equilibrium prices is impossible!

As can be seen, Agent I will go to market [A : C] because she demands good A and offers good C. But she has nobody to trade with. Agent II will go to market [A : B] because she demands one unit of B and offers one unit of A. But, again, she finds no counterpart. Finally, agent III will go to market [B : C] but she has no one to trade with. The barter operations needed to realize the optimal plans of the agents in this economy are not feasible, even if equilibrium prices have already been attained.

Of course, the source of the problem is the lack of a means of exchange. Things would be different if agents were allowed to demand a good in order to use it is a means of exchange. But Veendorp also shows that in larger economies (more than three agents), when everyone is allowed to demand goods in order to use them as means of exchange, we arrive at the same situation: pair wise barter may become impossible. (By a fluke, the configuration of the excess demand function may be such that trading can take place, but in general there is no reason to expect this will happen).

This simple example shows that trade cannot take place without money. Money is not a technology, it is a condition of possibility for trade: there is no trade without money! The metaphor of first a barter economy and then a monetary economy is false. We cannot abstract from money and pretend that we are analyzing the process of real exchanges. Economic theory took a wrong turn right from the beginning!

Veendorp’s analysis is compatible with an alternative narrative, one in which money and markets develop together, and one that is more closely linked to the notion of monetary production in capitalist economies. In this alternative view (where one meets authors like Michael Polanyi, John Maynard Keynes and L. Randall Wray) money is not an instrument that facilitates exchanges, but a social device originating in debt creation and forming a socially acceptable unit of account, a far cry from the misleading story of orthodoxy.

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Hahn, Frank (1982). Money and Inflation. London: Basil Blackwell

Vendorp, E. C. H. (1970) “General Equilibrium Theory for a Barter Economy”, Western Economic Journal. 8 [1 – 23]

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