A Primer on Say’s Law and Walras’s Law

Say’s Law, often paraphrased as “supply creates its own demand,” is one of oldest “laws” in economics. It is also one of the least understood and most contentious propositions in economics. I am now in the process of revising my current draft of my paper “Say’s Law and the Classical Theory of Depressions,” which surveys and clarifies various interpretations, disputes and misunderstandings about Say’s Law. I thought that a brief update of my section discussing the relationship between Say’s Law and Walras’s Law might make for a useful blogpost. Not only does it discuss the meaning of Say’s Law and its relationship to Walras’s Law, it expands the narrow understanding of Say’s Law and corrects the mistaken view that Say’s Law does not hold in a monetary economy, because, given a demand to hold a pure medium of exchange, real goods may be supplied only to accumulate cash not to obtain real goods and services. IOW, supply may be a demand for cash not for goods. Under this interpretation, Say’s Law is valid only when the economy is in a macro or monetary equilibrium with no excess demand for money.

Here’s my discussion of that logically incorrect belief. (Let me add as a qualification that not only Say’s Law, but Walras’s Law, as I explained elsewhere in my paper, is not valid when there is not a complete set of forward and contingent markets. That’s because to prove Walras’s Law all agents must be optimizing on the same set of prices, whether actual observed prices or expected, but currently unobserved, prices. See also an earlier post about this paper in which I included the relevant excerpt from the paper.)

The argument that a demand to hold cash invalidates Say’s Law, because output may be produced for the purpose of accumulating cash rather than to buy other goods and services is an argument that had been made by nineteenth-century critics of Say’s Law. The argument did not go without response, but the nature and import of the response was not well, or widely, understood, and the criticism was widely credited. Thus, in his early writings on business-cycle theory, F. A. Hayek, making no claim to originality, maintained, matter of factly, that money involves a disconnect between aggregate supply and aggregate demand, describing money as a “loose joint” in the theory of general equilibrium, creating the central theoretical problem to be addressed by business-cycle theory. So, even Hayek in 1927 did not accept the validity of Say’s Law

Oskar Lange (“Say’s Law a Restatement and Criticism”) subsequently formalized the problem, introducing his distinction between Say’s Law and Walras’s Law. Lange defined Walras’s Law as the proposition that the sum of excess demands, corresponding to any price vector announced by a Walrasian auctioneer, must identically equal zero.[1] In a barter model, individual optimization, subject to the budget constraint corresponding to a given price vector, implies that the value of the planned purchases and planned sales by each agent must be exactly equal; if the value of the excess demands of each individual agent is zero the sum of the values of the excess demands of all individuals must also be zero. In a barter model, Walras’s Law and Say’s Law are equivalent: demand is always sufficient to absorb supply.

But in a model in which agents hold cash, which they use when transacting, they may supply real goods in order to add to their cash holdings. Because individual agents may seek to change their cash holdings, Lange argued that the equivalence between Walras’s Law and Say’s Law in a barter model does not carry over to a model in which agents hold money. Say’s Law cannot hold in such an economy unless excess demands in the markets for real goods sum to zero. But if agents all wish to add to their holdings of cash, their excess demand for cash will be offset by an excess supply of goods, which is precisely what Say’s Law denies.

It is only when an equilibrium price vector is found at which the excess demand in each market is zero that Say’s Law is satisfied. Say’s Law, according to Lange, is a property of a general equilibrium, not a necessary property of rational economic conduct, as Say and his contemporaries and followers had argued. When our model is extended from a barter to a monetary setting, Say’s Law must be restated in the generalized form of Walras’s Law. But, unlike Say’s Law, Walras’s Law does not exclude the possibility of an aggregate excess supply of all goods. Aggregate demand can be deficient, and it can result in involuntary unemployment.

At bottom, this critique of Say’s Law depends on the assumption that the quantity of money is exogenously fixed, so that individuals can increase or decrease their holdings of money only by spending either less or more than their incomes. However, as noted above, if there is a market mechanism that allows an increased demand for cash balances to elicit an increased quantity of cash balances, so that the public need not reduce expenditures to finance additions to their holdings of cash, Lange’s critique may not invalidate Say’s Law.

A competitive monetary system based on convertibility into gold or some other asset[2] has precisely this property. In particular, with money privately supplied by a set of traders (let’s call them banks), money is created when a bank accepts a money-backing asset (IOU) supplied by a customer in exchange for issuing its liability (a banknote or a deposit), which is widely acceptable as a medium of exchange. As first pointed out by Thompson (1974), Lange’s analytical oversight was to assume that in a Walrasian model with n real goods and money, there are only (n+1) goods or assets. In fact, there are really (n+2) goods or assets; there are n real goods and two monetary assets (i.e., the money issued by the bank and the money-backing asset accepted by the bank in exchange for the money that it issues). Thus, an excess demand for money need not, as Lange assumed, be associated with, or offset by, an excess supply of real commodities; it may be offset by a supply of money-backing assets supplied by those seeking to increase their cash holdings.

Properly specifying the monetary model relevant to macroeconomic analysis eliminates a misconception that afflicted monetary and macroeconomic theory for a very long time, and provides a limited rehabilitation of Say’s Law. But that rehabilitation doesn’t mean that all would be well if we got rid of central banks, abandoned all countercyclical policies and let private banks operate without restrictions. None of those difficult and complicated questions can be answered by invoking or rejecting Say’s Law.

[1] Excess supplies are recorded as negative excess demands.

[2] The classical economists generally regarded gold or silver as the appropriate underlying asset into which privately issued monies would be convertible, but the possibility of a fiat standard was not rejected on analytical principle.

3 Responses to “A Primer on Say’s Law and Walras’s Law”


  1. 1 lewisb2014 December 20, 2020 at 6:44 pm

    Excellent points, and also testimony to the amount of energy that went into trying to figure out whether an economy would end up in equilibrium–without your very useful exposition. DSGE seems to have some of the same fixation.

  2. 2 Henry Rech December 30, 2020 at 7:30 pm

    Just exactly which “Say’s Law” is under consideration here?

    Say published several editions of his Treatise. His position on his “law of outlets” shifted as time went on.

    Then came the many interpretations and embellishments on the theme over the course of the next150 years.


  1. 1 Welcome to Uneasy Money, aka the Hawtreyblog | Uneasy Money Trackback on July 5, 2021 at 7:52 am

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.




About Me

David Glasner
Washington, DC

I am an economist in the Washington DC area. My research and writing has been mostly on monetary economics and policy and the history of economics. In my book Free Banking and Monetary Reform, I argued for a non-Monetarist non-Keynesian approach to monetary policy, based on a theory of a competitive supply of money. Over the years, I have become increasingly impressed by the similarities between my approach and that of R. G. Hawtrey and hope to bring Hawtrey's unduly neglected contributions to the attention of a wider audience.

Archives

Enter your email address to follow this blog and receive notifications of new posts by email.

Join 2,836 other followers

Follow Uneasy Money on WordPress.com

%d bloggers like this: