# Say's theorem

The saysche (or Say'sche ) theorem (also saysches ( Say'sches ) law ) goes back to Jean-Baptiste Say (1803) and James Mill . It formulates a causal relationship between the economic variables of supply and demand . The theorem is one of the classical or neoclassical theorems and is a key component in understanding modern supply-side economic policy .

## The theorem in the classical representation

### Origin and core idea

Say's theorem was coined and known as part of the classical / neoclassical alongside Say about James Mill and John Stuart Mill , as well as John Maynard Keynes (who viewed the theorem critically). A popular summary is:

Every offer creates its own demand.

At James Mill it says z. B. in Elements of Political Economy :

“But if the demand and supply of every individual are always the same, then the demand and supply of all individuals in the nation taken together must be the same. Whatever the annual output, it can never exceed the annual demand. The total annual production can be broken down into a number of shares that correspond to those of the people to whom it is distributed. The total demand corresponds to the amount of the total shares that are not retained by the owners for their own consumption. However, the total of the shares corresponds to the total production. The verification is thus complete. "

In 1803, Say wrote in his Traité d'economie politique :

“When the producer has finished working on his product, he is eager to sell it immediately so that the product's value does not decrease. He is no less anxious to use the money invested from it, because its value may also decrease. Since the only use for the money is in buying other products, the circumstances of the creation of one product open a path for other products. "

In the discussion at the time, Say turned against the fear expressed by some economists that technical progress would lead to overproduction crises in the long term . According to Say, the production of goods was necessary in order to provide the means necessary for the purchase of goods; thus the production of goods creates supply and demand at the same time. With his theorem, Say did not want to deny short-term sales crises, cyclical depressions and the involuntary unemployment caused by them, as it then became customary with reference to his theorem.

This view of Say was later carried over by the neoclassics to aspects such as relative prices and unemployment. An increased planned supply of goods therefore automatically generates a correspondingly higher planned demand. An inadequate level of demand can therefore - apart from short-term fluctuations - not exist in the economy as a whole. According to this, there can be no involuntary unemployment (→ full employment ) as long as the state does not take economic policy , e.g. B. through minimum wages or tax regulations , intervenes in the market and thereby restricts the demand for workers or products.

A partial overproduction is possible, which corresponds to an underproduction elsewhere. Such an imbalance is only temporary and will be eliminated by the price mechanism .

### Save up

In a pure exchange economy , Say's theorem is a tautologically fulfilled identity equation .

In a multi-period money economy , however, the theorem cannot claim any tautological validity for a partial period, because people then also have the opportunity to hoard or save money without the goal of buying goods themselves at the current point in time . Every production creates income in the exact amount of this production, so that the goods produced can be demanded with this income, but production and income that are high during a boom can fall very low in a crisis. Production is always based on demand, so that in a sales crisis, production and income can fall far below potential production if demand suffers from the attempt to build financial assets from excess income. In doing so, companies will avoid producing in stock just to utilize production potential and achieve the savings they are aiming for.

Say's theorem is only valid in a modern monetary economy if there is a mechanism that ensures that the investments match the targeted savings with optimal utilization of the production potential . Most followers see this mechanism as the interest rate . According to Say's theorem, the goods market in a money economy is therefore not cleared through the price, but through the market interest rate. Partial goods markets (e.g. the grain market) are cleared by price.

According to the classical view, Say's theorem is also valid when money is saved. It is assumed that banks would lend the money saved, which ultimately means that it remains demand-relevant, as it allows companies to request capital goods. According to the classic view, the market interest rate regulates the balance of supply and demand when the production potential is fully utilized.

### Hoard

In contrast to saving, market participants do not bring their money to a bank when hoarding . Instead, they keep it at home, for example in the piggy bank. Liquid money stocks accumulate, which do not affect demand. Under the gold standard , the amount of banknotes in circulation was once limited by the gold reserves , so that the hoarding of banknotes or even gold could force the central bank to raise interest rates.

Even the classical economists argued here with the quantity theory of money : Even if money were withdrawn from the cycle through hoarding, Say's theorem is still valid if one assumes that the reduced amount of money ensures that the average price of all goods falls. This would increase the value of the money still in circulation and preserve the total value.

The classics assumed that the now lower price of money would provide an incentive to spend the money again and that a balance would be restored.

Normally, however, the central banks today compensate for reductions in the speed of money circulation by increasing the money supply in line with the expected slowdown in the speed of circulation. Decreases in the velocity of circulation do not necessarily have to lead to deflation or (in the case of rigid prices) to gaps in demand. In the event of a liquidity trap or a credit crunch , however, the central banks may not be able to compensate for the decrease in the speed of money circulation.

### Consequences for economic policy

Since, according to Say's theorem, a market equilibrium always arises, the supporters of the theorem reject a demand-oriented policy by the state or the central bank and demand a supply-oriented policy .

## criticism

Comparison of the classic / neoclassical model with Keynes and the balance mechanics

With the neutrality of money, the orthodox economy assumed that if consumption fell, more would always be invested in its volume. From a monetary point of view, however, the investment can be less profitable than financial investments, so that the investment is not made and a production gap arises (see figure on the right). With the output gap, household income and savings decrease. Household income is determined by spending and economics are determined by investment.

John Maynard Keynes disputed the validity of Say's theorem. Keynes argued above all against the assertion, derived from the quantity theory of money, that wages and prices could fall automatically and without crisis and unemployment. Rather, the central bank will deliberately cause a sales crisis with mass unemployment with high interest rates and a restrictive credit policy, in order to achieve the lowering of wages and prices on the market, which is sought after and after the return to the gold standard to the pre-war parities.

Keynes assumed that even low interest rates would no longer induce companies to invest in a crisis if profit expectations were only sufficiently low. This case is called underemployment equilibrium . The savings would not necessarily offset each other with the investments (→ liquidity and investment trap ). A self-reinforcing mechanism to exacerbate the crisis would thus be set in motion.

In order for savers to be willing to lend their money instead of hoarding it, they must be given an incentive. However, since there may be very few demand for capital on the capital market (e.g. recessive mood, low sales expectations, low capacity utilization, etc.) and deflation may also prevail due to the low speed of money circulation , it could be that the (nominal) market interest rate is not clearing the market is. The speed of money circulation would then decrease further (increased money hoarding). It is a self-reinforcing process because the speed of money circulation also has an impact on the national product (→ recessive mood) and the price level (deflation). Expected deflation in turn increases the incentive to hoard money. In order to ensure a market-clearing real interest rate, a moderate (but as constant as possible) inflation rate is very helpful. It even enables negative real interest rates. With a constant inflation rate, planning security is guaranteed for economic agents, and the disadvantages of such moderate inflation are therefore limited. In addition, low inflation penalizes money hoarding, which is ultimately the cause of every demand gap (or actually an increase in money hoarding is the cause of demand gaps - i.e. the 1st derivative of money hoarding), and thus offers an incentive to keep little cash (and instead to invest).

Several recent publications also see no connection between saving and investing. The DIW sees no connection between saving and the economy.

In the course of working through David Ricardo's theory, Karl Marx also deals with Say's theorem and criticizes the fact that Say chose his model requirements in such a way that crises are logically impossible. He further criticized the fact that Say interprets the capital relationship merely as a natural exchange relationship and thus ignores the internal contradictions of the capital-based valorisation processes in the event of overproduction. Marx therefore counted Say's approach to be vulgar economics . In contrast, Marx praises Ricardo for his scientific objectivity in his chapter on mechanical engineering and overlooks the inconsistency: Ricardo's theory as a whole assumes the validity of Say's theorem. According to this, unemployment is theoretically excluded even when new machines are introduced.

## Individual evidence

1. James Mill: Elements of Political Economy . 3rd ed. 1844, p. 96ff.
2. z. B. with Ulrich van Suntum: The invisible hand. Economic thinking yesterday and today . 3rd edition 2005, ISBN 3540252355 , pp. 104f.
3. This summary is from John Maynard Keynes . "Supply Creates its own demand", In: The General Theory of Employment, Interest and Money ( The General Theory of Employment, Interest and Money .), John Maynard Keynes, Chapter 2, Section VII of content very similar formulations of the theorem under exist among others in the writings of James Mill and John Stuart Mill (to which Keynes refers in his criticism).
4. See in: James Mill: Elements of Political Economy . 3rd ed. 1844, p. 96. In the English original: “But if the demand and supply of every individual are always equal to one another, the demand and supply of all the individuals in the nation, taken aggregately, must be equal. Whatever, therefore, be the amount of the annual produce, it never can exceed the amount of the annual demand. The whole of the annual produce is divided into a number of shares, equal to that of the people to whom it is distributed. The whole of the demand is equal to as much of the whole of the shares as the owners do not keep for their own consumption. But the whole of the shares is equal to the whole of the produce. The demonstration, therefore, is complete. "
5. Jean Baptiste Say: A treatise on political economy: or The production distribution and consumption of wealth. Translated from the fourth edition of the French. Batoche Books Kitchener 2001, p. 57.
6. a b Karl Mai: Historical-critical comments on "Say's Law" (PDF; 87 kB), January 1999, pp. 2–3
7. a b Jan A. Kregel : The Renewal of Political Economy ISBN 3-926570-03-2 , p. 19
8. Don Patinkin: WALRAS 'LAW (PDF; 899 kB), 1987 p. 8:
“In brief, and again in today's terminology, Say's concern was to deny the possibility of secular stagnation, not that of cyclical depression and unemployment.”
9. http://wirtschaftslexikon.gabler.de/Definition/saysches-theorem.html
10. ^ A b Cf. Jean-Baptiste Say: Traité d'économie politique . 6th edition, Ed .: Say, H. Paris 1841, p. 138 ff.
11. General Theory (there Chapter 2, II)
12. T. Hildebrandt: Keynes balance
13. ^ John Maynard Keynes: The Economic Consequences of Mr. Churchill In: Essays in Persuasion. WW Norton & Company, 1991, p. 259
14. Karl Marx: Theories about the surplus value. Vol. II, MEW 26.2. P. 495ff
15. Michio Morishima : Ricardo's Economics. A general equilibrium theory of distribution and growth. Cambridge University Press 1989. ISBN 0-521-36630-5 . P. 11