The Connection Between Says Law (corrected) and the Quantity Identity – ‘Horton’s Law’

We are on a roll today with Says Law.  Just a short note which will be elaborated on in future posts.

Arising from the classical position we have both ‘Says Law’ and the Quantity Theory of Money.  However the classical dichotomy between the real and monetary economies has meant little cross-fertilisation between the two.  When both have been assumed then Walras Law – as an extension of Says Law across multiple markets rather than just two – is assumed to dictate relative prices, whilst the quantity theory is assumed to mark the real price level.  However we know this dichotomy is untenable in not explaining the demand for and supply of money.  Indeed much of the origin story of macroeconomics was various attempts to explain money in terms that would fit within an equilibrium framework.  Oscar Lange in a well known article in 1942 considered that Says Law and the Quantity Theory were entirely incompatible, he reasoned that an excess supply of commodities required an excess demand for money however ‘

“the total demand for commodities (exclusive of money) is identically equal to their total supply”, eliminated this possibility.’

So for him monetary economics had to begin with the rejection of Says Law.  However note how from my previous post how the assumption is made of an economy of barter – goods exchanging for goods – rather than goods exchanging for money and demand for money as a commodity being excluded from the excess-supply/excess demand world of Walras’s Law.

However a number of writers have attempted to correct Walras’s law by including within it the production of money as well as the production of goods.   Recently we have had Fontana and Steve Keen both independently coming to the same conclusion – that effective demand is equal to (crudely speaking) income plus the change in debt. This idea is not new and I know of at least three major works in the early years of the 20Th Century even before the main writings on the subject by Schumpter – Pigou (see this new post by Steve Keen today), Hawtry and John P. Horton.

Today ill focus on Horton has his ideas are the least well known and in some ways more mathematically interesting

In  Statistical Studies in the New York Money Market (1902)  Interestingly he doesn’t approach it from the angle of Says Law but from one of the many pre-Fisher formulations of the Quantity theory.  Basically he takes the MV side as bank assets and the PQ side as bank liabilities/consumer spending power.  Interestingly he discounts the consumer side by the interest rate, reasoning I presume that as an ex-poste accounting identity as well as the additions to expenditure from credit creation over a ‘period’ there will also be repayments in that period.  His basic argument that money creation creations adds to expenditure and loan repayment destroys it is there.  His formulation suggests an interesting and little explored relations between Walras’s law/Says Law the Quantity Identity and the interest rate.

So if Horton is right is the correct formulation of the effective demand equation:-

(1) ED=Income + Delta Debt i – Delta Savings i + Net Asset Receipts

Lets tackle each element in turn:

Income is straightforward, defined as net income from production in the Marshallian tradition, rather than profits from sale of assets which are simply transfer payments.  This is only true in a closed economy however in an open economy we need to add the term to reflect net asset receipts.  Of course it is possible for rent from asset to erode labour share and suppress demand, but that is a separate issue (distribution I hope to show in the next article affects the effective supply curve).

Secondly delta debt, as we explained in the last article where the rate of credit creation proceeds at the same pace as credit repayment and destruction then it #nets# out, but if you have net leveraging or delivering it doesn’t.

Similarly with savings (using the Keynsian definition of savings = non consumption), if savings proceed at a steady rate with savings being simply consumption smoothing with the savings rate never changing it also nets out.   This appears to be a hidden assumption of many economist heading back to Adam Smith, the rate of non-consumption doesn’t matter because money will erode in value over time and will eventually be spent.  However if the rate of savings changes this will not be true.  Remember income is a flow whilst purchasing power and savings are stocks, purchasing power can be increased above the rate of income by raiding savings and purchasing power can be less than income if the savings rate increases.

As this is MV, if we have a numeraire units of exchange then changes to the numeraire Delta N  multiplied by turnover (the reciprocal of velocity), will equal velocity, hence we can relate changes to the unit of exchange to prices.

Now lets consider the liability side of the Equation  – in modern terms PY


(2) P(C + I + G + NX)

Because this is an assets=liabilities + equity equation (the fundamental equation of accounting) we need to add a term E equal to equity investment in financial services.


(3) P(C + I + G + NX)+E

or put together

(4) (Y + Delta D i – Delta S i + NAR)/ Delta N = P(C + I + G + NX)+E

A simple but powerful identity relating the monetary and real economies in a stock-flow consistent manner.

From our previous article on the LP-RL model (Lending Power Required Leverage) we can derive i, S and D interdependently.  S0 therefore we can derive an Effective Demand Curve, the next step in development a fully model of both effective demand and effective supply.   The next step is the effective supply curve.  However it doesn’t take a genius to show that if we have total income and interest rates we can derive wages share and prices without use of dodgy production functions. Watch this space.

2 thoughts on “The Connection Between Says Law (corrected) and the Quantity Identity – ‘Horton’s Law’

  1. Andrew: the classic analysis of the relation between Say’s Law, Walras’ Law, the mirroring of an excess demand for money with an excess supply of goods, and the Quantity Theory, is Don Patinkin’s Money, Interest and Prices. In the 1950’s and 1960’s, this was the last word on the subject, until Clower noted problems. The Clower/Leijonhufvud approach was developed especially by Malinvaud in the 1970’s. Then this “Disequilibrium Macro” approach disappeared under the New Classical/New Keynesian onslaught. Almost nobody remembers it now, or even understands the question. I’ve done a few related posts.

    • Patinkin of course was a pupil of Lange who pioneered this area. That (complex) tradition is almost forgotton now. What I aimed to do was show that simple identities could produce similar results. Im interested in your thoughts on my critique of Mengers value of diamonds theory.

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