The False Classical Dichotomy in Sraffa, Walras, & DGSE

The Classical Dichotomy and the Assumption of Money Neutrality

What is the ‘classical dichotomy’. For Patinkin it was it was the core belief in classical economics that value theory explained relative prices and the quantity theory explained nominal prices. In our previous article we showed how this dichotomy is implicit in Sraffa’s revival of classical economics. His theory can fully explain relative prices, of corn, iron etc. but only at the expense of dispensing with all monetary phenomenon, as this requires a theoretical understanding of interest, which requires also making labour exogenous to theory as production through labour takes time – so the costs of labour production always have an interest component. So his theory is essentially static, able to show how any given technique of production requires a certain set of relative prices This is Sinhas time invariant view of Sraffa which is I believe correct. But one cannot, as I showed in the previous post, translate this into nominal prices without some kind of classical assumption about the stock and flow of funds (such as a ‘wages fund’) to sustain production over the period of investment before a surplus is realised. This is the ‘hidden’ view of money in Sraffa I spoke of, proportional wages together with the flow of capital advanced determine the money wage and prices. This is exactly the classical dichotomy. Sraffa (in his published writings) is silent on this issue, but most classical theorists were not, the assumption was of a quantity theory mechanism which related the flow of money to nominal prices. Sinha argues that this view of Sraffa is incompatible with the classical competition process. I only agree in part, because I think Sinha is correct in that the pure relative price system that Sraffa invokes depends on maintenance of the classical dichotomy, as his discarded all aspects which required treatment in real time variant forms. Once one introduces money and time however one has to introduce some mechanism whereby similar capitals earn similar returns (Sinha refers to mechanisms for redistributing surpluses and shortages but gives no clue as to what this is, and his models exclude the main means whereby this occurs, equity markets).

Whilst this dichotomy is implicit in classical writers such as Ricardo with their focus on relative prices some held a harder line of pure money neutrality, that the quantity of money could only ever effect relative prices, which implies entirely separate systems for real production and monetary relations. This tradition stems at least from Hume, money is purely a ‘veil’. …

Given a separation of monetary and real sectors the excess demand equations of the real sector can then be used to determine the equilibrium values of the relative prices (in terms a numéraire) of all goods, while the excess demand equation for money can be used to determine the money price of the numéraire. Multiplying the money price of the numéraire by the relative prices of the other goods, yields then the money prices of all goods.

This approach has been carried over from a classical divide to the neo-classical world. In monetary DSGE models approach is to eliminate one market by Walras’ Law and to add a money equation, where money demand, based on a cash-in-advance or some such function, is equalized with money supply. This is little more than disguised quantity theory, typically modelled as a direct money transfer to the household budget constraint.

The Classical Dichotomy in Walras

Lets get back to Patinken’s critique, which was made in the context of Walras. His critique is important because it directly led to a stream of thought via Tobin and Godley which has become central to modern post Keynesian thinking. Walras in his earliest editions spent most of his chapters of his pure theory in a none monetary world of barter. Then he used a variant of the quantity theory to resolve nominal as opposed to relative prices. Despite their differences both Walras and Sraffa both share this classical dichotomy, that systems of simultaneous equations can be used to determine relative prices (and in Sraffa the ‘proportional wages’ or wages share) but not nominal prices. Walras however recognised that the quantity theory needed to be modified to included a notion of cash balances – the ‘encasse desiree’ – a point later taken up with force by the Cambridge school. The point being that cash held in idle cash balances is not used for spending, therefore the quantity of money used in consumption is that proportion held liquid and not saved.

However, as Patinkin (1965) showed, Walras’s specific procedure is self-contradictory because a doubling of the money prices of all goods leaves the relative prices of these goods unchanged because the money price of the numéraire also doubles. As a result the arguments of the excess demand equations in the real sector, which are pure relative price equations, do not change. Consequently, the markets of the real sector of the economy stay in equilibrium. There are no forces outside equilibrium to adjust it.

If the dichotomy approach is to have any bite then there would have to be a mechanism whereby the , the resulting excess demand for money would then, by whatever means, because the money prices of goods to fall back to the equilibrium values dictated by the real side of the equations. However, by Walras’ Law this cannot happen, since, if all other markets stay in equilibrium, the money market too must stay in equilibrium. Therefore an excess demand for money cannot ever emerge. So Walras’ Law, by itself, is insufficient to determine the money prices of goods stays as opposed to the relative prices of goods. As such despite differences in equilibrium assumptions both Sraffa and Walras are on all fours.

The doubling of money prices will however halve half real money supply. a doubling of the money prices of all goods does, as before, not affect the relative prices of goods, but it does now reduce the value of money holdings by half. This was Patinkin’s solution, a ‘real balance effect’, the real value of existing cash holdings would reduce, a wealth effect. This causes an excess supply of goods, which, by Walras’ Law corresponds to an excess demand for money. This disequilibria causes a shift in prices. Patinkins solutions depends on breaking the dichotomy by treating the value of money and the value of goods as part of the same system. (note: whether Walras himself abandoned the dichotomy in later editions is a matter of some controversy not aided by his difficult exposition. In any event his metallist commodity view of money made incorporation of money within production equations difficult – ultimately he assumed that metal money is the numéraire).

Patinkin’s solution was attached by Weil who argued that cash balances have no wealth effect, because holding banknotes forgoes the net present value of the interest foregone. Holding aside the issue that most reserves in the banking system do pay interest Weil’s critique is flawed as the opportunity cost of holding banknotes is simply the value of those banknotes discounted by the interest rate for the period for which they are held. It is not that there is no wealth effect, simply that it is declining and variant upon the interest rate. As the classical economists rightly argued there is a cost to waiting.

As a result of Weil’s flawed critique most DGSE approaches have taken after Lucas in including a ‘cash in advance’ constraint. But this is little more than a classical wages fund, the fund of cash in circulation necessary to sustain production over the period of investment, hence the false classical dichotomy is firmly embedded in DGSE.

Interest and Own Rates

On potential line of attack to resolving this dichotomy is to consider the production of money within the series of production equations rather than in a separate system. This course is often criticised by followers of Sraffa because of his 1926 article on own rates (criticising Hayek). I hope to show here that his theory is only true if we assume the classical dichotomy and vanishes when we remove it.

In a money free world Sraffa was quite right to say that there was no single natural rate of interest, rather a series of own rates for each commodity depending on the rate of surplus in production of that commodity. In a monetary world however as Nick Rowe Points out

The “own rate of interest on apples” is the nominal rate of interest minus the rate of inflation of apple prices.

So even in the narrowly focused case of own rates we must breach the classical dichotomy.

But once this allowance for a monetary economy is made, as well as trading in equity between firms with different rates of profit, then the rate of return on investment is effected by equity prices. Capital advanced as money will have differential returns in different techniques depending on their productivity, however a market in equities will lead these to gravitate, as Ricardo theorised, around an average rate of profit. This rate of profit in equity markets will influence the rate of profit earned in debt markets. Capital will be transferred between equity and debt markets if the rate of profit is higher in one than another. If a firm runs a technique which, at current and anticipated nominal prices, has a rate of return lower than the prevailing average rate of profit it will be forced to borrow at higher rates.

This in the cost of borrowing money not so much a different rate of interest but an insurance, a charge and risk premium on top of the prevailing rate of interest. We have modelled this is double entry terms here. The prevailing rate of interest being the minimum upon rate at which any profit can be made on lending money assuming a borrower with ‘no risk’ and full security. Chapter 17 of the General Theory sees Keynes describe a similar process.

the total return expected from the ownership of an asset over a period is equal to its yield minus its carrying cost plus its liquidity-premium, i.e. to q – c + l. That is to say, q – c + l is the own-rate of interest of any commodity, where q, c and l are measured in terms of itself as the standard.

Or with Rowe’s correction, measured in terms of how the purchasing power of apples relative to the money commodity retains its value.

Then Keynes set out an investment schedule

As output increases, own-rates of interest decline to levels at which one asset after another falls below the standard of profitable production; — until, finally, one or more own-rates of interest remain at a level which is above that of the marginal efficiency of any asset whatever.

We have seen in the previous post the ordering of these investment returns are not immune to the market rate of interest

Given the cost addition In the production of money this sector is likely to earn lower rates than the average rate of profit and see capital switched to higher earning sectors. In this way multiple own rates see a convergence of interest rates around a single money market rate of interest . This rate is not the same as the rate in a barter economy – as Hayek believed – rather it is the average rate of profit – weighted by capital advanced in all sectors. (this weighting acting to normalise the quantity of money). Hence even though Central Banks might set a rate of interest we can still talk about a market or ‘natural’ rate of interest (I prefer market rate), which would be that rate which would exist if there were no central bank. In practice Central Banks try to follow this rate with some inevitable lag – so they are far from exogenous – being part of the political economy.

In the last couple of years there has been a debate in the blogosphere about the validity of the Sraffa critique of the ‘natural rate’. For example Grasner here invokes intertemporal equilibrium.

The latest round was started by Andrew Lainton who wrote about multiple own rates of interest. Lainton apparently thinks that there could be multiple real own rates, but seems to me to overlook the market forces that tend to equalize own rates, market forces wonderfully described by Keynes in chapter 17. Nick Rowe followed up with a post in which he seems to accept that real own rates could differ across commodities, but doesn’t think that that matters.

Glasner and his co-author state

Own rates, in any intertemporal equilibrium, cannot deviate from each other by more than expected price appreciation or depreciation plus the cost of storage and the service flow provided by the commodity, so that the net anticipated yield from holding assets are all are equal in intertemporal equilibrium. Thus, the natural rate of interest, on Keynes’s analysis in the General Theory, is well-defined, at least up to a scalar multiple reflecting the choice of numeraire. However, Keynes’s revision of Sraffa’s own-rate analysis provides only a partial rehabilitation of Hayek’s natural rate. Since there is no unique price level in a barter system, a unique money natural rate of interest cannot be specified.

RP Murphy correctly sees the ‘gotcha’ here, it assumes the classical dichotomy.

In other words, they conclude what–I claim–was Sraffa’s original point.

Please note that the explanation I give above has no equilibrium assumption and so doesn’t fall into this trap, rather it suggests a mechanism of market forces to change interest rates whether or not this reaches, if ever, any state of equilibrium, and without any hidden assumption of exogenous money with its implicit omnipotent monetary authority.. My approach accepts Sraffa’s point that in a barter system there is no unique rate of interest but instead suggests a process whereby market rates of interest are arrived at in a monetary economy.

In my revised approach I fully account for all force causing an increase or decrease in price of investment returns, and make I the clear distinction that without inflation own rates are a purely real phenomenon. if all agents correctly forecast all own rates of commodities then the term structure of nominal interest rates becomes calculable and we have inter-temporal equilibrium. Of course this will not happen, so the market rate of interest will shift and we will get a reallocation of capital, which will affect the process of production in none linear ways (see the previous post regarding Wicksell effects). I think Grasner jumps too quickly to intertemporal equilibrium and neglects the market processes affecting nominal prices.

Including Money in the Theory of Production

I hope to have demonstrated above that in a monetary economy there is only one single money rate of interest. As such it becomes possible to model interest as a cost in a cost of production approach to value. We have previously tackled this here, where we again demonstrated that Böhm-Bawerk’s objection to a cost of production theory of interest again relied on the classical dichotomy and was false in a creditary monetary economy.

I illustrate this approach graphically here, where the black is the interest cost of each factor, and capital services are simply the rental costs of fixed capital goods including depreciation.


From this we are able to devise a linear production theory including money. Interest is an ex ante cost imposed from the previous production period, a linear system can then determine prices for the future (or rather changes to all prices in continuous time) including the interest price of money. Money is modelled as a commodity produced by banks at a profit – the business model of banking, where money production has a cost and is produced if there is anticipated to be an acceptable profit. Money in circulation is modelled by a portfolio equation with one term being cash balances.

As inputs one takes the existing stocks of money and other assets – these flows coming from factor incomes in a model where income is composed of factor incomes not abstracted away –  and the prevailing market money rate of interest. The system then fully determines prices, including the price of money, Because of the potential for arbitrage between current and future interest rates it needs to be modelled in continuous time. However under normal circumstances the existence of positive growth and inflation rates eliminate the potential for such price ‘backwardation’. Allowing for the scope for such backwardation is a feature not a bug of the model. Interest then is only a partially exogenous variable, determined in expectation of production, and then determined by this for future periods. In effect current money and future created money are treated as different commodities. Wages become the residual of the model. The baseline model assumes competitive markets, but if these are not competitive then firms can charge ‘mark ups’ on prices and employers can be in monopolistic circumstances further squeezing the labour share.

In a follow up far more mathematical post I hope to set this out.

Crucially we have now embodied money production in the system of production – avoiding the classical dichotomy. As a result however money in circulation enters into the definition of the basic good and the numeraire, so it has a direct rather than an indirect effect of excess demand for money and other goods. As a result we have to modify Walras’s law, as a number of monetary theorists (notably Steve Keen) have posited, to include the excess demand for money at the given interest rate within the definition of money required to satisfy the demand for consumption. So money produced, debt, is not a veil, its creation and destruction directly modifies effectual demand.

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