John McDermott


The counter scientific character of the reigning mainstream Neo-Classical Economics is demonstrated under 7 headings, variously factual, methodological, including mathematical, and historical.

JEL Codes: B41, D41, L13.
Keywords Perfect Competition, Public Sector, Mathematics, Labor force Production

COPYRIGHT: American Review of Political Economy; John McDermott


There is no such thing as a free-standing, self-regulating “free-enterprise” or “private sector economy” in the US. Contemporary, mainstream, Neo-Classical Economics, whose pinnacle reaches to General Equilibrium Theory is pseudo-science.


The facts here are as follows:

  1. In the US, arguably the gold star “private enterprise” economy, public investment in the period 1970-2010 exceeded the private variety by a ratio of approximately 1.8 to 1. (McDermott 2017) [i] If the nature and sources of investment are decisive for identifying the character of an economy, then the US economy is overwhelmingly of a public, not private character.
  2. Since Schumpeter our conception of “private-enterprise” revolves around the entrepreneur, that daring figure who, it is said, introduces dynamic change and growth into market economies. In a modern economy, this change centers on technological innovation.

But such celebrated innovators as Gates and Zuckerberg have typically  “productivized” scientific and technological advances funded by government. The technological dynamism of the so-called private sector has a largely external source. The overarching pattern has been that the public sows broadly whence private firms selectively reap.

  1. That stand-alone private economy is said to be self-regulating. But in the leading capitalist economies a central bank regulates the amount, the timing, the forms, the availability and the cost of credit, hence exerts an almost decisive influence over the timing, the amount, the forms, the availability and the costs of private investment.
  2. We are said to have an economy in which price relationships are dominantly of a competitive nature. But…

Firm-to-employee: we have had long experience of our central bank, the Fed, “cooling” the economy against the threat of “excessive wage” demands. In a modern economy only labor prices (wages) are so “cooled”, virtually all others left free to seek their own temperature.  Further, for 1 in 4 full-time workers an effect of that “cooling” is that wages fall below the cost of reproducing the worker and his/her family. The short-fall is made good by socializing their incomes via government subsidies in housing assistance, food stamps, the earned income tax credit, some direct grants, extended disability benefits, and so forth. In addition, local, state and the federal tax systems favor higher income over low, property income over wage income. In sum and outcome, the firm-to-employee price relationship is dominantly socialized, only episodically “private’.

Firm-to-consumer: Endless studies, confirmed by our own retail experience, show that very, very few of these prices are set by any sort of classical bargaining. In general the studies show that consumer prices are set by sellers’ mark-ups, different historical rates governing in different industries: astronomical in pharmaceuticals, high in clothing, low in groceries, oscillating in appliances, and so on in other areas.

Firm-to-firm: Frederic Lee 1998 has shown in his encyclopedic review of pricing and cost accounting studies that firm-to-firm pricing in the US (and UK) is dominantly consensual and not competitive in nature, both seller and purchaser sharing an informed judgment about mark-up prices that are set and maintained by mutual consent and not by classic zero-sum bargaining.

The key to the non-existence of classic price bargaining here is that firm-to-firm relationships are not, as in the familiar bargaining scenarios, one-offs where, one grants, it makes sense to drive for the lowest price. But as soon as one introduces repeated and/or continuing relationships between the purchasing and selling firms the economic health of each side becomes a substantive concern to both. Pricing here is and has to be dominantly consensual between mutually well-informed parties.


We will limit the discussion to only two of the unacceptable methodological devices that are central to the theorization of a stand-alone, self-regulating private competitive economy.

  1. 5 . There cannot be – not even just conceptually – a Perfect Competition . One normally says of perfect competition that, of course, there isn’t and likely never was anything of the sort. On the other hand, it is a rare piece of Economics theorizing that somewhere doesn’t include the expression , “Assuming perfect competition…..” whereupon one spins one’s argument.

The problem here is that the term “perfect competition”, like, say, “the largest integer” embodies a logical contradiction. There can’t be such a thing! Hence any and all inferences embodying the conception itself are themselves invalidated.

The proof of the contradiction is relatively long and somewhat technical. It can be accessed under my name as “Perfect Competition, Methodologically Contemplated” ( The Journal of Post Keynesian Economics. 37(4), pp. 687-703. (2015)). It begins with a critique of George Stigler’s classic “Perfect Competition, Historically Contemplated” which appeared in The Journal Of Political Economy 65(1), pp. 1-17. (1957). There, Stigler defined perfect competition in terms of nine other “ perfect ”s, as for knowledge, tastes, inter-communication and so forth. But that still left unaddressed the analytical content of those  “perfect”s,

In Economics, expressions employing “perfect” typically have had a comparing logic and function, as in ‘This market is more perfect than that.” Here one envisions a set of possible competitive markets arranged serially by a logic of greater and lesser  competitiveness. Accordingly to speak of “perfect” competition is to argue that the series has a unique maximal element.

Following that lead, the JPKE article constructs such a series and then hypothesizes that the series does indeed have such a terminal element. But then on that same hypothesis one can equally show that it cannot. Hence the contradiction.

The proof is elegant in a mathematician’s sense. The very elements in it which are needed so as to assure that the series will be complete — will exhaust all the kinds and degrees of competition —  are also the elements which form the resulting contradiction.

In short, the JPKE proof holding, the “perfects” that we employ is Economics demonstrations are illicit and must accordingly be banned from all theoretical work.

  1. The contemporary mathematicization of Economics is mathematically unsustainable. It is a Mis-Mathematics.

Here we are obviously not referring to ordinary quantitative studies but to the mathematicization that is required to demonstrate a General Equilibrium and its Welfare and Efficiency Theorems for a modeled competitive economy.

The point, of course, of General Equilibrium Theory is to show that our elementary notions of competitive economy, reaching back to Adam Smith, are consistent within themselves and, when carefully systematized, “prove” that there exists a general equilibrium position within which that economic model exceeds any other possible form of economy in the most efficient use of economic resources and distributes them with maximal  fairness to the economic actors.

As corollary, within a General Equilibrium every Price (= exchange ratio) is a unique measure of economic value and not merely an approximating index. But…

… under the reigning economic assumption of methodological individualism one cannot guarantee the existence even of special equilibria much less the General Equilibrium claimed by Debreu and Arrow.

To illustrate the mis-mathematics we begin with Jevons who introduced the now standard diagrammatic representation of the equilibrium of  supply and demand in the form of a two-dimensional mathematical field in which price is measured along a vertical axis and quantity along a horizontal axis crossing it perpendicularly. The resulting representation of supply and demand “curves” is so simple, so clear, so vivid, so convincing that it seems beyond possible criticism.

There are two distinct methodological faults here. First, in the Jevons procedure one prescribes how one will view economic reality and to that extent departs from the strictly descriptive, empirical canons that we identify with genuine science.

In the second, we can identify an unbridgeable gap between the Economics analysis and the mathematics into which it has been cast. Briefly the Mathematics, brilliant and valid as it is, is not supported by the Economics. [ii]

6a. Description and Prescription :  if there is to be an equilibrium position in the conventional  Jevons scheme between supply and demand the “lines” – the functional values – must share a common point (value).

Here one assumes, “ All things holding equal , the greater the supply the less the price” and opposite for the demand side. Those ceteris paribus prefixes are employed to guarantee that the supply curve will have a positive slope over its entire range and the demand curve a negative one. Thus they’ll have to cross – but only once. If, for example, the demand curve wiggled, say, fell normally, then rose for a segment and then resumed falling again, one opens the possibility of the supply curve passing through it more than once – i.e., the uniqueness of the equilibrium position would be compromised. In an empirical study this would be entirely familiar and non-upsetting.

But in basic theory, the ceteris paribus construction establishes that whatever may be the real, imagined, even empirical nature of any arbitrarily chosen supply(demand), curve, it will always – at every point – lie on a (positive) negative slope. That is, the ceteris paribus enters a prescription into the analysis.

I will forego a lengthy discussion, almost surely familiar to the reader, of the alleged merit for entering this prescription. But the deeper point is that in so prescribing one has departed empirical, positive science, period. Whatver the reasons! The procedure in question has overtly and explicitly departed the indicative mood for the subjunctive, for good or bad mixed a prescription into the description, thus to that extent departed from a strictly empirical, hence strictly scientific analysis.

One would not prescribe from the start how a cancer cell ought to behave, nor set a rule governing how DNA ought to alter, nor tell electro-magnetic phenomena how fast they may travel. One discovers these things and, because these are matters for discovery, one thereby accepts that new discoveries might force changes in the science. But one cannot ever discover that consumers act with less than full rationality to do whatever it is they are said to do. That prescription stands as part of the unchanging substance of Economic “science” – not just as a discardable procedural sort of thing.

There is a second, strictly mathematical objection to the Jevons procedure and it is that which is referred to in the expression “Economics and Mis-Mathematics”.

6b. Systematic Mis-Mathematics: In the Jevonian idiom we can actually “see” the crossing of the two “lines”, thus making diagrammatically visible the desired equilibrium between supply and demand.

But whether in print or on the chalk-board DD’ and SS’ must enjoy the mathematical character of continuity . The functions which define them must be continuous over their range. If they are not, then there may be a gap at the crossing point, hence no unique equilibrium. Repeating, both DD’ and SS’ must be continuous over their range – i.e., must both exemplify there the properties  of the mathematical continuum .

But it is also methodologically insisted  – I know of no departure on this point – that a competitive market economy is characterized by “methodological individualism”.

That is to say that every transaction in such an economy is in principle individually discriminable. In our narratives we imagine that every transaction has been uniquely bargained by its transactors. This is the very  reason that it represents an equilibrium between supplier and demander – the equilibrium is the outcome of that unique bargaining.

In short, we imagine DD’ and SS’ to consist of individual points aggregated to form  continuous lines, thus their crossing identifies the equilibrium point. Then a General Equilibrium is methodologically conceived as the aggregate of these special equilibria.

But no segment of the continuum can be constructed in this way. Aggregating point-values can add up to a very dense set/line indeed – but the work of Georg Cantor (Cantor 1915) has shown that no possible aggregation, no matter how large or even dense,  is sufficient to form the continuum . Depending on the density of the points/values of the line/set we can closely approximate the crossing point – but the further inference structure of theoretical Economics is not satisfied by an approximation; one needs the unique equilibrium itself.

Aggregating points/values to form a line/set may possibly give us what Cantor calls  a first order or denumerable (countable) infinite but he has shown that the continuum cannot in principle be formed in this way. It represents a second, larger  kind of infinite, the infinite of the Real Number continuum. [iii]

When in Economics analysis, we call upon limits, maxima and minima, employ differential equations and so on, we enter the realm of the Real Numbers and thus violate that difference. The principle of “methodological individualism” restricts the number systems  that may be legitimately employed in Economic analysis to those which represent countable aggregates.

In short, the mathematicization of Economics that underlies the regnant proofs of General Equilibrium is illicit. It represents a gross violation of the Theory of Measurement, a point that long ago should have been understood and acted upon. It is this very obvious and avoidable violation of method in the General Equilibrium Economics that supports the judgment that the outcome  is not merely inadequate science but pseudo-science.

  1. Labor or the labor force originates outside the economy : In general equilibrium analysis one assumes that labor is a non-produced input into the economy. [iv] A convenient and not too falsifying assumption in a traditional economy where the labor force is produced more or less spontaneously and out-of-sight in the recesses of “society”. But not in every modern economy where, since roughly the 1890’s, vast resources and attention have been devoted to producing a labor force of apt size and of differential productive characteristics —  and even to shaping ‘cooperative’ social attitudes within it. To erase this world-historic change, and to do so as a fundamental assumption for Economics theorizing again confirms  not merely the influence of a non-critical, non-scientific culture in the profession but of a profoundly anti-scientific one.

Premature ‘Science’

Economics’ claim to be a true science is highly premature and evidently faulty. I would hypothesize two villains here. Who can forget one’s Intro class and the marvels made so vivid by virtue of chalk swipes on an unresisting board? But, as we have seen from the casual way the Jevons scheme has been adopted, the idea that Economics was a ‘quantitative’ discipline, unlike its ‘soft’ social science relatives, encouraged an equally too casual stance towards the Theory of Measurement and its apposite Mathematics.

The other villain is not so innocent as the foregoing. To cast Economics in a template of exchange is to cast it in the template of the exchange of private property. But then in methodologically perfecting’ a logic of private exchange, by that very fact  one espouses the unique superiority of privately controlled and to that extent socially unconstrained property. Whence also follows the discipline’s traditional preference for the social dominance of property’s owners. In short, the contemporary Neo-Classical Economics per se represents and embodies a whole social ideology disguised as neutral science.

A scientific Economics is yet to be born although much of the information it will ultimately systematize is already in our hands. But I venture that that project is as yet unripe. A much more critical, sceptical, value-free approach to its construction will be required before we can expect our Newton or our Darwin.


Arrow, Kenneth and Frank H. Hahn. 1971 . General Competitive Analysis. San Francisco: Holden-Day

Cantor, Georg. 1952 (1915). Contributions to the Theory of Transfinite Numbers. Translated by Phillip Jourdain. New York: Dover Publications.

Courant, Richard and Herbert Robbins. 1969 (1941) What is Mathematics?: An Elementary Approach to Ideas and Methods . Oxford and New Yor: Oxford University Press

Lee, Frederic. 1998. Post Keynesian Price Theory. Cambridge and New York: Cambridge University Press.

McDermott. John. 2015. “Perfect Competition, Methodologically Contemplated” The Journal of Post Keynesian Economics. 37(4), pp. 687-703. (2015).

McDermott, John. 2015. “We” Invest More Than “They”. URPE Newsletter . Vol 46 (4). Pp, 6-9.

McDermott, John. 2017. Employers’ Economics Versus Employees’ Economy: How Adam Smith’s Legacy Obscures Public Investment in the Private Sector . Cham (Switzerland): Palgrave Macmillan)

Stigler, George. 1957 “Perfect Competition, Historically Contemplated” The Journal Of Political Economy 65(1), pp. 1-17. (1957).


[i] The data tables appear at pp. 24-7 and were earlier published in the URPE Newsletter .  2015. Vol. 46. No. 4. Pp, 6-9.

[ii] For this demonstration, see McDermott 2017, Chapter 3

[iii] For the non-mathematician, Courant and Robbins 1969 (1941) pp. 77-86 provide a lucid discussion.

[iv] Arrow and Hahn 1971: p. 64