William Paul Bell Queensland University Researcher

Why is mainstream economics not a social science but ideological mathematics?

The G8 protests and the logically inconsistent foundations of neoclassical economics

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Neoclassical economics is deductive, using a mathematical axiom-proof-theory format.   Arnsperger and Varoufakis (2006) list the three basic axioms of neoclassical as methodological instrumentalism, methodological individualism and methodological equilibration.   In such an approach the basic axioms have to be correct otherwise the whole framework becomes unsound.   In contrast to the deductive approach, the scientific approach is inductive, forming theories from observation and using prediction to falsify the theories (Neuman 2003, p. 51).   Neoclassical economists have become adept at avoiding empirical falsification by creating ad-hoc explanations as to why their theories fail to work when confronted with empirical evidence, for example the Efficient Market Hypothesis predicting dividend volatility in excess of price volatility but the converse is observed (Shiller 1981).   Falsification avoidance is the sign of a degenerative research program (Lakatos 1976).   So, rather than use empirical falsification, a more suitable approach to disprove deductive frameworks is to use a logical proof showing their axioms lead to an absurdity.   The Sonnenschein–Mantel–Debreu Theorem (Debreu 1959) proves the basic axioms of neoclassical economics are logical inconsistent.   The Sonnenschein–Mantel–Debreu Theorem (Debreu 1959) shows that starting with the first two axioms leads to a shapeless excess demand curve.   The shapeless excess demand curve means that there are multiple equilibria and equilibrium are unstable making the third axiom untenable.   To fix this problem, it is assumed that all goods have constant Engel curves.   A good would have a constant Engel curve if somebody spends the same proportion of their income on the good as their income grew (Keen 2001).   This is an unlikely scenario as when income grows then people consume more luxury goods and basic goods become a smaller fraction of their income.   Can you think of a good with a constant Engel curve?   Colander (2000, p. 3) equates neoclassical economics “to the celestial mechanics of a nonexistent universe” for using theory outside its domain assumption (Musgrave 1981).   That is neoclassical economics as a pursuit in pure mathematics for intellectual exercise is fine but claiming applicability to the real world is misleading.

Computable General Equilibrium (CGE) and Dynamic Stochastic General Equilibrium (DSGE) models provide two examples of neoclassical theories that governments and world trade organisations use when formulating policy.   Two CGE models that are currently in use, are the Global Trade Analysis Project (GTAP 2009) and Dixon and Rimmer’s (2002) model of the Australian economy, which has been continuously developed at the Centre of Policy Studies (2009) at Monash University, Australian since the late 1970s.    As neoclassical theories, the  CGE and DSGE models use the three logically inconsistent axioms and with slight of hand just assume equilibrium when there is no theoretical justification (Mitra-Kahn 2008).    Consequently, any policy  recommendations derived from these models could well be misguided.  My post, titled G8    or G20 Protests and Computable General Equilibrium (CGE) modelling and   its Dual Instability Problem, further discusses the inconsistent  foundations of CGE and DSGE.

This post is not anti free market but against the distorted worldview of the free market peddled by neoclassical economics, which is that taught in the majority of undergraduate courses.   To the protesters at the G8 summits, keep up the protests but do add to the demands that economists and policy makers using these models go back to the drawing board and create models of the economy that are theoretically sound and applicable to this world.  My post, titled EU  acknowledges the failure of traditional economics to predict so adopts  agent based modelling, discusses one movement to address the logically inconsistent foundations of neoclassical economics.

The ideas discussed in this article are taken from and elaborated in Adaptive Interactive Expectations.


Arnsperger, C & Varoufakis, Y 2006, ‘What Is Neoclassical Economics? ‘ Post-autistic Economics Review, vol. 38, no. 1.
Centre of Policy Studies 2009, Economic Models at CoPS, Department of Business and Economics, Monash University, viewed 15 Feb. 2009, .
Colander, DC 2000, The complexity vision and the teaching of economics, E. Elgar, Cheltenham, UK ; Northampton, MA.
Debreu, G 1959, Theory of value: an axiomatic analysis of economic equilibrium, Wiley, New York.
Dixon, PB & Rimmer, M 2002, Dynamic general equilibrium modelling for forecasting and policy: a practical guide and documentation of MONASH, Contributions to economic analysis, Elsevier, Amsterdam.
Keen, S 2001, Debunking economics: the naked emperor of the social sciences, Pluto Press, Annandale, N.S.W.
Lakatos, I 1976, Proofs and refutations: the logic of mathematical discovery, Cambridge University Press, Cambridge & New York.
Mitra-Kahn, BH 2008, ‘Debunking the Myths of Computable General Equilibrium Models’, Schwartz Center for Economic Analysis, DOI Working Paper 2008-1, .
Musgrave, A 1981, ‘”Unreal assumptions” in economics theory: the F-twist untwisted’, Kyklos, vol. 34, no. 3, pp. 377-87.
Neuman, WL 2003, Social research methods: qualitative and quantitative approaches, 5th edn, Allyn and Bacon, Boston; London.
Shiller, RJ 1981, ‘Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends?’ The American Economic Review, vol. 71, no. 3, pp. 421-36.

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