Variations on the Theme of Conning in Mathematical Economics

The mathematization of economics is almost exclusively in terms of the mathematics of real analysis which, in turn, is founded on set theory (and the axiom of choice) and orthodox mathematical logic. In this paper I try to point out that this kind of mathematization is replete with economic infelicities. The attempt to extract these infelicities is in terms of three main examples: dynamics, policy and rational expectations and learning. The focus is on the role and reliance on standard xed point theorems in orthodox mathematical economics

Economics and the Complexity Vision: Chimerical Partners or Elysian Adventurers?

This work began as a review article of: "Complexity and the History of Economic Thought", edited by David Colander, Routledge, London,UK, 2000; & "The Complexity Vision and the Teaching of Economics", edited by David Colander, Edward Elgar, Cheltenham, UK, 2000. It has, in the writing, developed into my own vision of complexity economics

Sraffa's Mathematical Economics - A Constructive Interpretation

The claim in this paper is that Sraffa employed a rigorous logic of mathematical reasoning in his book, Production of Commodities by Means of Commodities (PCC), in such a way that the existence proofs were constructive. This is the kind of mathematics that was prevalent at the beginning of the 19th century, which was dominated by the concrete, the constructive and the algorithmic. It is, therefore, completely consistent with the economics of the 19th century, which was the fulcrum around which the economics of PCC was conceived

Origins and Early Development of the Nonlinear Endogenous Mathematical Theory of the Business Cycle

We study the origins of the nonlinear, endogenous, theory of the business cycle, in mathematical modes, within the framework of a macroeconomic theory, which was itself going through its own formal "birth pangs" at the same time, in the same years. The first part of the story begins in 1928 and ends, with the publication of Yasui's classic on Kaldor, Hicks and Goodwin, in 1953, and Hudson's classic of 1957. But there were other classics in the 1930s, even within some theories of the business cycles of the time - particularly the Austrian and that which may now be called the "time-to-build" tradition, which originates in Marx and Aftalion, independently, and reaches its nonlinear formalization origins in Tinbergen's work of 1931, followed by Kalecki's theories of the business cycle, substantially influenced also by Tinbergen's classic for mathematical method. There is also what may, for want of a better name, be called the "cobweb" tradition, on the one hand, and the tradition of Swedish Sequence Analysis, on the other (especially in the 1937 classic work of Lundberg, summarising the Swedish discussion on business cycle theory). The former having its origins, partly, in Austrian inspired search for an integration of dynamic method with equilibrium economic theory (especially represented by a series of classics by Rosenstein Rodan, from about 1929); and partly in the well known phenomenon of lagged responses in the supplydemand interactions in agricultural and commodity markets, particularly elegantly formalised by Leontief in 1934. From the point of view of economic theory, they were all part of the emerging consensus on the need to incorporate money and fluctuations in non-trivial ways as intrinsic components of orthodox equilibrium economic theory which was characterised as static theory. The implication was that the search was for a synthesis of dynamic method with traditional static equilibrium economic theory. The origins of macroeconomic theory, generally attributed to the post-depression development of monetary theory, business cycle theory and the theory of policy, could be traced to this particular search for a synthesis and was brilliantly summarised by Kuznets in a series of pioneering contributions in 1929-30. The story we try to tell is of mathematical business cycle theory in its non-linear modes, and how it emerged from one strand of macroeconomic theory, which, as just mentioned, was itself being forged, ab initio, dynamically

Notes on a 'Constructive Proof of the Existence of a Collateral Equilibrium'

In an interesting article in this journal, Ma (Comput Econ 45:1–30, 2015), claims that a constructive proof of existence of a Collateral Equilibrium (with a Leontief utility function) is provided in the paper. Moreover, there is also the additional claim that ‘on the basis of this proof, we can (and we shall) develop an algorithm for computing that equilibrium’ (ibid, p. 1). Thirdly, the statements that ‘the algorithm is shown by simulation to be effective’, and its effectiveness is demonstrated by ‘the accuracy of the equilibrium it provided’. These claims are, from a recursion theoretic (or computability theory) point of view, meaningless

Reflections on B P Adarkar's 'Years of High Theory' (1934-1941)

B P Adarkar's fundamental interwar contributions to the foundations of monetary theory and the theory of monetary policy, largely from the perspective of the evolution of Keynes's thoughts and insights into a monetary theory of production, are studied here sympathetically. A case is made that the issues at the frontiers of monetary macroeconomics--particularly, the nihilistic stance on monetary policy--can be criticised for illogical and empirically meaningless propositions, reflecting Adarkar's acute analysis during what this paper calls his "Years of High Theory" (1934-1941). Some conclusions are suggested on a revival of a Monetary Macroeconomic alternative to the varieties of orthodoxies now prevalent, based on Wicksell, Keynes--and Sraffa