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

Newcomb's Paradox: a Subversive Interpretation

A re-interpretation of the asymmetric roles assigned to the two agents in the genesis of Newcomb’s Paradox is suggested. The re-interpretation assigns a more active role for the 'rational' agent and a possible Turing Machine interpretation for the behaviour of the demon (alias 'being from another planet, with an advanced technology and science,..,etc.'). These modifications, while introducing new conundrums to an already diabolical interaction, do allow the 'rational' agent, as a computably behavioural agent, to make a clear decision, if any decision is possible at all. This latter caveat is necessary because in the Turing Machine formulation, the computably behavioural agent might have to face algorithmic undecidabilities

A Primer on the Tools and Concepts of Computable Economics

Computability theory came into being as a result of Hilbert's attempts to meet Brouwer's challenges, from an intuitionistc and constructive standpoint, to formalism as a foundation for mathematical practice. Viewed this way, constructive mathematics should be one vision of computability theory. However, there are fundamental differences between computability theory and constructive mathematics: the Church-Turing thesis is a disciplining criterion in the former and not in the latter; and classical logic - particularly, the law of the excluded middle - is not accepted in the latter but freely invoked in the former, especially in proving universal negative propositions. In Computable Economic an eclectic approach is adopted where the main criterion is numerical content for economic entities. In this sense both the computable and the constructive traditions are freely and indiscriminately invoked and utilised in the formalization of economic entities. Some of the mathematical methods and concepts of computable economics are surveyed in a pedagogical mode. The context is that of a digital economy embedded in an information society

Negishi's Theorem and Method

Takashi Negishi's remarkable youthful contribution to welfare economics, general equilibrium theory and, with the benefit of hindsight, also to one strand of computable general equilibrium theory, all within the span of six pages in one article, has become one of the modern classics of general equilibrium theory and mathematical economics. Negishi's celebrated theorem and what has been called Negishi's Method have formed one foundation for computable general equilibrium theory. In this paper I investigate the computable and constructive aspects of the theorem and the methodComputable General Equilibrium, Fundamental Theorems of Welfare Economics, Negishi's Method

The Fundamental Theorems of Welfare Economics, DSGE and the Theory of Policy - Computable & Constructive Foundations

The genesis and the path towards what has come to be called the DSGE model is traced, from its origins in the Arrow-Debreu General Equilibrium model (ADGE), via Scarf's Computable General Equilibrium model (CGE) and its applied version as Applied Computable General Equilibrium model (ACGE), to its ostensible dynamization as a Recursive Competitive Equilibrium (RCE). It is shown that these transformations of the ADGE - including the fountainhead - are computably and constructively untenable. The policy implications of these (negative) results, via the Fundamental Theorems of Welfare Economics in particular, and against the backdrop of the mathematical theory of economic policy in general, are also discussed (again from computable and constructive points of view). Suggestions for going 'beyond DSGE' are, then, outlined on the basis of a framework that is underpinned - from the outset - by computability and constructivity considerationsComputable General Equilibrium, Dynamic Stochastic General Equilibrium, Computability, Constructivity, Fundamental Theorems of Welfare Economics, Theory of Policy, Coupled Nonlinear Dynamic