In a discipline such as economics, increasingly devoted to its computational content, the mathematical underpinnings of the computability assumptions of economic fundamentals have not been investigated systematically or reasonably exhaustively. In this book, such an attempt is made for the first time. Choice theory, adaptively rational behaviour, induction, learning, arithmetical games, computational complexity of decision processes, growth theory, and the theory of economic fluctuations are given recursion theoretic (i.e, computable) interpretations. Economic theoretic questions, posed recursion theoretically, lead to answers that are ambiguous: undecidable choices, uncomputable learning processes, algorithmically unplayable games, etc., become standard answers. The book also claims that a recursion theoretic formalization of economic analysis makes the subject intrinsically inductive and computational.

Stimulating comments and constructive criticisms made at the presentation and by an anonymous referee helped reduce ambiguities and some of the harsher, critical, tones in the original version. I am, in particular, indebted to Professor Deidre McCloskey for her extremely perceptive comments on existence problems as framed and presented in the earlier version. I am also indebted to general supportive reactions and clarifying comments from Tom Boylan, Francisco Doria, Duncan Foley and Marcelo Tsuji. Alas, the remaining errors and ambiguities are entirely my own responsibility.

No abstract

Three topics are discussed as pointers towards issues at the frontiers of computable economics: effectivizing the fundamental theorems of welfare economics; computable production theory; the effectivity of tâtonnement. Furthermore, in the appendix, an attempt is made to analyse the notion of finding a formally simplest theory of economic fluctuations. Some discursive notes on multiple equilibria in economic models and their possible generation due to various formal uncomputabilities is also presented.

Formally, the orthodox rational agent's "Olympian" choices, as Simon has called orthodox rational choice, are made in a static framework. However, a formalization of consistent choice, underpinned by computability, suggests by, satisficing in a boundedly rational framework is not only more general than the model of "Olympian" rationality, it is also consistently dynamic. This kind of naturally process-oriented approach to the formalization of consistent choice can be interpreted and encapsulated within the framework of decision problems-in the formal sense of metamathematics and mathematical logic-which, in turn, is the natural way of formalizing the notion of Human Problem Solving in the Newell-Simon sense.