Production Functions as Turing Machines

Kumaraswamy Velupillai and Stefano Zambelli - Aalborg University

In this paper production functions are modelled in terms of Turing machines or compositions of Turing machines. The input tape and the output tape of the machine are seen as encodings of respectively the inputs of production and the output. At the same time the configuration of the Turing machine is viewed as an encoding of the technology used. Here it is shown how, for example, research and development may be modelled as the producers' search for new production inputs (i.e., new encodings for the initial tape), new products (i.e., new encodings for the final tape), new technologies (i.e., new configurations for the Turing machines). Moreover the cost functions are defined in the simple terms of the algorithmic and computational complexity of the Turing machines. At the same time the very existence of the halting problem allows for the introduction of a non stochastic notion of uncertainty. In fact uncertainty may be modelled not as the outcome of a pre-defined probability distribution, but in terms of the randomness associated with the Halting problem. In this way the 'frequency distribution of innovations' turns out to be endogenously generated by the choices of the Turing machines. In this article actual examples of production Turing machines are presented and simulations are developed.

Scheduled for Session 1.6 Model Of Bounded Rationality