I propose to add two very general constraints to the standard rendition of production functions. These constraints naturally open the analysis of production functions to recursion theory. Some powerful results are exploited and applied to certain aspects of the theory of production. In particular, I prove some theorems and propositions that are indicate how research and development and the emergence of technological innovations (or ideas) are naturally embedded in this approach. Next, I show how some known contributions to economic theory from different fields, such as growth theory and production theory with indivisibilities, can also be interpreted as attempts to overcome certain shortcomings of the standard theory that, I argue, can be automatically dealt with in the same proposed framework.
