‘Not Even Wrong’
The production function is undoubtedly one of the most widely used concepts in economics. Students of economics are normally introduced to the theory of production at an early stage of their studies. Introductory microeconomics textbooks outline the production function, isoquants, the conditions for cost minimisation, the demand for factors of production (based upon the marginal product theory of factor pricing) and soon. At the same time, the production function is extended seamlessly in first-year macroeconomic textbooks to encompass individual industries or, indeed, the whole economy. There is, however, little, or more usually no, discussion about the conditions under which it is legitimate to sum micro-production functions to give a well-defined aggregate production function. That this should be considered is not simply for mere intellectual curiosity. Indeed, since the 1940s, economists such as Leontief, Klein, or Nataf, among others, studied the aggregation problem, and for very good reasons. The same functional form is often assumed to hold irrespective of whether the production function refers to an individual plant, firm, industry, or to the whole economy.