This paper gives an outline of evolution of the concept and econometrics of production function, which was one of the central apparatus of neoclassical economics. It shows how the famous Cobb-Douglas production function was indeed invented by von Thünen and Wicksell, how the Constant Elasticity of Substitution (CES) production function was formulated, how the elasticity of substitution was made a variable and finally how Sato’s function incorporated biased technical changes. It covers almost all specifications proposed during 1950 to 1975, as well as the linear-exponential (LINEX) production functions and incorporation of energy as an input. The paper is divided into single product functions, joint product functions, and aggregate production functions. It also discusses the ‘capital controversy’ and its impacts.

Production function has been used as an important tool of economic analysis in the neoclassical tradition. It is generally believed that Wicksteed (1894) was the first economist to algebraically formulate the relationship between output and inputs as P = f (x₁,x₂,...,x_m), although there are some evidences suggesting that Johann von Thünen first formulated it in the 1840s (Humphrey, 1997).

It is relevant to note that among others there are two leading concepts of efficiency relating to a production system—the one often called the ‘technical efficiency’ and the other called the ‘allocative efficiency’ (Leibenstein et al., 1988). The formulation of production function assumes that the engineering and managerial problems of technical efficiency have already been addressed and solved, so that analysis can focus on the problems of allocative efficiency. That is why a production function is (correctly) defined as a relationship between the maximal technically feasible output and the inputs needed to produce that output (Shephard, 1970). However, in many theoretical and most empirical studies it is loosely defined as a technical relationship between output and inputs, and the assumption that such output is maximal (and inputs minimal) is often tacit. Further, although the relationship of output with inputs is fundamentally physical, production function often uses their monetary values. The production process uses several types of inputs that cannot be aggregated in physical units. It also produces several types of output (joint production) measured in different physical units. There is an extreme view that (in a sense) all production processes produce multiple outputs (Faber et al., 1998). One of the ways to deal with the multiple output case is to aggregate different products by assigning price weights to them. In so doing, one abstracts away from essential and inherent aspects of physical production processes, including error, entropy or waste. Moreover, production functions do not ordinarily model the business processes, thereby ignoring the role of management, of sunk cost investments and the relation of fixed overhead to variable costs (Wikipedia-a).

Managerial Economics Journal, Production Functions, Neoclassical Economics, Production Processes, Business Processes, Linear Programming, Agricultural Production, Economic Optimization, Mathematical Enunciations, Doctoral Dissertation, Generalized Production Function, Cobb-Douglas Function, Technological Progress, Empirical Data, Production Vectors.