Non-Joint Technologies

Abstract

The hypothesis of non-jointness in input quantities (separate production functions) is well-known, and it plays an important role in many areas of economics. In this paper we define three additional forms of non-jointness which have received little or no attention in the literature, and which might be relevant for the firm as well as for the representation of the aggregate technology. We characterize all forms of non-jointness in terms of variable profit and joint cost functions. This yields a number of restrictions which are all testable empirically. The assumption that production is non-joint in input quantities (separate production functions, inputs allocated between the different production processes) plays a crucial role in many areas of economic theory. We need only think of international trade theory, public finance, macroeconomics, growth theory or traded-non-traded good models of international finance. In fact, it is safe to say that more often than not production is assumed non-joint in input quantities in multiple-output models. Little work has been done to test the empirical validity of the assumption of non-jointness in input quantities. Samuelson (1966) studies the characterization of non-joint technologies in terms of the transformation function. As pointed out by Hall (1973), however, Samuelson's results do not seem very useful for econometric work. Hall studies the characterization of non-jointness in input quantities in terms of the joint cost function; this leads to a number of restrictions which can easily be imposed or tested for, and which were used in empirical work by Burgess (1976) and by Kohli (1981). Lau (1972, 1978), finally, characterizes non-jointness in input quantities in terms of the profit function. Besides non-jointness in input quantities, Lau also examines the case of non-jointness in output quantities (when an input can be cracked into several outputs). In this paper we define two additional cases of non-jointness, and we characterize them in terms of the joint cost function and the variable (or normalized restricted) profit function. The new forms of non-jointness that we define may be useful to describe technologies at the level of the firm, and, may be even more so, at the aggregate level; some may be useful concepts in other areas of economics as well, such as consumer theory. By distinguishing between the various forms of non-jointness one obtains a number of testable restrictions on the corresponding joint cost or variable profit functions.