OF AGRICULTURAL ECONOMICS DECEMBER , 1974 PRODUCT COMPLEMENTARITY IN PRODUCTION : THE BYPRODUCT CASE *

The product-product relationship has been a traditional subject of most production economics and farm management courses for the past two decades. A l t h o u g h t h e t radi t ional examples of product-product optimization have come primarily from the agricultural production sector (e.g., legume-corn rotations and crop-livestock combinations), the concept is useful in analyzing the organization of any multi-product firm-including those firms which produce externalities in the form of environmental degradation. Three concepts or ideas usually are offered as giving rise to a positively sloped or complementary range on the product transformation surface-(l)one production process uses as an input a by-product of another production process, (2) one process uses quantities of a factor that are "surplus" to another, or (3) technical interaction (production function shifts) occurs. As Heady notes, the by-product idea is perhaps the most important of these concepts in the agricultural sector [6, p. 222]. However, this concept is (in our view) inadequately treated in most farm management and production economics texts. The purpose of this paper is to propose a more useful framework for considering by-products than that traditionally provided. Following a brief critique of the traditional treatment of the by-prpduct case, an alternative framework is proposed. The empirical and operational viability of the framework is demonstrated with a numerical example. A CRITIQUE OF THE TRADITIONAL FORMAT