Modelling the Structure of Cost and Production for Multiproduct Firms

Virtually all enterprises market a multiplicity of products; yet, most econometric models of production or cost presume a single homogeneous output. Moreover, models which do recognize multiple products typically specify transformation functions with severe a priori restrictions on the structure of production and cost. Recently McFadden [13; 14], Jacobsen [9], and Shephard [16] have used the principles of duality to demonstrate the existence of multiproduct cost functions corresponding to general production structures. This gives rise to the possibility of directly modelling the structure of cost for multiproduct firms without imposing arbitrary a priori restrictions on the structure of production. Two common restrictions on the structure of production are homogeneity and separability. In this paper we demonstrate that these restrictions can be relaxed by the use of a flexible multiproduct cost function. We illustrate the methodology with a data set which has been previously analyzed under restrictive specifications. The results indicate that the imposition of homogeneity and separability can greatly distort estimates of marginal costs and scale economics.