A Model of Production with Supply Management for the Canadian Agricultural Sector: Comment

Abstract

In a recent paper Moschini (1988) claims to prove that cost complementarities between outputs do not exist when outputs are joint because of fixed allocatable factors which are normal inputs. This comment demonstrates that Moschini's proposition is incorrect, shows where the proof of the proposition is faulty, and identifies the additional condition that must hold in order for Moschini's proposition to be true. Correct derivation of this proposition is important because technology with fixed allocatable factors and multiple outputs is common in agriculture and standard analyses of multiple output cost functions, such as Sakai's or Lau's, do not apply directly to this technology. Consider the multiple output cost function used in Moschini (1988) to characterize production which is joint in outputs because of constraints on allocatable fixed factors. Jointness is not present in the primal representation of this technology. The production possibility set can be represented with individual production functions for each output. But outputs are joint in the dual cost and profit functions because they must compete for a constrained quantity of some allocatable input. The joint cost function is defined by Moschini's equation (15), which is reproduced here as equation (1):