Joint Production with ‘Restricted Free Disposal’

A single production system with constant returns can produce any level and composition of demand by appropriate intensities of the cost‐minimizing processes. Hence, in the long run, products can never be in excess supply and there exists a system of prices of production which is semipositive and independent of demand. These (and other) properties do not, in general, carry over to joint production systems where one or several processes produce two or more different products. The proportions in which products emerge will generally be different from those in which they are required for use. The usual approach to that problem is to apply the rule of ‘free goods’. This assumption may be applied to goods which, if they are left where they are and as they are, cause neither costs nor benefits. But it cannot be applied to outworn machines, scrap, wastes or pollutants and is therefore not generally applicable. The present paper aims at finding conditions for the existence of cost‐minimizing systems for cases where this crucial assumption either is completely absent or is substituted by the assumption of ‘restricted free disposal’, i.e. by the assumption that excess production is permitted up to a certain tolerated limit. It will be proved that the conditions for the existence of cost‐minimizing systems with free disposal carry over to systems with restricted free disposal.