Up to now it has been assumed that each process produces one and only one commodity, that is, single production has been assumed. Let us now introduce some models which admit joint production, but only in a special way. These models are highly interesting in themselves since they deal with the presence of means of production which last more than one period, that is, fixed capital. But they will also be a useful way to introduce joint production. While at this stage general fixed capital models cannot yet be introduced (see Chapter 9), it deserves mention that the class of fixed capital models dealt with in this chapter is large: it covers all cases in which there is no joint utilization of old machines. In all models of fixed capital presented in this book it is assumed, however, that old machines cannot be transferred between sectors. (The interested reader will find at the end of the Section 2 of Chapter 9 a list of results which hold when machines are not utilized jointly and do not need to hold when they are.)

The structure of the chapter is as follows. Section 1 presents the assumptions underlying the following analysis. In Section 2 the properties of a given technique utilizing durable capital goods are studied. Section 3 introduces the useful concept of the “core processes.” Section 4 turns to a general discussion of the choice of technique problem and the determination of the cost-minimizing technique(s).