We are now to define a productive process as a scheme by which a flow of inputs is converted into a flow of outputs. A firm, when it is a producing unit, may itself be regarded as the embodiment of such a process; but there are many (perhaps most) actual firms which are combinations of several producing units, each of which may usefully be regarded as embodying a process. It will still be a process, in our sense, if it would be possible to carry it on in a single firm. We must be ready, at least, for that degree of sub-division.
The process may be regarded in two ways: ex-ante and ex-post. When it is regarded ex-ante, it is simply a plan 1 ; it is the set of relations which underlies a forward budget. Regarded ex-post, it is the set that underlies the actual achievement, such as is recorded in 'historical' accounts. Both aspects will have to be considered, before we have done; but throughout this chapter (until we come to its last section) the process will be considered in the ex-ante sense.
We are not to think of the flows as steady flows, proceeding at a constant rate over time. Later on we may allow some constancy, for special purposes; but if we began with constancy we should be giving our analysis a static character even at the start. In the course of the process inputs and outputs must be allowed to change; and there is in general no reason why they should not change in composition as well as in amount. Changes in composition will nevertheless, in most of our work, be neglected. That can easily be done, for the moment, if we take it that the prices of inputs and outputs are given (and are the same whatever the date to which they refer); the inputs and outputs can then be made homogeneous by taking them in value terms. That is what we shall be doing in the present chapter. 2
The process may then be expressed as a pair of flows, of inputs