ABSTRACT
Let us turn now to the way in which the Central Authority might cope with problems (3) and (4) on page 200, namely, the maximization and the optimization of production. For this purpose we regard the production system as being composed of a vast set of distinct processes as illustrated in Table XII. Each process is completely rigid in the sense that the ratio between any one input and any one output is fixed and unchangeable in any one process. Thus in process 1in Table XII if Z 1 units of product Z are to be produced, Y 1 units of product Y will necessarily also be produced and N 1 units of factor N will necessarily be employed, and similarly for every other output and input in process I. Each process is thus subject to constant returns to scale in the sense that ff each and every input were doubled then each and every output would be doubled. For each process we define arbitrarily a unit for the scale of its operation. Thus, for example, we define a unit of process I as the production of amount Z 1 of Z and thus amounts Y 1 X 1 and W 1 of outputs YX and W the use of amounts N1M1L1 and K1 of inputs NMLK. Since Z 1 205the output of Z which comes from process I when process I is operated on a unitary scale, the total amount of Z produced by process I is ZXSX where 5, measures the scale on which process I is operated. For example, if Sx =21, then the output of Z from process I is 21 times Zx and similarly for the other outputs and inputs in process I.
