## A Seven-Sector Model

Let us start with a consideration of the production system. We will treat this as it was treated in Chapter XV of The Growing Economy. There are a large number of processes of production-a, b, c, d, etc. Each process of production for its operation on a given unitary scale needs a fixed input of labour and of various man-made intermediate products, and it produces a fixed output of various products either for use as intermediate products or for final consumption. Thus process a requires for its operation on a unitary scale inputs of Lla units of labour of type 1, L2a units of labour of type 2, and inputs of Xla units of product 1, X2a units of product 2, etc.; and process a then produces Xla units of product 1, X2a units of product 2 and so on.i

On day t the various processes are operated on various scales, namely Sa(t\ Sb{t), Sc(t), etc. It follows that the total input into the production system at 8 a.m. on day t of labour of type 1 is expressed by

Lx{t) = LlaSa(t) + LlbSb(t) + LlcSc(t) + . . . . Similarly the total input of product 1 at 8 a.m. on day 1 is expressed by:

* i W = XlaSa(t) + XlbSb(t) + XlcSc(t) + . . . and the total output of product 1 at the end of day t, available to be used at 8 a.m. on day t + 1 is expressed by:

* i W = XlaSa(t) + XlbSb(t) + XlcSc(t) + â€¢ â€¢ â€¢ 1 There are two minor ways in which this formulation differs from that used in

We shall treat technical progress exactly as it was treated in Chapter XV of The Growing Economy. A technical improvement introduces the possibility of using a new process of production in which the same amount of some output can be obtained for a smaller amount of some inputs (cf. pp. 348-50 of The Growing Economy). Formally we can treat the problem in the following way. We can assume that the technical ideas behind every process that will ever be invented already exist in some heavenly workshop; but there is a constraint which makes S = 0 for every process which has not yet been invented; technical progress then removes this constraint on the scale of the various processes as they are 'invented'.