A word must be said, before going further, on the question of scale. This is a question which in the preceding chapter we were able to avoid. We were solely concerned with the capitalization of a given process; so we did not need to attend to the effects of 'horizontal' changes in size. What would happen if all (at, bt), all inputs and outputs, were increased in the same proportion? Would the process still be viable?
It would obviously be a great convenience if we could permit ourselves to say that it did not matter, if we allowed ourselves to introduce, at this point, the well-tried assumption of constant returns to scale. For by that assumption the scale of production and the technique of production are separated. The (at, bt) which we have been considering can then be regarded as determining a process of given technique and of unit size. We can vary size, without varying technique, by multiplying these coefficients (as they will have become) by a scale factor (x). Or, what comes to the same thing, processes of various sizes can be regarded as combinations of x unit processes. Can we venture to allow ourselves this simplification?
I think it may be justified, up to a point, in the following manner. Suppose we admit that there is a certain size of process that is the most economic. If an attempt were made to carry on the process at a little less, or a little more, than this optimum size, the inputs (proportionately increased) would not suffice to produce the outputs (increased in the same proportion). Then we must take the economic size as the size of the unit process. It will only be possible to vary size, without varying technique, by adding whole units.
This, I think, is by no means unreasonable. It does indeed exclude the possibility that there is no economic size: that as output is increased at all dates in the same proportion, the inputs at all dates that are required to produce them can be increased in what, for some at least, are smaller proportions. That, I suppose, is conceivable; but it may be doubted whether it is what even the