The Production Function

This chapter is somewhat different from those which have gone before primarily in paying a good deal more attention to the problems inherent in choosing specific functional forms to represent the production structure. We have, of course, discussed a number of particular functions elsewhere — the linear, the quadratic, the logarithmic, and even the CES — but the list of functions whose properties are well understood is more extensive than those just mentioned and, even for those just listed, detailed comparisons have not been made to this point. Normally, we might consider the study of production after we have studied investment, on the grounds that the latter is part of aggregate demand (two components of which we have already considered in Chapters 2 and 3) while the former is a key concept in aggregate supply. This procedure is not optimal in this study primarily because we use specific functional forms for the production function in our study of investment; that is, the production function (as it is studied here) is one input into an aggregate investment function. There are, of course, other inputs into the investment function — such as a specification of the cost of capital and of tax laws — which are also studied later. Of course, we do not mean to ignore the simultaneous equation nature of the production process either, so it is more a matter of logical order as designed in this study than a matter of principle. We should note, though, that all we have to say on the topic of “aggregate supply” is contained in Chapter 1.[1]