One of the first confusions of the traditional textbook production function Q = f(L,K) is that it's really a story about the production of value-added, not output. Students often wonder where raw materials are, or electricity, and so on, all products purchased from other firms. They are not there because value added is the value of the firm's output less the value of the inputs it buys from other firms, leaving the value added by the labour and capital employed in the firm itself.
Farnham's text doesn't mention this issue, but an even more important confusion is well explained. It is a confusion of stocks and flows.
Properly interpreted, Q is a flow of value-added that comes from a flow of labour services (L) and a flow of capital services (K). Yet in the story of the "short run", we are told that K is "fixed". But what is meant is that the stock of capital is fixed, not the flow of services from it.
Once this is clear, then it's easy to understand why the so-called "law" of diminishing marginal returns is not observed in practice. To quote Farnham (p.134):
Much research has indicated that inputs in these settings [ie manufacturing and industry] are likely to be used in fixed proportions up to the capacity of the plant. Although the stock of a fixed input is fixed, the flow of services from that stock may be varied and combined with the services of the variable input in fixed proportions. The size of a machine may be fixed, but the number of hours it is put in operation can be varied. Both capital and labor services are variable in the short run and can be changed together in fixed proportions, thus preventing diminishing returns and rising marginal costs from occurring in many manufacturing operations.Naturally, almost every other cost curve in the rest of the book reverts back to the 'textbook' model that lacks any solid empirical support, the usual practice of 'note-and-forget' that we point out in the Anti-Textbook as a favourite technique of authors who don't want the facts to get in the way of a useful story. Still, Farnham's treatment is far better than is normally found in most texts.
Farnham also discusses a reason for the deviation of the text's model from reality. He suggests that the text's model of production is really a model applicable to agricultural production, where we can imagine a crop (perhaps Halloween pumpkins?) being grown on a fixed amount of land with labour working the land. He writes (p.132): "There is no need to distinguish between the stock of the fixed input, land, and the flow of services derived from it. The land provides services continuously and is not turned off at night."
So, to sum up in the form of a supplementary "Question for your professor" to add to the questions in Chapter 5 of The Economics Anti-Textbook:
Isn't the short-run production function in the text confusing the stock of capital with the flow of services from it? If we properly make the stock-flow distinction, doesn't the story of diminishing marginal returns fall apart?
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