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Monday, December 03, 2012

The "Standard" View of the Production Function

I've been away for a while, settling into retirement and trying to get three home remodeling projects finished (which they--finally--are).  But I've been reading.

And one of the things I read recently was a blog post by Nick Rowe, which linked to a blog post by Steve Roth, in which Roth argued that the standard view of the (microeconomic) production function (specifically as presented in Mankiw's intro textbook), specifically the notion that marginal cost rises in the short-run as output increases (in the presence of one or more fixed resources)

"...1. is ridiculous on its face, 2. is completely contrary to how profit-maximizing producers think, and 3. is based on just-plain incorrect math.* It’s just one of many central pillars of “textbook” economics that are still being taught with a straight face, even though they been resoundingly disproved by the discipline’s own leading practitioners, on the discipline’s own terms, and using its own language, constructs, and methods."
Why does he reach this conclusion?

"The rising marginal cost theory is ridiculous on its face because it assumes that producers add one factor of production at a time — hire more workers, for instance, without renting more space for them to work. (This is exactly what Mankiw describes in his textbook; see “Thirsty Thelma’s.”) Voila! Each worker’s productivity declines. This is of course not what producers do (my emphasis), which is why only 11% of top-corporation execs say they face rising marginal costs of production. (I’m wondering if that 11% made the mistake of taking an intro econ class in college.) For a nice recap of that executive survey, and the faulty math of rising marginal costs, see here (PDF)."
In fact, this is exactly what producers do in many, many instances.  Examples of producers doing exactly what Roth says they do not do  are all too easy to find:
  •  a gas station owner observes that her late evening sales have been rising and decides to see what will happen if the station remains open until midnight instead of closing at 10 PM.
  • a fast-food franchise adds additional workers during the late afternoon hours when it notices an influx of students stopping by on their way home from work.
  • retail stores add additional sales staff during November and December.
  • an indoor tennis faility extends its hours to accomodate increasing demand (and reduces its hours when demand falls).
  • steel companies increase (and reduce) their output (and use of labor) from existing production facilities.
Furthermore, we can extend this to non-labor inputs, by looking at some of the classic studies of a production functions, which I first ran across in Edwin Mansfield's intro to micro textbook.

    • studies of the use of fertilizer in the production of corn, where fertilizer use per acre of land was the variable in question, found a declining marginal product of fertilizer.
    • a study of throughput of an oil pipeline found declining marginal product from the use of higher pumping pressure in an existing pipeline.
All of these are examples of firms altering output without adding new capital equipment, or expanding existing facilities.  Is it even remotely plausible to think that US Steel, faced with an immediate ability to sell additional steel, would refuse to expand output until it had enlarged its steel mills?  Or that USS would reduce its output only by removing some production capacity?

Asking "top corporation execs" about their marginal costs, frankly, seems to me to be a fool's errand.  Most corporations do not seem to analyze their costs in that way, and there's no particular reason why people not involved on a day-to-day basis in cost analysis or pricing decisions would think in those terms anyway.

In part the difficulty here is in using a textbook presentation of a fairly complicated subject (the nature of production and a production function) as one's exemplar of how economists think about production.  When I teach this, I teach it as an abstraction, telling students that we reduce the problem to two resources (labor and capital) so as to be able to draw two-dimensional diagrams.  We know--believe it or not--that virtually every production process uses more than two resources--that, for example, when a power company increases its output of electricity from its existing generating facilities, it uses more fuel as well as more labor (and more of a lot of other "variable resources").

Capital is not quickly or (in a lot of cases) easily added or subtracted.  And production is not a case of expanding all resource use in the short or long run in fixed proportions (as, for example, input-output analysis would have it).  Furthermore, substitution possibilities constantly present themselves to firms (especially in the long-run, but also in the short-run), as in McDonald's making a (long-run) change to automatic-shut-off soft-drink equipment behind the counter and substituting the (unpaid) labor of their customers for the (paid) labor of their employees by placing soft-drink dispensers in the dining areas.  Or gas stations moving to pay-at-the-pump, which allows them to operate with fewer cashiers (or even to remain "open" all night with no cashiers.  Short-run substitution choices include, for example, power plants with the capability of using alternative feuls substituting toward the one whose relative price has declined.

Neoclassical microeconomics has  its problems, but the concept of fixed resources (in the short-run) and rising marginal costs are not, it seems to me, among them.


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