"...while never examining the units used to measure its ingredients..."
A matter I discussed on pages 204-208 of "The 'lump-of-labor' case against work-sharing" (Working Time: International trends, etc., 2000). See also "Dead Metaphors and Living Wages: On the role of measurement and logic in economic debates" by Ann Jennings. It's not a big deal? That supposes that the "real flaw" is elsewhere and therefore the unit fallacy is subsidiary. Although that is one possible interpretation, the other possibility is that the will to express relations in non-existent units that is at the bottom of all the rest of the hocus-pocus, in which case the unit fallacy is foundational and not ornamental. On Mon, Aug 13, 2012 at 11:35 AM, Jim Devine <[email protected]> wrote: > Gil's answer makes sense to me. The problem arose because of the > standard practice in NC macroeconomics of simply assuming that an > equation such as a Cobb-Douglas production function (my equation) > applies while never examining the units used to measure its > ingredients. It's not a big deal, of course: it only adds insult to > the injury (to knowledge and reason) arising the use of an aggregate > production function (along with the commonly unstated assumption that > Say's "law" applies). (I hope that NC economists outside of the > Chicago school are more sophisticated and honest.) > > On Mon, Aug 13, 2012 at 10:26 AM, Gil Skillman <[email protected]> > wrote: > > > >>Q has dimension leets to the power a times hours to the power 1-a [as > >>amended by Paul--GS]. > > > > Alternatively, within the equation expressed by the function, L, K and Q > > can simply be understood as pure numbers, so that the relationship > between > > them need only satisfy mathematical laws. This addresses Tom's point > about > > the meaning of "=". The interpretation one gives to the respective > > variables is logically separate from the equation itself, so that nothing > > compels us to understand the pure number Q as being measured in units > > composed of hours and leets. Rather, one *interpretation* of the > > relationship expressed by the equation is that given numerical values of > > leets and labor hours are mapped into given numerical values of tons of > > steel. To put this another way, in mathematical economic arguments the > > respective sets from which admissible values of independent and dependent > > variables are drawn are generally defined as subsets of the real numbers > > (say), not as subsets of a particular universe in which things like leets > > and labor hours (say) combine to form some composite units of labor hours > > and leets. > > > > If this reading bugs you, imagine instead that the independent variables > L > > and K are multiplied by respective parameters alpha (measured in steel > per > > unit labor) and beta (measured in steel per leet unit). Now set these > two > > ratios each equal to one, which gives us Jim's equation, and allows us to > > interpret the equation as saying that units of steel = (units of steel)^ > a > > * (units of steel)^(1-a)=units of steel, yielding the tautology required > by > > the "=" sign. > > > > Gil > > > > > > > > > >>--- original message --- > >>From: "Jim Devine" <[email protected]> > >>Subject: [Pen-l] math question > >>Date: 13th August 2012 > >>Time: 3:51:28 pm > >> > >> > >>suppose we have a function Q = K^a*L*^(1-a). Is it possible for K and > >>L to be measured in different units? different units from Q? (if, for > >>example, K is measured in "leets" and L is measured in hours, what are > >>the units of Q?) > >> > >>-- > >>Jim Devine / If you're going to support the lesser of two evils, you > >>should at least know the nature of that evil. > >>_______________________________________________ > >>pen-l mailing list > >>[email protected] > >>https://lists.csuchico.edu/mailman/listinfo/pen-l > >> > >>The University of Glasgow, charity number SC004401 > >>_______________________________________________ > >>pen-l mailing list > >>[email protected] > >>https://lists.csuchico.edu/mailman/listinfo/pen-l > > > > _______________________________________________ > > pen-l mailing list > > [email protected] > > https://lists.csuchico.edu/mailman/listinfo/pen-l > > > > -- > Jim Devine / If you're going to support the lesser of two evils, you > should at least know the nature of that evil. > _______________________________________________ > pen-l mailing list > [email protected] > https://lists.csuchico.edu/mailman/listinfo/pen-l > -- Cheers, Tom Walker (Sandwichman)
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