It's all a question of scale. Try simply Q/Q0 = (K/K0)^a (L/L0)^(1-a)
where the constant a is dimensionless, Q0 has dimensions of Q, K0 has dimensions of K, and L0 has dimensions of L. -- David Rosnick Economist Center for Economic and Policy Research On Aug 14, 2012, at 6:50 AM, Paul Cockshott wrote: > In either case, a theory which is dimensionally inconsistent is suspect. > However there is the problem that one can derive empirical observations that > are governed by some functional form and which do tell us something about > regularities which exist in the economy. One approach to this is to say that > if the functional form is a polynomial with constants p= a x^2 + b y+ cz^3 > say then we can assume that the constants a, b, c have dimensions such as to > cancel out the dimensions given by the polynomial terms. The constants of > nature are given explicit dimension in order for them to do this. > I am not quite sure how to handle this if the functional form we have is > exponential or logarithmic. > ________________________________________ > From: [email protected] [[email protected]] On > Behalf Of Tom Walker [[email protected]] > Sent: Monday, August 13, 2012 9:40 PM > To: Progressive Economics > Subject: Re: [Pen-l] math question > > As I said, that is one possible interpretation. The other possibility is that > the "more important" flaws you enumerated (with the notable exception of > "deliberate ignorance of class relations") are symptoms. I would suggest that > the unit fallacy is the pseudo-scientific "flip side" of "deliberate > ignorance of class relations." It has the dual function of diverting > attention from class relations while at the same time concealing that is its > intention. This dual function becomes clear if you trace its origins back to > its more overtly ideological precursors in the 18th and 19th century. > > On Mon, Aug 13, 2012 at 12:47 PM, Jim Devine > <[email protected]<mailto:[email protected]>> wrote: > me: >> "...while never examining the units used to measure its >> ingredients..." > > Tom Walker wrote: >> ... 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. > > I'd say instead that the willingness to use non-existent units is a > matter of sloppiness resulting from the insulation that many or even > most macroeconomists have from serious criticism. Of course, that > insulation is often created by economists themselves when they use > unnecessary mathematics in the first place. > > It's a definite flaw, but it seems less important than various other > macroeconomics sins, including (in no particular order of importance): > > - the very common failure to see the distinction between macro and > micro (preferring to reduce the former to the latter, even while > teaching students about the fallacy of composition); > > - the use of a timeless model (with no true uncertainty) having no > role for money (beyond being a means of exchange), so that Say's "law" > applies; > > - the use of an aggregate neoclassical production function; > > - ignorance of how the existence and persistence of unemployment feeds > back to transform micro-level results; > > - obsession with equilibrium as somehow describing a real-world state; > > - the assumption that the difference between idealized models and the > messy real world is unimportant; > > - deliberate ignorance of class relations; > > etc. > > -- > 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]<mailto:[email protected]> > https://lists.csuchico.edu/mailman/listinfo/pen-l > > > > -- > Cheers, > > Tom Walker (Sandwichman) > > 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
