>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
