>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?)
Sure. The function maps values from the K and L dimensions, measured in their respective units whatever they happen to be, into values in the Q dimension, measured in its units, whatever they happen to be. Let's say Q is measured in tons of steel. Divide both sides of the function by L (for example), and the dependent variable is then measured in tons of steel per unit of labor input. The dimensions have to be mutually consistent across the variables in an equation only if the equation is expressing a relationship within a given dimension, e.g. Q = (Q/L)*L. To take another example, if I say that global mean temperature is a function of tons of fossil fuel consumption and acres of forest, nothing compels me to understand global mean temperature in some composite of fuel tons and forest acres. Fwiw, Gil >-- >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 _______________________________________________ pen-l mailing list [email protected] https://lists.csuchico.edu/mailman/listinfo/pen-l
