How Energy and Work Drive Material Prosperity
Neoclassical equilibrium in a system that produces a single output Y from the factors K, L, X is characterized by the maximum of proﬁt (Y Ϫ C) at ﬁxed total factor cost C(K, L, X). The cost C is given by C(K, L, X ) ϭ PK · K ϩ PL · L ϩ PX · X (A.1) where PK, PL, PX are the unit prices of capital K, labor L and a third factor X (which need not be speciﬁed, although it can be equated either to commercial energy, E, or to useful work U). Neoclassical economics assumes that all combinations of factors that are consistent with ﬁxed total cost C are accessible without any further constraints, that is, they are mutually substitutable. This implies that the proﬁt maximum lies somewhere within the interior of accessible K, L, X space (that is, not on a boundary). According to the Lagrange multiplication rule, the necessary condition for a local extremum in K, L, X space is that, in equilibrium, for some real number l, the gradient of Y Ϫ lC must vanish: = 1 Y 2 lC 2 5 =Y 2 l=C 5 c 'Y 'Y 'Y , , d 2 l # 3 PK,PL,PX 4 5 1 0,0,0 2 'K 'L 'X (A.2) It follows from the equality of the individual vector components that the neoclassical condition for economic equilibrium is given by 'Y 5 l # PK 'K 'Y 5 l # PL 'L 'Y 5 l # PX 'X...
You are not authenticated to view the full text of this chapter or article.
Elgaronline requires a subscription or purchase to access the full text of books or journals. Please login through your library system or with your personal username and password on the homepage.
Non-subscribers can freely search the site, view abstracts/ extracts and download selected front matter and introductory chapters for personal use.
Your library may not have purchased all subject areas. If you are authenticated and think you should have access to this title, please contact your librarian.