Intensive quantities in an economy and conjugate variables

Abstract

In an economy, the flows of goods, resources, and money are extensive (additive) variables, while the prices, interest, and exchange rates serve as intensive variables. Using the simplest economic planning problem as an example, we show that these intensive variables arise naturally as conjugate variables to balance constraints under the decomposition of the planning problem into the problem of the dynamical (intertemporal) equilibrium of an economy. It is also shown that linear homogeneity symmetry, which is a natural feature of an economy, generates, by Noether’s theorem, an equity capital equation.