Duncan Foley, D. Smith

Paper #: 02-04-016

Careful examination of the axioms, and interpretation conventions, of utility theory and thermodynamics reveals that the two domains are more similar mathematically than their divergent approaches to problem solving would suggest. Their differences inhere primarily in the economic assignment of importance to initial endowments, versus the physical choice to emphasize reversible transformations. Using an analysis based on reversible transformations in economics, it is shown that utility theory can be represented as a theory of additive price potentials, and nondecrease of an additive entropy in closed systems. The standard money-metric utility is identified as a Gibbs potential for demands, and a new “contour money-metric utility” is introduced as the conjugate Helmholtz potential for prices. Examples show how the central problem-solving tools of thermodynamics apply in detail to conventional utility models, with emphasis on the concepts of reversible transformation, the equation of state, and engines.