An Integrability Condition, with Applications to Utility Theory and Thermodynamics

摘要: We establish a criterion alternative to the classical Frobenius condition for solvability of system nonlinear partial differential equations (or corresponding total equation) that arises in consumer choice theory. The condition, certain matrix be symmetric, translates theory into rather unmotivated requirement symmetry Slutsky or Antonelli matrix. In contrast, presented here is easily motivated from revealed preference considerations, and thus provides an economic justification condition. Such systems are significance not only theory, but also general equilibrium analysis welfare economics. addition they arise very different areas, such as physics thermodynamics. Wherever arise, their often critical step construction. As indicated by our applications section 3 (to theory) 4 thermodynamics), theorem may provide more plausible axioms theories, simplify task proving them.