The Futility of Utility: how market dynamics marginalize Adam Smith

TL;DR

This paper critically examines the foundational assumptions of utility in econometrics, arguing that market dynamics and equilibrium concepts are incompatible with utility-based models, and that real markets lack the stability predicted by classical theories.

Contribution

It reveals that utility as a potential function is incompatible with nonintegrable market dynamics and challenges the validity of equilibrium and utility maximization in explaining real market behavior.

Findings

Price cannot be expressed as a gradient of demand or supply in nonintegrable systems.

Utility maximization does not accurately describe market equilibrium.

Empirical evidence shows no stability in asset prices in free markets.

Abstract

Econometrics is based on the nonempiric notion of utility. Prices, dynamics, and market equilibria are supposed to be derived from utility. Utility is usually treated by economists as a price potential, other times utility rates are treated as Lagrangians. Assumptions of integrability of Lagrangians and dynamics are implicitly and uncritically made. In particular, economists assume that price is the gradient of utility in equilibrium, but I show that price as the gradient of utility is an integrability condition for the Hamiltonian dynamics of an optimization problem in econometric control theory. One consequence is that, in a nonintegrable dynamical system, price cannot be expressed as a function of demand or supply variables. Another consequence is that utility maximization does not describe equiulibrium. I point out that the maximization of Gibbs entropy would describe equilibrium, if equilibrium could be achieved, but equilibrium does not describe real markets. To emphasize the inconsistency of the economists' notion of 'equilibrium', I discuss both deterministic and stochastic dynamics of excess demand and observe that Adam Smith's stabilizing hand is not to be found either in deterministic or stochastic dynamical models of markets, nor in the observed motions of asset prices. Evidence for stability of prices of assets in free markets simply has not been found.