The relevance of Adam Smith for understanding human morality and sociality is generally accepted; witness the growing interest that his work is stimulating among scholars of various academic backgrounds (philosophers, political theorists, sociologists, economists). But, paradoxically, Adam Smith’s theory of economic value enjoys a less prominent stature today among economists, who, while they view him as the ‘father of modern economics’, considered him more as having had the right intuitions about a market economy than as having developed the right concepts and the technical tools for studying it. Yet the neoclassical tradition failed to provide a satisfactory theory of price formation owing to the dominant axiom of price taking behavior; for if everyone takes prices as given, how do these prices emerge in the first place? Who is giving the prices? One early escape from this crucial price-discovery problem consisted of assuming that all traders should have complete information of supply and demand and the consequent equilibrium prices (Jevons,  1888) ; the other, that formed the basis of general equilibrium theory, imagines a fictional auctioneer who finds the equilibrium prices by trial-and-error adjustments or tatonnement (Walras,  1954). Adam Smith’s theory of the market mechanism (Ch. 7, Book 1, Wealth of Nations, 1776), as we shall argue in this paper, offers the right conceptual framework for understanding competitive price discovery, for which we offer a mathematical formulation. Mathematically, the driving force behind competitive price dynamics is not excess demand per se, but its integral; we make this concept, explored at the beginning in experimental economics (Smith, 1962), part of our formalization of classical competitive price dynamics. Finally, we explain key propositions of Smith’s theory of value in the light of this mathematical formulation.
Inoua, S.M. & Smith, V.L. (2020). Adam Smith’s theory of value: A mathematical statement of his market price discovery process. ESI Working Paper 20-10. https://digitalcommons.chapman.edu/esi_working_papers/304/