Inoua, S. & Smith, V.L. (2020).
Classical versus neoclassical equilibrium discovery processes in market supply and demand theory.
ESI Working Paper 20-19. https://digitalcommons.chapman.edu/esi_working_papers/314/
We identify a consistent thread of development in classical economic thought that is directed toward a supply and demand theory of market price formation or discovery. The theory is articulated by Adam Smith and further developed and refined by his French, English, and Italian followers. The foundation is in classical descriptions of demand, expressed in markets as maximum willingness to pay reservation values, for given discrete quantities of goods desired for consumption by buyers. Sellers, likewise, harbor minimum willingness to accept reservation values for these quantities based on their unit costs. Although goods clearly have hidden utility value, individual reservation values and costs were respected classical measures grounded in observation, with buyers trying to buy cheaper than their maximum willingness to pay, and sellers trying to sell dearer than their minimum willingness to accept. Mathematically, demand is a distribution function of individual values reordered from highest to lowest that Cournot acknowledged. Supply is a distribution function of individual unit costs. Consequently, buyers and sellers arrive in the market with aggregate distributions of values, v = d (Q) and costs, c = s (Q). However, price, p, in this narrative is yet to emerge. Based on these reservation value data, Adam Smith’s description of price formation in market “higgling” involves two coordinate features: (1) a dynamic price-change version of the “law of supply and demand,” and (2) the concept that we call “short side rationing.” At a quoted offer too low, purchases cannot exceed the supply offered, and buyer competition for the marginal unit offered raises the price. At a quoted price too high, sales cannot exceed the amount demanded and sellers cut the marginal unit’s price. Hence, the dynamic implication is that price increases (decreases) if there is excess demand (supply). The 49 integral of this signed derivative, constrained by short side rationing, defines the short side rationed surplus profit of the traders, which is what directly motivates realized market gains from trade. Neither the so-called Walrasian excess demand, nor Marshall’s excess of demand price over supply price, are fundamental drivers of price adjustment but are merely correlates of the more fundamental classical adjustment process. Convergence can be toward states that include short side rationing as in a constant (unit cost) industry or in an English auction of a unique item. Contrastingly, in the neoclassical marginal revolution, demand is derived from individual utility functions defined over a continuous commodity space, subject to given prices and income. Demand is conceptualized as a price-conditional, pre-market maximization task, intended to be part of the equation structure of general equilibrium. Similarly, for individual producer-sellers, supply is a pre-market price conditional cost minimizing exercise. This equation structure end-objective, however, fatally undermines the task of articulating a theory of price formation emanating from interacting buyers and sellers. Price is “given” rather than a variable to be determined. Hence, knowledge of price seemed either to require complete information or an “as if” adjustment process whereby prices were determined by the law of one price in a market. This impasse ended with the Sonenshein-Mantel-Debreu theorems proving that general equilibrium was silent in yielding results and in failing even to imply the law of demand. We claim that this vacuous result is a consequence of the axiom of price-taking behavior and the law of one price in a market, thus justifying a reexamination of the more 50 observationally grounded, consistent, and rigorous classical conceptions of individual behavior in markets.
Classical versus neoclassical equilibrium discovery processes in market supply and demand theory.
ESI Working Paper 20-19. https://digitalcommons.chapman.edu/esi_working_papers/314/
We identify a consistent thread of development in classical economic thought that is directed toward a supply and demand theory of market price formation or discovery. The theory is articulated by Adam Smith and further developed and refined by his French, English, and Italian followers. The foundation is in classical descriptions of demand, expressed in markets as maximum willingness to pay reservation values, for given discrete quantities of goods desired for consumption by buyers. Sellers, likewise, harbor minimum willingness to accept reservation values for these quantities based on their unit costs. Although goods clearly have hidden utility value, individual reservation values and costs were respected classical measures grounded in observation, with buyers trying to buy cheaper than their maximum willingness to pay, and sellers trying to sell dearer than their minimum willingness to accept. Mathematically, demand is a distribution function of individual values reordered from highest to lowest that Cournot acknowledged. Supply is a distribution function of individual unit costs. Consequently, buyers and sellers arrive in the market with aggregate distributions of values, v = d (Q) and costs, c = s (Q). However, price, p, in this narrative is yet to emerge. Based on these reservation value data, Adam Smith’s description of price formation in market “higgling” involves two coordinate features: (1) a dynamic price-change version of the “law of supply and demand,” and (2) the concept that we call “short side rationing.” At a quoted offer too low, purchases cannot exceed the supply offered, and buyer competition for the marginal unit offered raises the price. At a quoted price too high, sales cannot exceed the amount demanded and sellers cut the marginal unit’s price. Hence, the dynamic implication is that price increases (decreases) if there is excess demand (supply). The 49 integral of this signed derivative, constrained by short side rationing, defines the short side rationed surplus profit of the traders, which is what directly motivates realized market gains from trade. Neither the so-called Walrasian excess demand, nor Marshall’s excess of demand price over supply price, are fundamental drivers of price adjustment but are merely correlates of the more fundamental classical adjustment process. Convergence can be toward states that include short side rationing as in a constant (unit cost) industry or in an English auction of a unique item. Contrastingly, in the neoclassical marginal revolution, demand is derived from individual utility functions defined over a continuous commodity space, subject to given prices and income. Demand is conceptualized as a price-conditional, pre-market maximization task, intended to be part of the equation structure of general equilibrium. Similarly, for individual producer-sellers, supply is a pre-market price conditional cost minimizing exercise. This equation structure end-objective, however, fatally undermines the task of articulating a theory of price formation emanating from interacting buyers and sellers. Price is “given” rather than a variable to be determined. Hence, knowledge of price seemed either to require complete information or an “as if” adjustment process whereby prices were determined by the law of one price in a market. This impasse ended with the Sonenshein-Mantel-Debreu theorems proving that general equilibrium was silent in yielding results and in failing even to imply the law of demand. We claim that this vacuous result is a consequence of the axiom of price-taking behavior and the law of one price in a market, thus justifying a reexamination of the more 50 observationally grounded, consistent, and rigorous classical conceptions of individual behavior in markets.
