Unified Micro/Macro-Economic Theory Linking Productivity to Risk and Completing Input/Output Substitution

Abstract

In his pivotal contributions during the marginal revolution, Leon Walras along with W.S. Jevons assigned subjective utility directly to commodities (goods and services) as, in effect, a simplifying assumption — an assumption destined to become the keystone of neoclassical economics. But this “keystone” assumption undermined consumption-duration as an important — in fact, essential — variable in economic behavior, by excluding it from the utility (satisfaction) function to avoid double-counting. In the present contribution we extend orthodox neoclassical mathematical economics by accounting for generalized consumption-duration while retaining the inviolable commodity-utility postulate — where the new constraint unites Gossenian and neoclassical mathematical economics after a 135 year separation. This step, in turn, permits a complete and explicit formulation of the basic durations (work, consumption, and leisure) within the intratemporal (e.g., single-day) interval. The resulting intratemporal formulation is then extended over the multi-day interval to the intertemporal horizon for a postulated periodic-equilibrium based on nested-characteristic-times — where single-day economic function is unaffected by multi-day intertemporal-utility discounting, which in turn is near 100% complete before the entire economic system significantly changes. Within the new general mathematical theory it is shown that neither orthodox neoclassical theory nor orthodox Gossenian theory can correctly model the fixed commodity-amount special case — relevant, for example, to the monthly “food-stamp” allocation (now assisting ~15% of the US population.) As an application, an intertemporal relationship between labor/capital marginal productivities and intertemporal-utility discounting is developed. Two additional applications conclude the paper: (1) Walras’ input/output substitution relations are completed using the present intratemporal system; and (2) forward substitution relations are formulated using the newly-derived intertemporal system. As part of (2), the natural interest rate is shown equal to the intertemporal discount rate for the economic system in equilibrium. …As a caveat to the theorist/analyst, retention of the neoclassical commodity-utility (keystone) assumption — instead of the exclusive identification of instant-utility (feeling-state) with human activity, real-time and expected — will frequently require exogenous consumption-duration curves for determinate solutions.

Keywords: Utility Theory, Consumption Theory, Microeconomics, Macroeconomics, Equilibrium, Marginal Productivity, Gossen Theory, Leisure, History

JEL Classification: B13, B21, D11, D57, D91, E13, E43, N01