Reconciliation of Economic Theory Leading to Revised Input/Output Substitution Equations

Completion of significant advances in any discipline can take extended time, and Leon Walras’s theory of the competitive economy in equilibrium is an example. In his pivotal contributions during the Marginal Revolution of the 1870s, Walras along with W. S. Jevons assigned subjective utility directly to market goods as, in effect, a simplifying assumption—an assumption destined to become the keystone of the discipline. But this “keystone” assumption caused a disregard of duration-for-consumption in mathematical economics because of the possibility of consumption-utility double-counting. Among others, Gary Becker has endeavored to account for duration on the consumption side as part of his “…systematic incorporation of non-working time.” However, the double-counting concern imparts uncertainty regarding aspects of his theoretical system. In the present work, we complete Becker’s vision by extending traditional neoclassical theory to account for the essential durations (production, consumption, and leisure) within the intratemporal (single-day) interval. The intratemporal system is then extended to the full, discounted intertemporal duration for assumed periodic-equilibrium. A basic concept in this regard is a new constraint on the utility function which determines the quantity of a market-good consumed by its corresponding duration-for-consumption, a constraint that preserves the neoclassical keystone while completing time as an analytic variable in economic theory. Using the resulting neoclassical intertemporal system, a relationship between intertemporal discounting and the marginal productivities of labor and capital, previously derived (for expected investment-risk) within the Gossenian School, is again derived. Two additional applications conclude the paper: (1) Walras’s input/output substitution relations are completed using the present neoclassical intratemporal system; and (2) The intratemporal system is extended to the full intertemporal interval accounting for interest and discounting, and again assuming periodic equilibrium. Because the fully temporal neoclassical system provided herein is functionally similar to the Gossenian system, the neoclassical and Gossenian theories of economic behavior, divided or separated since the 1870s, are brought into closer accord.