Feasible Sets and the Transformation of Values

TL;DR

This paper redefines the transformation of values problem by characterizing the feasible allocation space under physical constraints, demonstrating that classical macroeconomic equalities can coexist with physical minimum conditions.

Contribution

It introduces a new perspective on value transformation by modeling the feasible set of labor reduction vectors within physical constraints using an input-output framework.

Findings

Feasible sets of labor reduction vectors are bounded under physical surplus conditions.

Classical macroeconomic equalities hold within the feasible set for a range of profit rates.

Law of value and price systems can be consistent without violating physical reproduction constraints.

Abstract

This paper proposes a change in perspective on the ``transformation of values'' problem: from ``searching for a single constant solution'' to ``characterizing the allocation space under objective constraints imposed by the physical production network.'' Building an input--output model, we show mathematically that whenever the macroeconomy features a physical surplus, the set of skilled-to-simple labor reduction vectors that can sustain the subsistence floor of the entire labor force forms a bounded value-feasible set . Within this multidimensional region, the classical ``two great macro equalities'' necessarily hold simultaneously for a reasonable range of profit rates. Hence, without violating the physical minimum conditions for reproduction, the law of value and the nominal price system can be made logically consistent.