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Feasible Sets and the Transformation of Values

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  • Jiyuan Lyu

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.

Suggested Citation

  • Jiyuan Lyu, 2026. "Feasible Sets and the Transformation of Values," Papers 2603.09450, arXiv.org, revised Mar 2026.
    • Handle: RePEc:arx:papers:2603.09450
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    References listed on IDEAS

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    1. Isabella M Weber, 2019. "On the necessity of money in an exchange-constituted economy: the cases of Smith and Marx," Cambridge Journal of Economics, Cambridge Political Economy Society, vol. 43(6), pages 1459-1483.
    2. Yoshihara, Naoki, 2010. "Class and exploitation in general convex cone economies," Journal of Economic Behavior & Organization, Elsevier, vol. 75(2), pages 281-296, August.
    3. Bowles, Samuel & Gintis, Herbert, 1977. "The Marxian Theory of Value and Heterogeneous Labour: A Critique and Reformulation," Cambridge Journal of Economics, Cambridge Political Economy Society, vol. 1(2), pages 173-192, June.
    4. Flaschel, Peter, 1983. "Actual Labor Values in a General Model of Production," Econometrica, Econometric Society, vol. 51(2), pages 435-454, March.
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