Abstract
We present a simple mathematical formulation of an entropy theory of value, consistent with evolutionary economics. It is a non-equilibrium theory, logarithmic in form, which explains the roles of monopoly and oligopoly as well as scarcity in determining economic values. It is an objective theory, rooted in physical realities and economic institutions, similar to the information theory developed by Shannon (1948). We compare this theory to the subjective, utility theory of the Arrow–Debreu model, the foundation of general equilibrium economics.
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Notes
In an often-cited passage, Arrow concluded:
...the well-known Shannon measure which has been so useful in communications engineering is not in general appropriate for economic analysis because it gives no weight to the value of the information. If beforehand a large manufacturer regards it as equally likely whether the price of his product will go up or down, then learning which is true conveys no more information, in the Shannon sense, than observing the toss of a fair coin” (Arrow, 1973, p. 138).
But the Shannon measure actually does measure the weight of information. For example, N symbols with identical Shannon measure carry N times more information than a single symbol (Shannon, 1948). Similarly, the value of information about a future price is higher to a large manufacturer than to a small manufacturer, other things being equal; the large manufacturer has more at stake. Information, as an economic commodity, shares most of the important properties of physical commodities.
We can also understand the issue of weight from the perspective of physics. In physics, there are two types of quantity. The first type is called intensive quantity, such as temperature and pressure. The second type is called extensive quantity, such as volume and mass. You can double the mass of bricks if you put two bricks together. But you cannot double the temperature of bricks if you put two bricks together, for temperature is an intensive, not an extensive quantity. Entropy is an extensive quantity. It naturally carries weight.
References
Applebaum D (1996) Probability and information, an integrated approach. Cambridge University Press, Cambridge
Arrow KJ (1972) General economic equilibrium: purpose, analytic techniques, collective choice, Nobel Memorial Lecture, December 12. Harvard University, Cambridge, Massachusetts
Arrow KJ (1973) Information and economic behavior. Harvard University Press
Arrow K (1999) Information and the organization of industry. In: Chichilnisky G (ed) Markets, information, and uncertainty. Cambridge University Press, Cambridge
Arrow KJ, Debreu G (1954) Existence of an equilibrium for a competitive economy. Econometrica: Journal of the Econometric Society:265–290
Baran P, Sweezy P (1966) Monopoly capital. Monthly Review Press, New York
Bessen J, Maskin E (2009) Sequential innovation, patents, and imitation. RAND J Econ 40(4):611–635
Chen J (2005) The physical foundation of economics: an analytical thermodynamic theory. World Scientific, Hackensack, NJ
Chen J (2015) The unity of science and economics: a new foundation of economic theory. Springer
Colinvaux P (1978) Why big fierce animals are rare: an ecologist’s perspective. Princeton University, Princeton
Debreu G (1959) Theory of value; an axiomatic analysis of economic equilibrium. Wiley, New York
Debreu G (1983) Economic theory in the mathematical mode: Nobel Memorial Lecture. Economic Science 8:87–102
Debreu G (1991) The mathematization of economic theory. Am Econ Rev 81:1–7
Düppe T (2012) Gerard Debreu‘s secrecy: his life in order and silence. History of Political Economy 44(3):413–449
Galbraith JK (1958) The affluent society. Houghton Mifflin Harcourt
Galbraith, J. K. and Chen, J. (Forthcoming). Biophysical principles of value and production: bringing life to economics and economics to life, University of Chicago Press
Georgescu-Roegen N (1971) The entropy law and the economic process. Harvard University Press, Cambridge, Mass
Jevons W (1871) The theory of political economy. Macmillan and Co, London
Klug WS, Cummings MR (2003) Concepts of genetics (Ed. 7). Pearson Education, Inc.
Maxwell J (1871) Theory of heat. Green & Co., Longmans, London
Mehrling P (2005) Fischer black and the revolutionary idea of finance. Wiley
Michels, R. (1915). Political parties: a sociological study of the oligarchical tendencies of modern democracy.
Mill J (1871) Principle of political economy. Penguin books, London
Móczár J (2020) The Arrow-Debreu model of general equilibrium and Kornai’s critique in the light of neoclassical economics. Journal of Banking, Finance, and Sustainable Development 1(1):42–68
Pinker S (1997) How the mind works. W. W. Norton, New York
Prigogine, I. (1980). From being to becoming: time and complexity in the physical sciences.
Robbins L (1935) An essay on the nature and significance of economic science. MacMillan and Co, London
Scarf H (1960) Some examples of global instability of the competitive equilibrium. Int Econ Rev 1(3):157–172
Schrodinger E (1944) What is life? Cambridge University Press, Cambridge
Schumpeter J (1942) Capitalism, socialism and democracy. Harvard University Press, Cambridge
Shannon C (1948) A mathematical theory of communication. Bell Syst Tech J 27(379-423):623–656
Shiozawa Y (2016) The revival of classical theory of values, chapter 8 of Yokokawa and others (Eds.). The Rejuvenation of Political Economy, New York: Routledge, pp 151–172
Shubik M (1961) Theory of value: an axiomatic analysis of economic equilibrium, by Gerard Debreu. Canadian Journal of Economics and Political Science 27(1):133–133
Vilks, A. (2021) On an “Important Principle” of Arrow and Debreu. The B.E. Journal of Theoretical Economics, Vol. (Issue ), pp. 20210074. https://doi.org/10.1515/bejte-2021-0074
Walras L (1873) Elements of pure economics. Translated by William Jaffe, Homewood. Richard Irwin Inc, Illinois
Weintraub ER (2002) How economics became a mathematical science. Duke University Press
Acknowledgements
We thank the editors of REPE and five anonymous referees for comments. An Earlier draft of this paper was titled A Scarcity Theory of Value: With Reflections on the Arrow–Debreu Model. We thank Ali Khan, József Móczár, and Yoshinori Shiozawa for helpful comments.
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Chen, J., Galbraith, J.K. An entropy theory of value with reflections on the Arrow–Debreu model. Rev Evol Polit Econ 4, 221–247 (2023). https://doi.org/10.1007/s43253-023-00102-0
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DOI: https://doi.org/10.1007/s43253-023-00102-0