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.
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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