The Arrow-Debreu Model

David Ellerman ()
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David Ellerman: University of Ljubljana

Chapter Chapter 4 in Putting Jurisprudence Back Into Economics, 2021, pp 77-88 from Springer

Abstract: Abstract The Arrow-Debreu model of competitive general equilibrium and more recent variants are the highpoints of neoclassical microeconomic theory. They are usually criticized as being unrealistic but the analysis in this chapter is not based on that common criticism. Precisely because the Arrow-Debreu model is so idealized, it is easy to pinpoint the conceptual error in the assumption that production sets are “owned” by given legal parties (assumed to be corporations). In an idealized competitive market, any proposed equilibrium with positive pure profits in any productive opportunity would be immediately undercut by arbitrageurs offering slightly higher prices to input sellers and slightly lower prices to output buyers—so such a competitive equilibrium with positive pure profits is, pace Arrow and Debreu, impossible. As was consistently and correctly argued for decades by Lionel McKenzie, a competitive equilibrium is only possible in the pinpoint special case with constant returns to scale in all productive opportunities and zero pure profits. This realization also undercuts crucial assumptions in microeconomic modelling, e.g., the assumption that it is somehow “given” that a resource-owner is a resource-supplier rather than a demander for a complementary set of inputs needed to undertake production. This indeterminacy is traced back to the assumption that all that is needed to undertake production (e.g., the human actions of the people carrying out the productive activity) is available as commodities in the marketplace. If everything is marketable, then firmhood is indeterminate and can only be ignored (in price theory) in the rather special case of universal constant returns to scale.

Date: 2021
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DOI: 10.1007/978-3-030-76096-0_4

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