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The unique informational efficiency of the competitive mechanism in economies with production

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Abstract

The purpose of this paper is to investigate the informational requirements of resource allocation processes for convex production economies. First, we establish a lower bound of the message space of an informationally decentralized mechanism that realizes Pareto efficient allocations over the class of classical production economies. Then, it is shown that this lower bound is exactly the size of the message space of the competitive (Walrasian) mechanism, and thus the competitive mechanism is informationally efficient for general neoclassical production economies in the sense that it uses the smallest message space among the class of resource allocation processes that are informationally decentralized and realize Pareto optimal allocations. Further, it is shown that the competitive mechanism is the unique informationally efficient decentralized mechanism that realizes Pareto efficient and individually rational allocations. The results obtained in the paper may shed light on the socialist controversy between Mises-Hayek and Lange-Lerner.

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Notes

  1. A mechanism is called smooth if the stationary message correspondence is either locally threaded or if the inverse of the stationary message correspondence has a Lipschizian-continuous selection in the subset. Thus, the term “smoothness” used here is not referred as the usual differentiability of a function, but either as local threadedness or the Lipschizian continuity. This terminology was used by Hurwicz (1999). We will give the definition of the local threadedness below.

  2. As usual, vector inequalities, ≧, ≥, and >, are defined as follows: Let \(a,b \in \mathbb{R}^{m} \). Then a ≧ b means a s ≧ b s for all s = 1, ..., m; a ≥ b means a ≧ b but a ≠ b; a > b means a s > b s for all s=1, ..., m.

  3. R i is convex if for bundles a, b, c with 0 < ≦ 1 and c = a + (1−) b, the relation aP i b implies cP i b. Note that the term “convex” is defined as in Debreu (1959), not as in some recent textbooks.

  4. Notice that, the definition of the privacy-preserving mechanism does not exclude the possibility of the presence of externalities since a message reported by one agent may also include, say, the level of production by other producers.

  5. A stronger condition that can guarantee interior outcomes is that a mechanism is individually rational.

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Acknowledgments

I wish to thank an anonymous referee and the participants at the 2001 Decentralization Conference for valuable comments. This is a reversion of an earlier paper entitled, “The Competitive Mechanism is the Unique Informationally Efficient Process for Economies with Production”. Financial support from the Texas Advanced Research Program as well as from the Bush Fellow Summer Research Program, the Private Enterprise Research Center, and the Lewis Faculty Fellowship at Texas A&M University is gratefully acknowledged.

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  1. Department of Economics, Texas A&M University, 4228 TAMU, College Station, TX, 77843-4228, USA

    Guoqiang Tian

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  1. Guoqiang Tian
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Correspondence to Guoqiang Tian.

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I wish to thank an anonymous referee and the participants at the 2001 Decentralization Conference for valuable comments. This is a reversion of an earlier paper entitled, “The Competitive Mechanism is the Unique Informationally Efficient Process for Economies with Production”. Financial support from the Texas Advanced Research Program as well as from the Bush Fellow Summer Research Program, the Private Enterprise Research Center, and the Lewis Faculty Fellowship at Texas A&M University is gratefully acknowledged.

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Tian, G. The unique informational efficiency of the competitive mechanism in economies with production. Soc Choice Welfare 26, 155–182 (2006). https://doi.org/10.1007/s00355-005-0056-0

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