Can Markets Compute Equilibria?

Hunter K. Monroe

No 09/24, IMF Working Papers from International Monetary Fund

Abstract: Recent turmoil in financial and commodities markets has renewed questions regarding how well markets discover equilibrium prices, particularly when those markets are highly complex. A relatively new critique questions whether markets can realistically find equilibrium prices if computers cannot. For instance, in a simple exchange economy with Leontief preferences, the time required to compute equilibrium prices using the fastest known techniques is an exponential function of the number of goods. Furthermore, no efficient technique for this problem exists if a famous mathematical conjecture is correct. The conjecture states loosely that there are some problems for which finding an answer (i.e., an equilibrium price vector) is hard even though it is easy to check an answer (i.e., that a given price vector is an equilibrium). This paper provides a brief overview of computational complexity accessible to economists, and points out that the existence of computational problems with no best solution algorithm is relevant to this conjecture.

Keywords: Capital markets; Commodity markets; Prices; Economic models (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-cba and nep-cmp
Date: 2009-02-10
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