The Economics of Hilbert's Hotel: An Expository Note

Martin Hellwig

No 2023_05, Discussion Paper Series of the Max Planck Institute for Research on Collective Goods from Max Planck Institute for Research on Collective Goods

Abstract: This expository note uses Hilbert's "infinite hotel", a hotel where one can always find place for another guest even if the hotel is already full, to illustrate the failure of the First Welfare Theorem in "large-square" economies that have infinitely many participants as well as infinitely many goods. Hilbert's hotel with infinitely many guests has a similar mathematical structure as the overlapping-generations model of Allais (1947) and Samuelson (1958). The phenomenon of "dynamic inefficiency" in such models represents a failure of the First Welfare Theorem in "large-square" economies, rather than frictions from the sequential nature of markets.

Keywords: HilbertÂ’s hotel; overlapping-generations models; dynamic inefficiency; First Welfare Theorem (search for similar items in EconPapers)
JEL-codes: D15 D61 E62 (search for similar items in EconPapers)
Date: 2023-05
New Economics Papers: this item is included in nep-dge, nep-hpe and nep-mfd
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