The economics of Hilbert's hotel: An expository note

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.