Building Comparison Spaces: Harold Hotelling and Mathematics for Economics

Harold Hotelling's (1895–1973) articles in mathematical economics from the 1930s are classics. Some are keystones of entire sub-disciplines of economic theory such as location economics [Hotelling (1929). Stability in competition. The Economic Journal, 39(153), 41–57] and natural resource economics [Hotelling (1931). Review of Review of mathematical introduction to economics, by Griffith C. Evans. The American Mathematical Monthly, 38(2), 101–103. https://doi.org/10.2307/2301858]; others are associated with significant theoretical results [Hotelling (1932). Edgeworth's Taxation Paradox and the Nature of Demand and Supply functions. Journal of Political Economy, 40(5), 577–616; (1938). The general welfare in relation to Problems of Taxation and of Railway and Utility rates. Econometrica, 6(3), 242–269]. Yet, Hotelling's place in the rising of mathematical economics is mostly a black hole in the history of economic thought. The present paper aims to provide a better understanding of Hotelling's part in the history of mathematical economics. Using published as well as archival materials, it traces Hotelling's itinerary in mathematical economics, observes Hotelling using mathematics and scrutinizes Hotelling's methodological writings to capture the meaning of his models and concepts, in particular his concept of utility as a monetary surplus.