Market Value of Rarity: A Theory of Fair Value and Evidence from Rare Baseball Cards

Abstract

We investigate the market value of rarity theoretically and empirically. Prior studies find that the market value of rarity follows a power law, but this finding lacks a theoretical foundation. We provide a micro-foundation for this finding, demonstrating that the observed power law emerges in a competitive market where agents have rank-dependent utility preferences. The model leads to two new theoretical insights: (i) the rank of an item within a set of close substitutes and the quantity of that item known to exist are both natural measures of rarity, but rank is predicted to perform better; (ii) there is a systematic relationship between the estimated slope and intercept from a regression of log price on log rank. When we test the model on data from over 4000 auction records of rare baseball cards, we find that a regression with only log rank and grading company explains 60% of the variation in log price.

Keywords: Rarity, Rank Dependent Utility, Baseball Cards, Power Laws, Zipf's Law

JEL Classification: D00, D91