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.

中文翻译：

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稀有品的市场价值：公允价值理论和来自稀有棒球卡的证据

我们从理论上和实证上研究了稀有品的市场价值。先前的研究发现稀有品的市场价值遵循幂律，但这一发现缺乏理论基础。我们为这一发现提供了微观基础，证明观察到的幂律出现在竞争市场中，在该市场中，代理人具有与排名相关的效用偏好。该模型带来了两个新的理论见解：（i）一个项目在一组相近替代品中的排名和已知存在的该项目的数量都是稀有性的自然衡量标准，但预计排名会表现更好；(ii) 对数排名对数价格回归的估计斜率和截距之间存在系统关系。当我们使用 4000 多个稀有棒球卡拍卖记录的数据测试模型时，我们发现仅使用对数排名和评级公司的回归解释了对数价格变化的 60%。