Abstract This paper builds upon Caplin and Leahy (2014), which introduced a new mathematical apparatus for understanding allocation markets with nontransferable utility, as such covering the housing market and other markets for large indivisible goods. In the current paper we complete the study of comparative statics initiated therein. We introduce homotopy methods to characterize how equilibrium changes in response to arbitrary parameter changes. Generically, we show that there can be five and only five qualitatively distinct forms of market transition: Graft; Prune and Plant; Prune and Graft; Cycle and Reverse; and Shift and Replant. Our path-following methods identify new algorithms for computing market equilibria.

中文翻译：

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不可分割商品市场的比较静态

摘要 本文建立在 Caplin 和 Leahy (2014) 的基础上，他们引入了一种新的数学工具来理解具有不可转移效用的分配市场，例如涵盖住房市场和其他大型不可分割商品市场。在当前的论文中，我们完成了对比较静力学的研究。我们引入了同伦方法来表征平衡如何响应任意参数变化而变化。一般而言，我们表明可以有五种且只有五种在质量上截然不同的市场转型形式：嫁接；修剪和种植；修剪和嫁接；循环和反向；和转移和再植。我们的路径跟踪方法确定了计算市场均衡的新算法。