We consider a market where each firm is created by the combination of two complementary assets that are heterogeneous in their productivity. After assets match endogenously, their owners choose between two ownership structures: centralized organization (integration) and arm's length organization (nonintegration). Our main focus is on the interplay between productivity heterogeneity and firm boundary decisions. When firms choose between distinct ownership structures, the standard single-crossing condition that guarantees positive assortative matching may fail to hold. We provide a novel condition—the congruent marginal contributions property—which guarantees monotone matching with respect to asset productivity. Furthermore, we provide conditions under which integration at the bottom of the productivity ladder is the market equilibrium; an organizational pattern that has been largely unexplored by the theoretical and empirical literature. We investigate the effect of model primitives on the equilibrium distribution of output. Moreover, our model offers interesting testable implications regarding firm boundary decisions.

中文翻译：

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双边生产率异质性、企业边界和选型匹配

我们考虑这样一个市场，其中每个公司都是由两种生产力异质的互补资产组合创建的。资产内生匹配后，其所有者在两种所有权结构之间进行选择：集中组织（整合）和独立组织（非整合）。我们的主要关注点是生产力异质性和企业边界决策之间的相互作用。当企业在不同的所有权结构之间进行选择时，保证正选型匹配的标准单交叉条件可能不成立。我们提供了一个新颖的条件——一致的边际贡献属性——它保证了资产生产率的单调匹配。此外，我们还提供了在生产力阶梯底部的一体化是市场均衡的条件下；理论和实证文献很大程度上尚未探索过一种组织模式。我们研究模型基元对输出均衡分布的影响。此外，我们的模型提供了关于公司边界决策的有趣的可测试的含义。