We study frictionless matching in large economies with and without market imperfections, providing sufficient conditions for monotone matching that are weaker than those previously known. Necessary conditions, which depend on a key analytical object we call the surplus function, are also offered. Changes in the surplus yield valuable information about the comparative statics of matching patterns across environments. We apply our framework to some examples adapted from the literature, accounting for and extending several comparative-static and welfare results. We also explore the dependence of the matching pattern on the type distribution.

Members of a rock and roll band are endowed with different amounts of creativity. They match, compose songs, and share credit. The presence of more creative members increases the probability of success, but those more creative members may also claim a larger share of the pie. In our theoretical model, the nature of matching as well as the covariation between the probability of success and the allocation of credit among individual members are a function of the completeness of contracting. The data show that rock bands tend to enter into incomplete contracts and positive assortative matching.

We model technological progress as an external effect of organizational design, focusing on how factories, based on labor division, could spawn the Industrial Revolution. Dividing labor, as Adam Smith argued, facilitates invention by observers of production processes. However, entrepreneurs cannot internalize this benefit and choose labor division to facilitate monitoring. Equilibrium with few entrepreneurs features low wage shares, and high specialization, but a limited market for innovations. Conversely, with many entrepreneurs, there is a large market for innovation but little specialization because of high wage shares. Technological progress therefore occurs with a moderate scarcity of entrepreneurs. Institutional improvements affect growth ambiguously.