This paper studies how search externalities and wage bargaining distort vacancy creation and the allocation of workers to jobs in markets with two-sided heterogeneity. To do so, I propose a model of a frictional labor market where heterogeneous workers decide which job to look for and firms decide which technology to adopt. At equilibrium, there is perfect segmentation across sectors, which is determined by a unique threshold of workers' productivity. This threshold is inefficient because of participation and composition externalities. The Pigouvian tax scheme that decentralizes optimal sorting shows that these externalities have opposite signs. Furthermore, their relative strength depends on the distribution of workers' skills, so that when there are many (few) skilled workers, too many (few) high-technology jobs are created.

Contemporaries and economic historians have noted several features of medieval and early modern European monetary systems that are hard to analyze using models of centralized exchange. For example, contemporaries complained of recurrent shortages of small change and argued that an abundance/dearth of money had real effects on exchange, especially for the poor. To confront these facts, we build a random-matching monetary model with two indivisible coins with different intrinsic values. The model shows that small change shortages can exist, in the sense that adding small coins to an economy with only large coins is welfare-improving. This effect is amplified by increases in trading opportunities. Further, changes in the quantity of monetary metals affect the real economy and the amount of exchange as well as the optimal denomination size. Finally, the model shows that replacing full-bodied small coins with tokens is not necessarily welfare-improving.

We study comparative statics results for the steady-state monetary equilibria of a simple random matching model of money with endogenous prices and no extrinsic uncertainty. Some of the results appear counterintuitive (both when take-it-or-leave-it offer or when Nash–Rubinstein bargaining is used in the model). Consistency of the equilibrium expectations causes the partial equilibrium intuitions to be reversed. We then proceed to apply the new insights to the analysis of sunspot equilibria in these type of models of bilateral trade with money.