Perfect matching and search in economic models
This thesis uses general matching techniques - both perfect matching and search - to study some problems in economies that are characterised by heterogeneity of their agents. Here, matching in its broadest sense is interpreted as a form of trade that is strictly limited between two partners: transactions are one-to-one, between one buyer and one seller exactly. The first part proposes a framework that integrates two well documented strands of the existing economic literature. It is a search model that generalises the frictionless perfect matching model to a context where trade does not occur instantaneously. A general methodology with proof is given which allows us to derive the unique equilibrium allocation of agents. Though the limit case without friction reproduces the perfect matching result, with friction results deviate substantially from conclusions in both the perfect matching literature and the search literature. The second part of the thesis concentrates entirely on frictionless matching models. First, a general class of preferences is identified that yields a unique allocation. Second, the matching model is studied when endogenous choice of characteristics is allowed and has an intuitive application to the labour market. It is shown that in the presence of job heterogeneity, too many resources are spent in order to achieve a higher ranked job. The results, including issues of turnover and distribution, are verified with some stylised facts in the empirical literature. Finally, a model that mimics a matching equilibrium and that allows for endogenous choice of characteristics is applied to the context of education in the labour market. It is shown that multiple equilibria can exist in the presence of spillovers in production.