Bilateral Search with Horizontal Heterogeneity

We study a matching model with heterogenous agents, nontransferable utility and search frictions. Agents differ along a continuous horizontal dimension (e.g. taste) and a discrete vertical dimension, e.g. income. All individuals prefer the highest type along the vertical trait, but have different preferences regarding the horizontal trait. We characterize the equilibrium and study how matching occurs depending on the frictions in the market if income is exogenous. If the level of search frictions is low, assortative mating along both dimensions occurs. For greater levels of search frictions, equilibria with and without income segregation are possible. Finally, we study the impact of a redistributive tax on social welfare if agents decide on their effort levels before they enter the matching market.