Size and The City: Productivity, Match Quality and Wage Inequality

This paper elucidates the impact of city growth on wage and wage inequality using a search-theoretical approach. Firms differ in capital intensity and land intensity of the jobs created. When a worker meets a job via a matching technology, a match-specific productivity level is realized and they sign a job contract when they agree with the bargaining wage. A rise in population density leads to rental increment. As a consequence, a higher expected flow profit is required for the creation of a good job. Rent-sharing ensures an increase of the average wage in the good-job sector. This, in turn, increases the reservation wage of workers in the equilibrium. Although the rental increment does not affect the setup costs in the bad-job sector, higher realized productivity level is required to cover higher reservation wage. Since only job contacts with realized productivity levels exceeding reservation productivity threshold are observed, such increase in the threshold raises also the average wage in the bad-job sector. Hence, the average productivity, the match quality and wage go up in each sector unambiguously, giving rise to urban wage premium. In addition, this paper predicts that urbanization widens residual wage inequality of a city. Existing empirical evidence is presented to support the implications of this model.