The impact of the productivity dispersion across employers on the labor's income share

I study the distribution of income across the factors of production within the canonical on-the-job search framework. I show that, by weakening the competition between employers, a mean-preserving spread of the employers' productivity distribution decreases the share of the production output that the workers receive. This result is particularly intriguing in light of the rising productivity dispersion and the declining labor share in many countries.