Labor Market Power with Worker and Firm Heterogeneity

How do firms set wages? How should governments set income taxes? If labor supply is inelastic to wages, firms can pay workers less than their marginal products, and governments can increase taxes without eroding the base. However, the structure of labor supply elasticities in the economy is complex. Recent empirics document variation across workers, firms, and margins (which firm to work at versus how many hours to work). To account for this rich structure of labor supply elasticities we extend the neoclassical model to include a discrete choice over which firm to work at, production complementarities and strategic interaction between heterogeneous, granular firms. In terms of wage setting, we find that novel effects of worker heterogeneity account for 78 percent of the variable component of labor supply elasticities and markdowns, and 89 percent of differences between large and small firms. In terms of policy, higher progressivity makes labor supply less elastic, eroding the tax base by widening markdowns and worsening sorting. These channels (i) produce large declines in earnings following increases in marginal tax rates, consistent with empirical studies, and (ii) reduce optimal tax progressivity by one-third and associated welfare gains by two-thirds.