Abstract

How are workers matched to firms when their skills are multidimensional, firms a) differ in how they value each skill dimension in their production technology as well as in their productivity; b) aggregate their workers’ skills to produce; c) and optimally choose their size? When workers’ skills cannot be unpacked and sold separately on skill-specific markets, the implicit price of each skill can vary across firms and firms’ size is increasing in productivity. The equilibrium wage function is shown to be log-additive in worker quality and a firm-specific effect that reflects the firm’s aggregate skill-mix and equilibrium matching. When individuals choose the amount of skills supplied to their firms or when skills can be unpacked and purchased on markets (at a cost, thanks to new technologies or increased outsourcing), firms reinforce their hires of skills in which they have a comparative advantage yielding a more polarized matching equilibrium and a flattened wage schedule. Generalist workers – endowed with a balanced set of skills – are shown to benefit whereas specialists are negatively affected by markets opening. We extensively discuss how skilled-biased technical change affects the equilibrium outcomes. We also examine the empirical content of our theory.