This paper provides evidence from a natural experiment on the importance of workers' tacit knowledge about firms' intangible assets for competition in product and labor markets. Evidence is presented on product and labor market imperfections across manufacturing and services firms in the Netherlands. Price-cost markups and wage markups are both shown to be positively related to intangible intensity at the firm level. A model is developed of the processes of intangible investment and wage bargaining of heterogeneous firms, providing a mechanism that relates workers' tacit knowledge to firm-level product and labor market imperfections. The model also incorporates a role for non-compete agreements (NCAs) limiting worker mobility. Our main empirical contribution comes from using linked employer-employee panel data with information on NCAs and changes in enforceability of these agreements. Using an event-study framework, we demonstrate that the removal of NCAs leads to higher wages and worker mobility, especially for workers in intangible-intensive firms. We find that NCAs affect workers across the skill distribution. The causal findings from changes in the legality of NCAs correspond with the mechanism described in the model.