We study a two‐sector economy with investments in human and physical capital and imperfect labor markets. Investments are irreversible and noncontractible, due to random matching between firms and workers. Income is allocated according to the Nash bargaining mechanism. At equilibrium, given the distribution of the agents across sectors, there is underinvestment in both human and physical capital, due to the holdup problem generated by bargaining and noncontractibility. Self‐selection of the agents into the two sectors typically induces too many workers to invest in high skills. Compared to the constrained efficient allocation, at each equilibrium, there are too many people investing too little effort in the high‐skill sector. We also study the effects of several tax policies on total expected surplus.