How does wealth affect the extent to which the “right” workers are matched with the “right” jobs? Using the NLSY79 and O*NET, we document that wealth-poor workers are more mismatched with their jobs. We develop a model featuring worker and firm heterogeneity, search frictions, and incomplete markets. Workers and firms jointly face a trade-off between the speed and payoff of forming a match. A lack of wealth induces workers to trade off wages for finding a job faster due to precautionary motives, which in turn gives a wider range of firms the incentive to match. We refer to this phenomenon as “precautionary mismatch” and show that it leads to substantial within-type earnings and productivity gaps between the wealth-rich and the wealth-poor, especially among high-skilled workers. We estimate that total output would be 3% higher in the US if all employed workers were allocated to the right jobs. In a quantitative experiment, we find that wealth transfers from incumbent workers to young labor market entrants reduce within-type earnings and productivity inequality, improve sorting, and enhance labor productivity. Most of the productivity increase comes from reduced under-employment of high-skilled workers.