This paper extends a standard static structural labor supply framework by taking labor demand constraints into account. Contrary to previous papers the rationing risk is not only determined by exogenous demand side factors, but also depends on the individual's productivity. The resulting labor supply elasticities from the extended framework differ from the unconstrained model. This approach is shown to be particularly useful for evaluating policy reforms that affect labor supply incentives and have direct consequences for labor costs. We apply the model to analyze the employment effects of a federal minimum wage in Germany as well as the impact of employer- vs. employee-oriented wage subsidies under a statutory minimum.