This paper demonstrates how barrier methods can facilitate closed-form solutions for (simple) economic models with constraints. Barrier methods express constrained optimization problems as a sequence of unconstrained problems where the solution to the original problem arises as a limiting case. This paper shows that the limiting case boils down to solving a polynomial which can, for sufficiently simple models, be done in closed form. The method is widely applicable which is demonstrated with three examples. First, I develop a closed-form solution for a static portfolio choice model with fixed transaction costs. Second, I derive a closed-form solution for the Rothschild-Stiglitz-Wilson insurance problem with adverse selection. And third, I derive a closed-form solution for moral hazard problems, here a simple version of the classic Mirrlees problem.