In dynamic economic models characterized by limited commitment, participation constraints typically bind, resulting in equilibrium interest rates that may fall below growth rates. This undermines the validity of the Second Welfare Theorem under linear pricing conditions. Our research demonstrates that the First and Second Welfare Theorems can be upheld when introducing superlinear price functionals. The study unveils a novel application of nonlinear pricing in financially constrained settings and reveals an intriguing link with the ε-Nash equilibrium concept in the context of repeated games.