In recent years, the notion of Economic Model Predictive Control (EMPC) has gained significant interest. Despite a marked improvement in economic performance, it has been shown that this performance will degrade substantially if implemented with a horizon that is not sufficiently large. In the current effort, it is shown that if applied to a particular reaction process, EMPC performance will abruptly collapse at a critical horizon size. To alleviate this issue, we develop an Infinite Horizon EMPC (IH-EMPC) formulation. While this IH-EMPC problem is computationally intractable, it does lead to an approximation of the optimal policy. The resulting Approximate IH-EMPC (AIH-EMPC) is identical to the original finite horizon EMPC, but includes a final cost term that represents the objective function from the finite horizon to infinity. With two example systems, a chemical reactor and a power system with energy storage, it is shown that the AIH-EMPC policy is virtually insensitive to its computational horizon size. (C) 2018 Elsevier Ltd. All rights reserved.