This article presents a dynamic growth model with energy as an input in the production function. The available stock of energy resources is ordered by a quality parameter based on energy accounting: the "Energy Return on Energy Invested" (EROI). In our knowledge this is the first paper where EROI fits in a neoclassical growth model (with individual utility maximization and market equilibrium), establishing the economic use of "net energy analysis" on a firmer theoretical ground. All necessary concepts to link neoclassical economics and EROI are discussed before their use in the model, and a comparative static analysis of the steady states of a simplified version of the model is presented. (C) 2015 Elsevier Ltd. All rights reserved.