Different modeling and solution approaches to electricity tariff optimization for demand response management have received considerable attention recently. Yet, there are hardly any results available on the computational complexity of these problems. The clarification of the complexity status is crucial to understand for which models an efficient, polynomial algorithm, or a closed-form analytical solution can be expected, and when the application of heuristics delivering suboptimal solutions or time consuming search procedures is justifiable. In this letter, we define the Simple Multi-Period Energy Tariff Optimization Problem (SMETOP) and prove its NP-hardness. The result naturally applies to many models in the literature that generalize SMETOP, and whose complexity status has been unknown to date.