Economic Model Predictive Controllers, consisting of an economic criterion as stage cost for the dynamic regulation problem, have shown to improve the economic performance of the controlled plant, as well as to ensure stability of the economic setpoint. However, throughout the operation of the plant, economic criteria are usually subject to frequent changes, due to variations of prices, costs, production demand, market fluctuations, reconciled data, disturbances, etc. A different economic criterion determines a change of the optimal operation point and this may cause a loss of feasibility and/or stability. In this paper a stabilizing economic MPC for changing economic criterion for linear prediction models is presented. The proposed controller always ensures feasibility for any given economic criterion, thanks to the particular choice of the terminal ingredients. Asymptotic stability is also proved, providing a Lyapunov function.