The overall operational costs of home energy systems (HES) has been considered as an objective function (OF) by many articles. This paper shows that considering the energy cost as OF can lead to a decrease in the load elasticity against the electricity price, which can lead to demand response programs failure. So the distribution system operator (DSO) must stop this decline. A new index is introduced to calculate the responsiveness of the PV-integrated HES, based on which a new OF for home energy management system is proposed. This index shows the load elasticity against the electricity price. The relation between energy cost and load responsiveness index is investigated, and several scenarios are analyzed to demonstrate the applicability of the proposed approach in real cases. The proposed method is implemented to a PV- and ESS- integrated HES. The results show the relation between the responsiveness of the loads and the operational costs of home. A sensitivity analysis is added to the paper to show the robustness of the proposed control scheme.