Electricity is one of the most significant energy sources in the modern world. Over the last century, there has been no significant change in the centrally controlled structure of electrical power grids, especially in developing countries. Global population and economic expansion, together with air pollution, put further strain on the electricity industry. The power electrical grid, as the main structure for power transmission, has to reconsider its concepts. Currently, critical peak load caused by residential customers has attracted utilities to pay more attention to residential demand response (RDR) programs. With the rise in household computing power and the increasing number of smart appliances, more and more residents can participate in demand response (DR) management through the home energy management system (HEMS) to prioritize the start-up of electrical appliances according to the necessity of use and efficiency. This research is an applied case study designed for cold regions with an average household population of three people. It is suggested that, in addition to, time of consumption and household type, the cluster of appliances affects the price of consumption, and the cost paid by users varies depending on the cluster of appliances used by different households at different times. To evaluate the potential for changing prices to better consumption criteria, a multi-agent hierarchical model including utility and different types of households and appliances is presented in this study that takes into consideration two main objectives, including peak smoothing and energy consumption reduction. Based on the specified indicators, the analytical results of two scenarios were analyzed, and it was concluded that variable pricing of appliance consumption can reduce electricity consumption and smooth the peak load curve.