In the electricity market, the consumption of different parties has an effect on each other. This effect becomes more important when the energy poverty of low-income households is considered. Should everyone pay the price of excessive consumption along with the consumer? Can primarily low-income households be protected somehow from this interdependency among consumers? In the pursuit of a just electricity pricing mechanism, the 2015 Residential Energy Consumption Survey (RECS) of EIA is analyzed to understand the different residential energy consumption patterns among different income levels. Analysis of Covariance (ANCOVA) is conducted for "Total Energy Consumption", "Total Energy Consumption for Space Heating", and "Total Electricity Consumption". Finally, "Electricity Consumption per Household Member" is introduced as a new indicator for determining households' expected energy consumption level. Possible usage of such an indicator is suggested as a tax system that directs excessive consumers to the population median concerning their income levels. Illustrative calculations are presented for further understanding.