Distributed Energy Resources (DERs) can significantly affect the net social benefit in power systems, raising concerns pertaining to distributive justice, equity, and fairness. Electricity tariff and DERs share a symbiotic relationship whereby the design of the former directly impacts the economic efficiency and equity in the system. Current tariff design approaches suffer from opaque efficiency-equity trade-offs and are also agnostic of the externalities that affect both economic efficiency and equity. Therefore, this paper develops a justice-cognizant tariff design framework that improves the economic efficiency of tariff without sacrificing its distributional equity, and encompasses economic welfare, social costs of environmental and public health impacts, and socio-economic and demographic characteristics of electricity consumers. The proposed framework is based on a Single Leader Single Follower (SLSF) game incorporating a multi-objective optimization problem, and is evaluated on four different tariff structures. The SLSF game is reformulated as a Multi-Objective Problem with Equilibrium Constraints (MOPEC) and is solved by integrating the objective sum method for multi-objective optimization and Scholtes's relaxation technique for equilibrium constraints. We compare the economic efficiency and equity of the proposed framework using the 11-zone New York ISO and 7-bus Manhattan power networks. The results demonstrate that spatially- and temporally-granular tariffs ensure equity and economic efficiency at a lower energy burden to consumers.