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In this paper, we study the price elasticity of electrical demand in a smart grid framework where the loads of a power system are scheduled by energy management controller (EMC) units that aim to maximize users' benefits by considering both load utilities and real-time electricity price. We show that different price responsive behaviors of electrical loads result from interaction between their utilities and electricity prices. Here, the utility is modeled as a function of time in order to represent the timeliness of loads. Based on the developed theory, we introduce a parametric utility model from which the price elastic behaviors of aggregated loads from a power system are established statistically as multi-dimensional demand-price functions. Finally, we investigate the problem of optimal real-time electricity prices under the framework of social welfare maximization. Considering demand elasticity from users, we show here that the optimal real-time electricity prices that maximize the social welfare of a power system will match the marginal costs of energy production at load levels resulting from these optimal electricity prices. The solution for this can be pre-calculated using a simple iterative algorithm without the need for excessive information exchange between users and the utility company. Theoretical results from this paper are validated through numerical examples using a simplified power network.