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In this paper, the price elasticity of electrical demand is studied in a smart grid framework where electricity loads are scheduled by distributed Energy Management Controller (EMC) units. It is shown that different price responsive behaviors of electricity loads are results from interactions between their utilities to customers as a function of time and electricity prices. Based on this observation, a parametric utility model is introduced, from which the price elastic behaviors of aggregated loads are effectively modeled as a set of multi-dimensional demand-price functions. The developed demand elasticity model is further utilized in determining the optimal price signal for Real-Time Pricing (RTP) based Demand Response (DR) programs. Considering price elastic behaviors of customers, it is shown that the optimal real-time prices to induce the desired power consumption behaviors from customers for social welfare maximization can be effectively pre-calculated by utility company using the developed demand elasticity model without the need for excessive information exchange among end users and utility companies. Typical results of the proposed methods are further illustrated through numerical examples from a 6-bus test system.