Ever since its inception, the concept and application of demand-side response have continued to evolve and take a new shape in microgrid energy management. The application of demand response programs in the microgrid literature lacks the consideration of flexible price elasticity of different load categories. The realistic characterization of load-responsive models with a combination of both linear and nonlinear models is necessary to study the effect of demand response programs. To cover this research gap, the impact of price-based demand response programs on the optimal scheduling of microgrids is investigated in the presence of linear and nonlinear load models. The flexible elasticity model is adopted to characterize the actual behavior of customer responsiveness towards changes in electricity price. Five load models, namely linear, logarithmic, exponential, power, and hyperbolic, were derived for each price-based demand response program. Furthermore, the stochastic-based scenario modeling is considered to cope with the volatile renewable generation in the microgrid network. The recently reported swarm intelligence-based algorithm called the sparrow search method is intended to solve the proposed microgrid energy management issue for the first time in the literature. Fifteen case studies on the basis of distinct linear and nonlinear load scenarios have been carried out to assess the effectiveness of the methodology proposed. Finally, various techno-economic performance indices were evaluated for all case studies, and a priority-wise ranking is assigned based on the multi-criteria assessment technique.