In smart grid, demand side management is the main component that adapts elastic demand to fluctuating generations. Classical demand theory is a branch of microeconomics and it is about the study of consumer demand in the context of a market economy. Important tools in this theory are utility functions and two constraints i.e., physical and budget constraint. In this paper, two models for demand response are analyzed based on the well known Cobb-Douglas utility function. Both models maximize their utility subjected to different constraints. The result shows the effectiveness of the models for different values of elasticity parameter. © 2019 IEEE.