In this study, a customer reward scheme is proposed to build an effective demand response program for improving demand elasticity. First, an objective function has been formulated based on the market operation and an optimal incentive price has been derived from this objective function. Second, the incentive price is employed as a part of a reward scheme to encourage customers to reduce their electricity demand to a certain level during peak hours. Two typical customer response scenarios are studied to investigate the impact of customer response sensitivity on the loss of utilities' and customers' profits. Finally, a dataset for the state of New South Wales, Australia is employed as a case study to examine the effectiveness of the proposed scheme. The obtained results show that the proposed scheme can help improve the elasticity of demand significantly thereby reducing the associated financial risk greatly. Moreover, the proposed scheme allows customers to get involved voluntarily and maximise their profits with minimum sacrifice of their comfort levels.