Interest in electricity-gas demand response (EGDR) programs has been growing, especially with respect to Energy Hub (EH) systems, which are typically large industrial multi-energy users involving electric, heating and cooling loads. A key component in modeling EGDR is the electricity-shifting curve (ESC), which is usually obtained empirically. However, rigorous and systematic approaches to obtaining and understanding the ESC are lacking. In this article, a quantitative modeling approach is proposed based on the aggregated utility curve of multi-energy demands such as electricity, heating and cooling loads. First, an ESC based on consumer psychology and behavior is adopted. Second, utility curves of different loads (electricity, heating and cooling) are aggregated to a single utility curve, which is then combined with the theory of consumer choice to develop the ESC with regard to the price ratio of different energy sources. Third, various factors affecting the shifting curves are identified and then analyzed. Based on the case studies, generalized guidelines for improving the ESC are provided. Additionally, a multi-energy user with a higher heating-to-electricity ratio (HER) is verified as having better performance in obtaining a broader shifting area, and a multi-energy user with lower HER has a larger shifting amount in common range of price ratio. In summary, this work presents a quantitative and systematic approach to modeling the ESC in an EH and to understanding EGDR behaviors which can be used to improve EH response flexibility.