This paper estimates price and income elasticities of electricity demand for four consumer categories, Agriculture, Commerce, Industry and Domestic, for two major utilities (one public and the other private) that supply electricity in West Bengal, India. We use panel data analysis covering 15 years for the four consumer categories. The comparison of the responsiveness in demand due to changes in tariff for the two utilities reveals some interesting differences in the demand pattern of the consumers served by the different utilities when the private sector supplies to the highly urbanized areas and the public sector supplies to the rest of the state. We get an idea about the difference in tariff structure of a public and a private utility as well. Our study suggests that any policy to entirely remove the cross subsidy is not a viable option as there is considerable differences in the elasticity of demand for power among the different category of consumers. Further, for the success of the policy of 'open access' which is an important and integral part of the power sector reform some regulatory mechanism is required to control market power in the power sector.