Restructuring of the electric power industry has brought the issue of market competitiveness to surface. Recent years have witnessed the appearance of a particular seller or group of sellers exercising market power in electricity supply. In fact, much scholarly work has been done on how to identify and mitigate such abuse by market management rules. In this paper we assess the possible market power on the basis of pivotal supplier test and propose the method to determine the reasonable quantity of long-term contracts which can play a crucial role in mitigating the market power for a pivotal player. Furthermore the market efficiency is guaranteed by making long term contracts with a pivotal player up to the quantity to ensure that the pivotal player has no incentive to abuse the pivotal quantity in the electricity market.