One of the most important aspects that may affect market welfare is that related to the low demand responsiveness to price. This situation may greatly impact the market performance causing low efficiency, high prices and a disproportional allocation of surpluses. The structure of electricity markets is usually oligopolistic; producers may bid prices higher than their marginal costs to the short run wholesale market, inducing outcome deviations from the perfect competitive benchmark. The possibility of gaming the market is amplified in the presence of low demand responsiveness to price. This paper proposes a model to assess the role of demand elasticity in mitigating the effects of supply side strategic bidding behavior. We model the supply side in a conjectural supply function (CSF) framework, which allows incorporation of exogenous changes in demand elasticity and different levels of competition in a given market. The impacts of demand responsiveness on the market performances are assessed through a set of proposed indices that are applied to a model of the Italian market.