The past papers assuming consumer income to be evenly distributed use duopoly model for analyzing the impact on the social welfare caused by price ceiling. Changing this assumption and assuming the income distribution is a rightly skew one. It is explored in this paper whether the price ceiling can expand the market coverage and increase the social welfare or not. It is found that price ceiling can expand the market coverage, however, consumer surplus and the whole social welfare may be reduced and give rise to welfare loss. The more significant the price ceiling, the greater the loss is. Improving the income standard can not only expand the market coverage but also increase consumer surplus and social welfare.