Under the assumption that demand function is convex and has the non-decreasing price elasticity，this paper analytically studies the losses of both social welfare and operational efficiency in decentralized supply chains with price-sensitive demand，respectively． We consider the following system: A single supplier sells homogenous products to multiple identical retailers at the same wholesale price such that the market selling price can be determined under quantity competition． By virtue of the concept PoA ( Price of Anarchy) ，the whole profit or social welfare in the decentralized supply chain are compared with that in the integrated supply chain or the social optimal model，respectively． Then，the upper bounds for the losses，independent of the specific forms of demand functions，are derived analytically in detail． It is found that compared with the case of stochastic demand with fixed selling prices and inventory decision consideration，the inefficiency in the decentralized supply chain with price-sensitive demand has obviously higher upper bound when inventory decision is not integrated． Furthermore，the upper bounds increase with respect to the largest gross promargin per product and decrease as the competition at the downstream become keen．