We consider a quantity flexibility contract in a supply chain, under price dependent demand. The demand is random and follows a multiplicative model. We show that the retail price that maximizes expected retailer profits, is higher than the price that would maximize profits if there was no demand uncertainty. We then show that if the wholesale price lies in a certain range, there is a positive buyback fraction that the manufacturer would prefer. This preference is in comparison to not entering into a quantity flexibility contract at all. Finally, through numerical work we find that the contract results in a win-win situation for both the manufacturer and the retailer in the case of price dependent demand. Keywords: Supply Chain Management, Quantity Flexibility Contract, Price Dependent Demand