The steady rise of e-commerce marketplaces underscores the need to study a market structure that captures the key features of this setting. To this end, we consider a price-quantity Stackelberg duopoly in which the leader is the marketplace operator and the follower is an independent seller. The objective of the marketplace operator is to maximize a weighted sum of profit and a term capturing positive customer experience, whereas the independent seller solely seeks to maximize their own profit. Furthermore, the independent seller is required to share a fraction of their revenue with the marketplace operator for the privilege of selling on the platform. We derive the subgame-perfect Nash equilibrium of this game and find that the equilibrium strategies depend on the assumed rationing rule. We then consider practical implications for marketplace operators. Finally, we show that, under intensity rationing, consumer surplus and total welfare in the duopoly marketplace is always at least as high as under an independent seller monopoly, demonstrating that it is socially beneficial for the operator to join the market as a seller.