Motivated by digital marketplaces such as Uber and Airbnb, we study how a two-sided platform designs a menu of qualities, consumer prices, and provider wages. Consumers and providers self-select according to their private values and costs, so the platform must design its menu to attract consumers while inducing enough supply to meet their demand. We study this coordination problem over a continuous quality space, requiring supply to cover demand at every quality threshold. We formulate menu design as an optimization over trading distributions, which specify how much trade occurs at or above each quality. Through convexification of the technological cost function, we characterize the profit- and welfare-optimal trading distributions. This characterization shows how production technology alone can reduce menu size without sacrificing optimal profit or welfare, regardless of the type distributions, and determines when optimal menus can be finite. We then show that profit maximization can be highly efficient: under monotone hazard rate conditions on both sides, a profit-optimal menu achieves at least $1/(e-1)$ of optimal social welfare. We next consider the practical setting in which the menu size is restricted to a prescribed number of offers. We establish how the restricted menu approximates the unrestricted optimum in profit. We develop an algorithm that computes a menu within this size limit in polynomial time. The computed menu simultaneously approximates the unrestricted optimal profit and social welfare with additive error.

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