  The growth of the sharing economy is driven by the emergence of sharing
platforms, e.g., Uber and Lyft, that match owners looking to share their
resources with customers looking to rent them. The design of such platforms is
a complex mixture of economics and engineering, and how to "optimally" design
such platforms is still an open problem. In this paper, we focus on the design
of prices and subsidies in sharing platforms. Our results provide insights into
the tradeoff between revenue maximizing prices and social welfare maximizing
prices. Specifically, we introduce a novel model of sharing platforms and
characterize the profit and social welfare maximizing prices in this model.
Further, we bound the efficiency loss under profit maximizing prices, showing
that there is a strong alignment between profit and efficiency in practical
settings. Our results highlight that the revenue of platforms may be limited in
practice due to supply shortages; thus platforms have a strong incentive to
encourage sharing via subsidies. We provide an analytic characterization of
when such subsidies are valuable and show how to optimize the size of the
subsidy provided. Finally, we validate the insights from our analysis using
data from Didi Chuxing, the largest ridesharing platform in China.
