Peer-to-peer markets, collectively known as the sharing economy, have emerged as alternative suppliers of goods and services traditionally provided by long-established industries. We explore the economic impact of the sharing economy on incumbent firms by studying the case of Airbnb, a prominent platform for short-term accommodations. We analyze Airbnb's entry into the state of Texas, and quantify its impact on the Texas hotel industry over the subsequent decade. We estimate that in Austin, where Airbnb supply is highest, the causal impact on hotel revenue is in the 8-10% range; moreover, the impact is non-uniform, with lower-priced hotels and those hotels not catering to business travelers being the most affected. The impact manifests itself primarily through less aggressive hotel room pricing, an impact that benefits all consumers, not just participants in the sharing economy. The price response is especially pronounced during periods of peak demand, such as SXSW, and is due to a differentiating feature of peer-to-peer platforms enabling instantaneous supply to scale to meet demand.