This paper studies the social value of closing price differentials in financial markets. We show that arbitrage gaps (price differentials between markets) exactly correspond to the marginal social value of executing an arbitrage trade. We further show that arbitrage gaps and measures of price impact are sufficient to compute the total social value from closing an arbitrage gap. Theoretically, we show that, for a given arbitrage gap, the total social value of arbitrage is higher in more liquid markets. We apply our framework to compute the welfare gains from closing arbitrage gaps in the context of covered interest parity violations and several duallisted companies. The estimates of the value of closing arbitrage gaps vary substantially across applications.