We focus on the implications of the shale oil boom for the global supply of oil. We begin with a stylized model with two producers, one facing low production costs and one higher production costs but potentially lower adjustment costs, competing á la Stackelberg. We find that the supply function is atter for the high cost producer, and that the supply function for shale oil producers becomes more responsive to demand shocks when adjustment costs decline. On the empirical side, we apply an instrumental variable approach using estimates of demand-driven oil price changes derived from a standard structural VAR of the oil market. A main finding is that global oil supply is rather vertical, practically all the time. Moreover, for the global oil market as a whole, we do not find evidence of a major shift to a more price elastic supply as a result of the shale oil boom.