We analyze the price responsiveness of US conventional and unconventional oil supply across three key stages of oil production: drilling, completion, and production. Drilling is the most important margin, with price elasticities of 1.3 and 1.6 for conventional and unconventional drilling respectively. Well productivity declines as prices rise, implying smaller net supply elasticities of about 1.1 and 1.2. Despite similar supply elasticities, the price response of unconventional supply is larger in terms of barrels because of much higher production per well (~10x initially). Oil supply simulations show a 13-fold larger supply response due to the shale revolution. The simulations suggest that a price rise from $50 to $80 per barrel induces incremental US production of 0.6MM barrels per day in 6 months, 1.4MM in 1 year, 2.4MM in 2 years, and 4.2MM in 5 years. Nonetheless, the response takes much longer than the 30 to 90 days than typically associated with the role of "swing producer."