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"Is there a ban on printing more money? If so he should lift that too and fix the economy while he's at it."
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Increasing oil supply lowers value of oil -- which would be good.
Printing more money = inflation -- which is very bad.
Not that drilling offshore would somehow fix oil prices, but the analogy here is horrible.
But inflation also lowers the price of oil. Printing money actually was the strategy used by the United States to deal with previous price hikes. (The Onion is often very preceptive.) The pump price (paper dollars) did not come down much, but the cost in real terms did.
http://oregonstate.edu/cla/polisci/faculty-research/sahr/gasoline.pdf
Compare 1981 to 2002. Same pump price (about 1.30 per gallon), but inflation drove the value from 3.26 to 1.60 in current dollars. If oil ends up effectively priced in Euros or Yuan, the same thing might not happen this time.