Actually, there was both a U.S. and a global recession in 1981-82 that resulted in a sudden price drop from its overall highs.
But oil prices remained rather high until the mid to late 1980s when the so called "oil glut" caused a price collapse.
Reagan and Casey were the reason behind the oil glut, which of course wouldn't have worked without the Saudis.
The logic we laid out to them was rather simple. The Soviets had a strategic interest in cutting off the West's oil, which would require taking down Saudi Arabia or cutting them off from the West. Iraq was a Soviet proxy on Saudi Arabia's border, and the Iranian regime would love to cross the Persian Gulf and run both Mecca and the Saudi's oil. Both Iraq and Iran massively outnumbered the Saudis, and though their conflict was stalemated, it would inevitably end, leaving them with millions of trained combat veterans, massive debts, and the world's largest oil field sitting right within reach.
If oil prices stayed high, Iraq and Iran would retain their massive numerical advantage in personnel
and gain parity or even advantage in weapons purchased with petro-dollars. If oil prices were to become very low, Saudi Arabia would still have a huge monetary advantage (because their production costs are virtually nil), while Iraq and Iran would hardly break-even, make no profit, and thus couldn't maintain and upgrade their armies or extend their reach to a level that could take and hold Saudi Arabia against a hypothetical Western relief force.
Meanwhile, on the larger world stage, high oil prices benefited the Soviet Union (which was an oil exporter) and gave it the majority of its hard currency, which it desperately needed to purchase various strategic materials and buy influence around the world. High oil prices also had a crippling effect on Western economies, weakening both NATO and the US which kept Soviet ambitions in check, and making the US less able to defend Saudi Arabia in the event of an attack by the Soviets, their proxies, or Saudi Arabia's more nefarious and populous neighbors.
Interestingly, the point wasn't to boost the US economy, other than that was part of multiplying the West's advantage over the Soviets to win the Cold War, one of many pressures we were applying, like smuggling burst-mode radios and fax machines to Polish strikers, enlisting the help of the Pope, labor union leaders, and far-left European Prime Ministers who the Soviets wouldn't suspect.
This was in books by Reagan Administration officials and Cold War historians written after the collapse of the Soviet Union, when some of it could be declassified.
Here's just one I enjoyed reading:
http://www.amazon.com/We-Now-Know-Rethinking-Relations/dp/0198780710
I can't remember if Brent Scowcroft's book got into those operations, or whether his focused on changes that occured under GHW Bush. (However, I do remember Scowcroft's book as being quite long and boring).