You'll find some details explaining the phenomenon and results here:
So you don't understand it and send me to a link. I'll play:
Because petrodollars are denominated in U.S. dollars—or greenbacks—their true purchasing power relies on both the core rate of U.S. inflation and the value of the U.S. dollar. This means petrodollars will be affected by economic factors the same way the U.S. dollar is affected. So if the value of the dollar falls, so does the value of petrodollars, and thus the government's revenue.
So in your own words, please explain how pricing oil in dollars keeps the dollar from falling.
By the way, the article is junk. If the value of the dollar falls, usually government revenue, measured in dollars INCREASES, e.g. during an inflation you get higher COLAs, which means higher tax revenues.
Here's what I remember:
Before petrodollar recycling was Bretton Woods, where the U.S. dollar was used as a global reserve currency, with the purpose of establishing stability, and it worked. The reason was actually quite reasonable: the U.S. had the largest manufacturing base, a large supply of oil, and lots of gold thanks to, among other things, payments and loans made by other countries which needed armaments during WW2.
The catch is that it also made the dollar more valuable: more countries needed it for trade, and the only way they could earn more was to sell to the U.S. With no competition, the U.S. could buy cheap and spend a lot, which they did. But at the same time, it also made the goods they produced more expensive, which meant other countries had to import less to save more dollars and export more in order to earn more dollars in order to industrialize.
One problem is that the U.S. also had superpower ambitions, and needed higher military costs to counter the Soviets and, among other things, prevent a "domino effect" in places like Indochina. That's why it spent large amounts of money to build more military bases and engage in proxy wars in various countries. Those higher costs made their allies edgier, and in turn encouraged them to pull out gold that they had deposited in the U.S. That's why amidst the Vietnam police action debacle, Nixon ended up dropping the gold standard. But that plus U.S. conventional production peaking two years earlier plus what would become a series of oil shocks did not help. So, they tried to kill two birds with one stone and make deals with the Saudis, who like more producers, were wrestling oil fields away from Western countries and taking over, by encouraging them to price oil in dollars. In return for that and investing their profits in U.S. businesses, the U.S. would provide military aid and armaments. Thus, many birds were killed: the Saudis and others got their military hardware to counter Israel (which the U.S. was also arming), the Soviets which were attempting to strike deals with countries like Egypt could be deterred, the U.S. had a steady supply of oil, its economy could receive some support from petrodollars invested, it now had "allies" like Israel and Saudi Arabia and could play one against the other, and many countries still remained dependent on the dollar because they could only buy oil using that or by exchanging their currency for such.
It even reached a point when, a few years after, petrodollar recycling took place, such that through the IMF-WB, the U.S. could extend low-interest loans to countries in South America and the Philippines to kill more birds with one stone: they developed economically through cheap loans, and the U.S. got more "allies."
The problem, just like that of Bretton Woods, is probably seen in light of the Triffin dilemma: the country whose currency is used as a reserve currency or valued globally will eventually experience trade deficits because its exports would be to expensive and imports cheaper. With that borrowing and spending will begin to increase significantly across the board.
That might explain why chronic trade deficits took place from the 1970s onward, then coupled with increased debts and spending from the early 1980s thanks to voodoo economics:
http://blogs.reuters.com/rolfe-winkler/2009/09/30/krugman-and-the-pied-pipers-of-debt/Now, more countries want to form their own oil bourses and use different currencies for trade, if not to use SDRs or even engage in bilateral deals.