In the wake of Osama bin Laden’s death, the peso continued its relentless run on the U.S. dollar, closing Monday’s spot quote at 11.17. The situation isn’t likely to change anytime soon, because the dollar influx will continue as risk appetite remains unabated.

It’s worth pointing out that the peso’s strengthening has sparked varying impacts on the nation’s business structure, improving the competitiveness of multinationals like cement giant Cemex, while hurting the profitability of major exporters like brewer Grupo Modelo, whose main market is the United States.

According to Santander analyst Gonzalo Fernández, the current parity situation benefits companies like Cemex because it basically does not rely on exports from Mexico, but rather has overseas production facilities where the appreciation of strong currencies such as the euro and pound compensate for the dollar drop.

On the other hand, companies that rely on exports and dollar-pegged revenues, such as Modelo, Alfa, Mexichem and miner Grupo México are hurting from a stronger peso. The top exporter, which is the automobile sector, has also been affected by the peso’s strength, because it exports to the U.S. market about 80% of total production, yet has to pay wages and other production costs in pesos.

The bottom line is that no matter how you slice it, the dollar doesn’t have much clout these days. The greenback (a term that was invented in Lincoln’s days 150 years ago) has lost 12 percent of its value against foreign currencies since the chaotic period after the failure of Lehman Brothers in 2008, and nearly five percent since the end of 2010.

It may seem like an exercise in futility, but experts are debating the end of the era of the dollar, while news media portray the currency as a weakling. The so-called fiat currency, backed only by the full faith and credit of the U.S. government, no longer commands respect. So wouldn’t the world be better off without it?

This hypothetical exercise was conducted by Barry Eichengreen, a professor of economics at the University of California at Berkeley and the author of Exorbitant Privilege: The Rise and Fall of the Dollar and the Future of the International Monetary System. Imagine, says the professor, that you wake up tomorrow and the dollar has vanished. The Federal Reserve is out of the business of supplying money. How would people here, there and everywhere go about their everyday affairs?

Probably, life would become one big swap meet. It would be like a giant farmers market, except that instead of a vendor selling carrots in exchange for dollars, he would have to trade them for the onions in the neighboring stall or for the paring knife of the cook. Then you’d have a situation that economists call non-coincidence of wants the carrot seller may not want onions, and those onions may spoil before he finds someone who does.

This, of course, underscores the convenience of currency as a medium of exchange and a store of value. It follows that in a world where the United States no longer had a currency, there would be an incentive to use someone else’s.

History is the best teacher. Britain’s 13 North American colonies were prohibited from operating a mint or otherwise coining money. So the colonists turned to the silver coins that were then circulating in Mexico, which they obtained by exporting dried fish and whale oil to the West Indies. Were the dollar to magically disappear, our neighbors would again resort to using other monies. When Republican Ron Paul says end the Fed, he presumably doesn’t realize that he would be giving a valuable franchise to the Bank of Canada.

Realistically, U.S. currency needs could be met only by another large economy, and Canada might be too small an issuer of currency. But the only other potential candidates Europe and China both have drawbacks. Europe is bogged down in a debt crisis, while China limits the use of its currency abroad partly to prevent its exchange rate from rising.

Thus, imagine instead that we do not start using another country’s money. Figuring out how many carrots to offer for an onion, how many onions to offer for a potato and how many potatoes to offer for a paring knife would be complicated without a common measuring rod. We would therefore gravitate to one commodity as the standard by which the value of all other commodities was expressed.

In a hypothetical world without dollars, it follows, the right to issue notes would have to be limited to a set of regulated entities call them banks. This was how currency entered circulation before the Civil War. Banks printed up and lent out engraved bank notes. State legislatures required them to hold gold or securities sufficient in value to redeem their notes.

Critics of the dollar are having a field day. But, says Eichengreen, when you think about our current monetary arrangements, I am inclined to paraphrase Winston Churchill on democracy: Ours is the worst possible system, except for all the others .