Concern is growing in New York, in the wake of last week’s meeting of the Federal Reserve Board, over the quickening collapse of the value of the dollar, as foreign investors proclaim that a “for sale” sign has been hung on the city and economists and analysts warn that a collapsing currency bodes ill for the economy.

In the week since the Fed’s meeting, the soundness of the dollar has been ebbing rapidly, with the greenback’s value plunging to a 732nd of an ounce of gold from a 708th of an ounce when the Fed moved to ease the money supply in hopes of preventing a collapse of the credit markets. It was the dollar’s lowest level since 1980, with some analysts expecting it to drop even further, to 800th of an ounce in the next six months.

For the first time in three decades, the dollar is now equal in value to the Canadian loonie, and the euro, which is trading at a high of $1.41 this week, is the strongest it has ever been against the dollar in its eight-year history. This is not good news for America’s economy, experts say. “No country in the world has ever fought itself to prosperity by weakening its currency,” the manager of the Merk Hard Currency Fund, Axel Merk, said. “The Fed decision to cut rates last week was wrong.”

Some economists argue that a weak dollar, particularly against other currencies, helps American exporters, at least in the short term. “But on the whole, a cheap, and cheapening, dollar exchange rate is bad medicine. It’s bad medicine for Americans,” the editor of Grant’s Interest Rate Observer and author of four books on finance, James Grant, said. “It reduces the value of American wealth in terms of other currencies, and of the nations that print them. It tends to mean a rise in the cost of imported goods and services — that is, it’s inflationary.”

The Federal Reserve chairman, Ben Bernanke, has not shied away from talking about an increased risk of inflation, but has argued that this risk will be kept in check, and that the Fed first must tackle the current liquidity crisis.

“The inflation rate is something we pay close attention to,” Mr. Bernanke said last week. “An economy cannot grow in a healthy, stable way when inflation is out of control, and we will certainly make sure that that doesn’t happen.”

Despite these assurances, a number of analysts argue a weak dollar is already hurting Americans by curtailing their purchasing power. “Among the big losers are American households that buy imports as part of their everyday shopping,” the director of the Center of Trade and Policy Studies at the CATO Institute, Daniel Griswold, said. “All things being equal, we are better off with a stronger dollar.”

The image of the dollar as the benchmark currency for the world is also taking a bashing. Several large central banks — such as those in Russia, China, and some Middle East countries — hold billions of dollars in cash in their reserves. Since the greenback has been falling in value, however, many of these institutions are starting to diversify their holdings, dumping the dollars for other, stronger currencies, such as the euro.

Russia, for example, now holds only about 40% of its reserves in dollars; at one point it held more than 70%. The United Arab Emirates converted 8% of its dollar reserves to euros in December. China, which doesn’t release data on its foreign currency holdings, has said it is slowly diversifying its dollar-dominated reserves.

“Reserve diversification is a inevitable gradual process, and the world economy can no longer be dependent on America as the only reserve economy,” a senior economist for Moody’s Economy.com, Tu Packard, said.

This diversification process acts like a sell-off, because by holding dollars in their reserves, these central banks are in essence buying shares in the American economy. As they sell the dollars, they are selling their interest in our economy, Ms. Packard said.

“The dollar is the world’s currency — most greenbacks circulate outside the 50 states — but America’s monetary policy is designed for America and no other country. That is certainly a nice convenience for us. But it will tend to weaken foreigners’ confidence in our Fed and our Treasury,” Mr. Grant said. “You’ve got to remember that this country produces much less than it consumes. It finances the difference with dollars. Here is one of the sweetest arrangements on the face of the earth, but it will last only so long as non-Americans willingly accept our dollars, these green pieces of paper of no intrinsic value.”

Still, the administration in Washington is exuding confidence. “I think I’ve been pretty clear on this — a strong dollar is in our nation’s interest,” the treasury secretary, Henry Paulson, said in a press briefing Friday. “And our currency values are always determined — and I believe they should be determined — in a fair, competitive marketplace based upon underlying economic fundamentals. And so what we do in the United States and what I very much advocate is policies that are going to increase confidence, maintain confidence in the U.S. dollar and in our economy.”