My colleague Lou Cannon reports from the West Coast -- where President Reagan is enjoying yet another vacation -- that, buoyed by his victory on the tax bill and declining interest and inflation rates that revived the stock market, the Great Communicator talks as if prosperity is just around the corner.

"The president was an optimist when everything looked bad to the rest of them," Cannon quotes White House Deputy Press Secretary Larry Speakes as saying. "Now, he really believes that the recovery is at hand."

To be sure, everybody feels better when the stock market is going up than when it's going down. The bulls' week on Wall Street therefore provided a welcome psychological boost. And in a real sense, it was important because it gives a needed lift to a lot of hard-pressed corporations that can improve their balance sheets by selling new stock issues.

But neither the Wall Street boom nor plunging interest rates have changed the fundamental economic problems of the country. The president and his entourage do the nation a disservice to suggest anything else.

Speakes indulged himself the simplistic observation that the recent interest rate decline is "remarkable," with a prediction that it would lead to a reduction in home mortgage rates and a continued reduction in inflation.

A business lobby, the American Business Conference, is much more restrained. Speaking for the conference -- which, by the way, supported Reagan in his tax bill fight -- president Jack Albertine said:

"There is good news and bad news from the Bureau of Labor Statistics on the July consumer price index . The good news is that the rate of increase in the CPI is relatively slight. The bad news is that the improved inflation picture is largely the result of the continued weakness of the American economy.

"I think it would be a serious mistake for policy makers and consumers to believe that inflation is no longer endemic to the American economy. While we have won a few battles in the fight against inflation, the war is far from over."

Nonetheless, Reagan grows euphoric in the comforting surroundings of his mountaintop ranch near Santa Barbara, where -- according to the Associated Press -- he's spent one day out of 10 since his election. Perhaps any politician would find it difficult not to try to derive some political benefit from rising stock market prices, and even to try to push things along a little further with some confidence-generating jaw-boning.

But what lies ahead is a kit full of unsolved problems: A deficit of $150 billion for fiscal 1983 remains to be financed. As useful as the tax bill is in plugging some loopholes and raising a bit of money to trim the deficit, it made no progress in cutting back military expenditures, or making sense out of the Social Security System and some other "entitlement" programs.

And that's not all that the optimistic California White House ignores. Unemployment is near 10 percent, the highest rate since the 1930s. Corporate profits are weak, threatening many companies with bankruptcy. The banking system has been rocked by domestic and international disasters, which probably have not yet run their course.

On top of the financial crisis in Mexico, the latest news to shake the markets is that Brazil may also petition for a rescheduling of its debt, which at $74 billion runs a close second to Mexico's.

So the president is being badly advised if he's willing to make the long leap from the spectacular jump in stock prices to an assumption that the tax legislation -- or anything else that has taken place in the past few weeks -- has cleared the way for recovery.

Stock prices went up some 80 points on huge volume the week before last for exactly the opposite conclusion: People (especially institutions) rushed to buy stocks on the assumption that interest rates would continue going down because the economy, instead of recovering, would remain in recession.

There would be frowns rather than smiles in Santa Barbara if they acknowledged what is really going on: the Federal Reserve Board has loosened the strings on credit, not to accommodate Ronald Reagan, but because there's reason to worry about the economy.

"The Federal Reserve's easing must represent some combination of concern over the state of domestic business and the fragility of the banking industry, which is its first concern as lender of last resort," say officials of the Girard Bank of Philadelphia.

"The lowering of rates helps the economy, of course. What investors are not sure of is whether this is being done because the Fed knows of banking industry problems even more serious than those that have surfaced thus far."

The Girard Bank is not alone in worrying that all the bad news is not yet out. The economy is probably walking a very narrow path where a sudden new strain could cause a lot of trouble. There is more concern than anyone wants to express about over-extended banks.

"For the moment," says one of the bright people on Wall Street, "everything depends on how delicately they the Fed can manage monetary policy. Now that the tax bill is out of the way, there's no more help to look for from fiscal policy."

Felix Rohatyn of Lazard Freres in New York told me recently that the Reagan administration is brushing the real problems under the rug with "theatrics" like the New Federalism and the balanced budget amendment proposal. "The markets are always more skeptical than you think," Rohatyn observed. "You cannot assume that the financial markets are illiterate, and the more one debases the governmental process, the more the feeling that things are out of control. And that gets you back to 1932, and Franklin Roosevelt saying 'there is nothing to fear but fear itself.' "