Why do investors buy stocks? Simple: To share in corporate profits.

Of course, many don’t see it that way. Most investors focus instead on the opportunity to make money if a stock’s price rises. But corporate profits are the key to that.

That’s why investors should be concerned about Tuesday’s Commerce Department report that corporate profits, after taxes were paid, had dropped 2 percent between the second and third quarters. If profits sink, stock prices ought to follow.

The report showed the largest quarterly profits decline since the third quarter of 2001, when stock prices were plunging.

The department said the recent drop was caused in part by four hurricanes that hit the southeastern United States during the third quarter. The storm damage to property hurt rental income, caused businesses to shut down and forced insurers to make big payouts.

Bad as the problems were, they basically were temporary and therefore should not have much long-term effect on share prices.

More worrisome were the effects of rising prices for labor, fuel and other raw materials. Those could well continue.

The third-quarter figures are especially troubling because they fit a pattern. Corporate profits rose 22.6 percent in 2002 but 13.8 percent in 2003. And the gain for the 12 months ended with the third quarter was just 8.1 percent.

The trend has been worsening: Profits were up 7.1 percent in the fourth quarter of 2003 but up only 3.7 percent in the first quarter of 2004. They dropped 0.7 percent in the second quarter before skidding the additional 2 percent in the third quarter.

Stocks returned a stunning 28 percent in 2003, as corporate profits soared. But share prices have languished as profits dwindled this year.

It’s not always easy to see a direct connection between share prices and corporate profits — at least, not in the short run.

After all, there are always examples of companies that have great share-price gains even though they’re losing money. During the bubble of the late ’90s, investors bid up the prices of Internet companies that had never shown profits.

In such cases, investors are doing one of two things. They’re betting a company will enjoy big profits in the future. Or they recognize there’s no sound reason for the share price to go up but figure overly enthusiastic investors will continue to bid the price higher anyway.

This is known as “the greater-fool theory.” Anyone who invests on this basis should have a plan for selling before the fools realize how dumb they’ve been and scram for the exits, causing share prices to plummet.

Bottom line: To be a sound, long-term investment, a company must make a profit — if not now, sometime later. Obviously, you’d expect that if you were to buy the entire company. It’s the same even for a small shareholder who buys just a tiny sliver.

Over the long term, stock investors have shown a willingness to pay about $15 for every $1 in annual corporate profits. This is like earning 6.7 percent on your investment — $1 divided by $15.

If you assume that ratio stays the same, every $1 increase in profit will cause a $15 increase in the share price. And if profit fell to, say, 50 cents, the share price would fall to $7.50.

Decades ago, most corporate profits were paid out to shareholders through dividends. But since dividends are taxed in the year they’re received, many companies nowadays reinvest profits in ways meant to push share prices up without triggering annual tax bills for shareholders. Companies may buy back shares, thus reducing the supply and driving the share price up. Or they might invest in research or plant expansion.

However they are used, profits are the measure of business success. Investors would be wise to scrutinize the profit reports for the coming quarters, less the recent worrisome trend continues.