For the past 10 months, Bell and Thorn Inc. in Chicago has lost money on a long-running contract to supply industrial valves to one of its largest customers. But Bell and Thorn refuses to raise its prices or drop the customer.

Like thousands of other U.S. companies, Bell and Thorn has pushed its prices below the break-even point to keep an important customer from switching to a competing foreign supplier. It has spent months fighting off competitors from South Korea, Singapore and Taiwan, hoping for a decline in the dollar that would reduce the price advantage that the strong U.S. currency gives to imports.

With the decline in the dollar during the past three months, some economists hope that manufacturers may begin to see an improvement in their balance sheets by the end of the year as their goods become more competitive in price against foreign products. Since March the dollar has declined about 13 percent against an index of currencies of major industrial nations -- leaving it about 30 percent above the 1980 average.

But even with the the dollar's shift, Bell and Thorn is facing a new round of price-cutting and may lose the contract to suppliers in Belgium or West Germany, it has been told. A healthy recovery for many manufacturers such as Bell and Thorn depends on a continued decline in the dollar.

Economists say that the change in the dollar is a sign that the steep growth in the trade deficit -- which hit a record $123.3 billion last year -- may be over. Deficits will continue to pile up -- a $150 billion total is expected this year -- but at a slower rate, thanks to a declining dollar.

The political question is whether such a slowdown would ease the growing pressures in Congress for action against imports. Economists do not expect much change in the trade figures by this fall when protectionist sentiment is expected to erupt in moves to impose quotas and tariffs on imported goods.

Economists disagree on how much the dollar will have to fall to produce a change in the terms of trade between countries or how long it will take to produce an effect.

The change may be relatively rapid in some industries such as pharmaceuticals and in many consumer goods in which contract lead times are short, economists said. In others, such as Wortell's firm, new orders are placed for equipment six to nine months before shipment, so a change in the dollar today will take a long time to bear fruit.

However, even with a decline in the dollar, foreign firms are expected to fight aggressively to keep their market share by cutting prices and accepting losses, economists said. While the dollar was high, foreign firms were able to raise prices and increase profits in the face of higher prices of U.S. goods. Now, if the dollar falls and foreign goods become relatively more expensive, foreign companies will be willing to take losses for some time to maintain their newly acquired market share.

In addition, during the four years that the dollar has risen sharply and U.S. firms have begun to lose market share, many countries have developed sophisticated distribution networks in the United States and also have maintained consumer loyalties, said Robert Hormats, former assistant secretary of State and now a vice president for Goldman Sachs.

Meanwhile, the deterioration in the trade deficit should not be as strong in the next few months as it has been earlier this year, economists said.

"The negative increment in the trade deficit should get smaller," said Allen Sinai, chief economist for Shearson Lehman Brothers. But he added that industries aren't yet recouping lost market share.

Sinai said that some economists believe that the West German mark must come down to a level of $2.75 from about $2.85 before trade will be affected. "It would be surprising to see improvement after 3 1/2 months," he noted.

Sinai said he expects a better U.S. net export position in the fourth quarter of this year. "The worst of the problem probably is over, but the problem is with us for some time to come," he added.

Economist Alan Greenspan wrote this month that "the foreign exchange value of the dollar stands near or below levels of a year ago against major foreign currencies. In addition, sufficient time has now passed for the lagged effects of much of the dollar runup to have fed through to trade patterns; a year ago we had not seen the totality of the bad news, by now we may have."

Greenspan said that, although some people fear that the continued siphoning off of business to foreigners will cause a recession, what is more likely is that U.S. businesses' market share won't deteriorate much further.

Hormats said an improvement in the trade statistics probably will show up in the next four to six months. Likely to see changes first are price-sensitive industries such as chemicals, synthetic fibers, drugs and pharmaceuticals, Hormats said.

Orders for durable goods began to pick up slightly in May and June, but it isn't clear whether the dollar was a factor, economists said. "In the near term, there won't be too much reduction in pressures for import restrictions," Hormats said. "But in nine months to a year," if the dollar continues to decline, "pressures will abate somewhat."

C. Fred Bergsten, director of the Institute for International Economics, said that the trade picture is "bound to get worse" because the dollar hasn't changed enough to affect relative prices significantly and economic growth is so poor in the rest of the world that it won't be enough to absorb a greater amount of U.S. exports.

Bergsten said it takes from one to two years for exchange rate changes to affect trade. He also said that the dollar hasn't declined very much and is about 2 percent higher than the average of last year.

For the dollar's decline to have any effect on industries such as steel and chemicals, the dollar would have to drop by 40 percent, the amount it has risen in four years, Bergsten said.

For the high-tech industries to turn around, the dollar would have to decline by about only 20 percent, because they have more underlying strength and competitiveness than many other industries, he continued.

For business to improve in the machine tool industry -- which has lost half of its market share in the last four years -- the dollar would have to decline by at least 25 percent, said Joe Franklin Jr., statistical director for the national Machine Tool Builders Association.

A lot of that market share never will return because many U.S. companies began to build divisions overseas where wage rates are lower and they can sell goods to foreign countries for less, Franklin said. In addition, the quality of foreign work forces and management are good, Franklin said.

The industry is concentrating new business in countries that are not competitors, but because many are operating offshore, benefits to the economy such as higher employment will be lost to the United States. Additionally, even if the dollar declined, companies that had moved overseas would be reluctant to come back to the United States because of the large investments they have made in overseas operations, Franklin said.

"What we have to do is do what Americans traditionally have done and that's move to the cutting edge of the new frontier" of technology, Franklin said. "We can't possibly beat them on price."

According to Franklin, the machine tool industry's exports have dropped from $1.0 billion in 1981 to $409 million last year. Imports of machine tools, on the other hand, have risen from $1.5 billion to an estimated $1.7 billion this year, Franklin said.

And the hopes of machine tool companies and other core industries for a comeback are clouded by a general pessimism about their prospects. To become more competitive, Bell and Thorn has tried to automate, but has met resistance from bankers who wonder aloud why anyone would invest in a U.S. manufacturing company. Invest in a fast-food chain instead, the bankers said. But Bell and Thorn balked.

"We don't own any Burger Kings," company Vice President Brent Wortell said. Supplying machinery to other companies is "the business we're in."