WASHINGTON (AP) _ Every time a shirt is scrubbed by hand with bar soap in Colombia, Venezuela or the Dominican Republic, the financial position of American cattle producers is improved a teeny bit.

Some Central and South American countries have become a thriving market for U.S. inedible tallow, the fat from cattle which cannot be consumed by humans. Tallow is favored for making soap in several countries, particularly in the Caribbean Basin, says an Agriculture Department expert.

Although tallow exports to many countries have declined since the early 1980s, shipments to the Caribbean nations have risen steadily, said David Young of the department's Foreign Agricultural Service.

Colombia, Venezuela and the Dominican Republic are the top U.S. tallow markets in the region. Almost all the inedible tallow is used for soapmaking.

Shipments to Colombia rose from an average of 43,500 metric tons in 1981-82 to 54,200 in 1985 before dropping slightly last year, Young said in an article to appear in USDA's Foreign Agriculture magazine.

U.S. tallow exports benefit from Colombia's limited production, he said. Unlike the animals produced in U.S. feedlots, Colombian cattle yield little tallow, not enough to meet soap requirements.

''Bar laundry soap rather than detergent is still the dominant choice for washing clothes, and no change is seen in this trend,'' Young said. ''Colombia's soft water, along with the traditional custom of washing clothes by hand and the general availability of maids, has kept the demand for bar laundry soap high.''

Moreover, he said, the number of washing machines in Colombia is increasing slowly because of their cost, roughly 100,000 pesos or $450 each.

Young, who recently visited the region, also noted the growth of tallow exports to Venezuela, Dominican Republic, Haiti, Jamaica and other countries. Overall, he said, U.S. tallow shipments increased to about 137,000 tons last year from 109,300 tons in the early 1980s.

Tallow is one of the major byproducts of U.S. cattle production. In all, exports of inedible tallow last year were about 1.13 million tons valued at $350.4 million, according to USDA records.

Regionally, Latin America was the top market at 384,215 tons valued at $124.4 million, followed by Asia at 243,935 tons worth $74.6 million; Western Europe, 224,870 tons and $65 million; and Africa, 223,335 tons and $70 million.

Mexico was shown as the largest single importer of U.S. tallow at 92,992 tons last year valued at $32.5 million.

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WASHINGTON (AP) - A long-awaited economic recovery in the nation's agricultural sector is being led by some of the states hit hardest the last several years, according to Agriculture Department analysts.

At the beginning of 1986, says the Economic Research Service, 10 states in the upper Midwest each had 4,000 or more commercial farms with a high probability of being unable to repay their loans.

The states also tended to have the highest level of financial stress, which affected an average of 15 to 25 percent of their commercial farms.

''This region is now leading the economic turnaround in agriculture,'' the agency said in a new outlook report.

The region includes five western Corn Belt states of Illinois, Iowa, Minnesota, Missouri and Wisconsin; and five plains states: Kansas, Nebraska, North Dakota, Oklahoma and South Dakota.

Net cash income - the difference between cash expenses and cash receipts - rose nearly 60 percent in the five Corn Belt states between 1984 and 1986, from about $7.3 billion to $11.5 billion, the report said. In the five plains states, net cash income collectively rose 50 percent to $7.8 billion from $5.42 billion.

''This strengthening will continue in 1987, especially in these plains states, which contribute nearly one-third of U.S. cattle production and nearly one-sixth of hog output,'' the report said.

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WASHINGTON (AP) - The nation's cotton inventory continues to drop from the high level of last year, according to Agriculture Department estimates.

At the beginning of the 1986-87 cotton marketing year last Aug. 1, the carryover from previous crops was 9.35 million bales. By the time the new 1987-88 season begins on Aug. 1, the carryover is expected to be trimmed to around 4.3 million bales. And by Aug. 1, 1988, the stockpile may be about 3.8 million bales.

One reason has been the rising world demand for cotton. Along with reductions in the U.S. price supports, the demand has made American cotton much more competitive in global markets.

According to the department's Foreign Agricultural Service, world cotton use in 1986-87 is expected to be a record of 81.4 million bales, up from 76.9 million bales consumed last season.