GREENWOOD, Miss. (AP) _ As cotton planters begin harvesting in this Delta county and around the nation, farm officials are predicting that higher market prices will save the U.S. government $1 billion in subsidies.

''The outlays will probably be a billion dollars less this year than last year,'' said Dean Ethridge, director of economic services for the Memphis, Tenn.-based National Cotton Council. ''The difference is that the farmer will be getting the money from the market and not the U.S. government.''

In 1986, market prices for cotton dipped to an average of 53.8 cents per pound, the lowest price since 1975. But Ethridge said the federal government gave growers $1.8 billion in subsidies to make up the difference between the market price and a target price of 81 cents per pound.

Since January, the market price has risen from 57.2 cents to 73.1 cents, while this year's federal target price has been lowered to 79.4 cents.

Ethridge said demand for cotton remains strong because poor weather has prevented a bumper crop in China, the world's leading producer. Another major producer, India, has indicated it may import cotton because of poor harvests.

He said the falling dollar also has strengthened demand for U.S. cotton.

The combination of factors brought a smile to L.A. Gray, manager of Leco Gin Co., a busy cotton gin near here in an area that boasts some of the nation's richest fields.

''I'm looking for the biggest year I've ever had,'' said Gray, who started ginning at the 45-year-old plant Friday. Screened cotton trailers already are lined up outside the plant, and Gray is hoping for a long season.

Mississippi, ranked third nationally in cotton production after Texas and California, should expect yields of cotton up 30 percent this year, said Hugh McWilliams, deputy state statistician for the Mississippi Crop and Livestock Reporting Service in Jackson.

''We have a good crop and it's starting to come out of the fields now,'' McWilliams said.

McWilliams said the service in August projected yields of 793 pounds of cotton per acre in Mississippi this year, up from 571 pounds per acre last year. In addition, he said, an estimated 1.09 million acres of cotton were planted this year, up 9 percent from last year.

Without torrential rains or other severe weather, cotton and cottonseed, which contributed $318.3 million to Mississippi's economy last year, could challenge poultry's $488.6 million top agricultural share in revenue this year, McWilliams said.

Amid the good market news, however, the Southeast has the worst infestation of boll weevils in 15 years, said entomologist Bob Head of the Mississippi Cooperative Extension Service.

Head said that without drastic measures, damage from the pests could double last year's $10 million figure in the state.

A mild winter enabled many of the beetles, which prevent cotton from blooming by puncturing the bud, to survive and increase their numbers this season, Head said.

Ed King, a laboratory director for the U.S. Department of Agriculture in Stoneville, said another factor contributing to the weevils' return was the use of pesticides that attacked bollworms and budworms but not the weevils.

King and Head said producers should take advantage of the strong market and spend more money on insecticide.

''It will be a good year from the standpoint of price,'' Head said. ''It will be a good year from the standpoint of yield. But it won't be done cheaply.''