With all the problems farmers face -

including drought, high production costs, foreign imports, over-production and surpluses - how do many American farmers stay in business?

They work off the farm at second jobs.A study by the U.S. Department of Agriculture, reported in a bulletin published this month by the Utah Agricultural Statistics Service, says nearly half of the net income of American farm households comes from off-farm sources.

Since 1960 - except for two peak periods - the study says, off-farm income has accounted for 40 percent to 55 percent of the net incomes of farm households.

Dependence on off-farm income varies considerably throughout the nation and correlates generally with farm size, what is grown and where the farm is. In Davis County, for instance, many farmers have full-time jobs at Hill Air Force Base or drive school buses for Davis School District.

In addition, in many farm households in Utah and elsewhere in the nation, wives have taken jobs as store clerks, secretaries, school-teachers, saleswomen and factory workers. In some instances where brothers or a father and his sons work a farm, all have taken jobs off the farm to bring in needed extra income.

USDA economists say the smaller the farm the greater the average reliance on off-farm income. On the smallest farms, more than 96 percent of the total household income in 1986 came from off-farm sources.

Nearly three-fourths of America's 2.2 million farms have annual farm product sales of less than $40,000. These small farms actually hold about 30 percent of the nation's farmland, but take in less than 10 percent of the total receipts from crop and livestock sales.

Only 4 percent of the nation's farmers - whose farms gross $250,000 or more annually - report earning 95 percent of their incomes from farming.

And, despite high average incomes for the large farms, expenses are so high and net profits so low, the USDA estimates that 20 percent of these households have actual incomes below the poverty level.