Tuition for undergraduates at Georgetown University will increase by 11.1 percent next fall to $8,500, the smallest rise in four years but still more than double the rate of inflation. Since 1980, Georgetown tuition has risen by 71 percent.

The new increase, which was announced yesterday following a decision last week by Georgetown's board of directors, is part of a nationwide pattern of moderating rises in college tuition costs, though so far it has slowed much less than general inflation.

With room and board included, the average bill for a Georgetown student next year will be $12,091. Including books, transportation and incidentals, total costs for the year will come to about $13,500, according to university treasurer George R. Houston Jr. This would put the expense for the four undergraduate years of college at about $54,000.

In 1980-81, at the start of the current price spiral, Georgetown's undergraduate tuition was $4,970. Despite the increases since then, the number of applications rose almost 10 percent in 1981, and then held steady for three years. It has increased for next fall's freshman class by a record 15 percent.

"Obviously, the demand is there and the aid available for students is substantial," said D. Kent Halstead, a research economist for the National Institute of Education. "Of course, the colleges are keeping up with their own costs, but if they feel they can get away with it, they are raising tuition as much as they can."

Among other local private colleges, George Washington University has announced a 10 percent tuition increase to $6,710 next year, and American University has raised its tuition 8.6 percent to $7,600. Elsewhere, price rises of 7 and 8 percent are widespread, compared with boosts averaging 11 to 13 percent over the previous three years.

According to the government's Consumer Price Index, inflation from 1979 to 1983 amounted to 37 percent but trailed off in the past two years to 6.1 and 3.2 percent.

But Halstead, who has developed a widely used Higher Education Price Index, said university costs, mostly wages, are more stable than prices generally, rising less when inflation soars and slowing less when it abates.

At Georgetown, Houston said, almost a quarter of the increased tuition revenue will be used for financial aid to needy students, which will rise by 24.9 percent. The remainder will provide for salary increases and for improvements in graduate programs and libraries.

Houston said the university will continue to meet 100 percent of the financial needs of all its students through a combination of grants, loans and campus jobs. Because federal aid has been steady for several years, he said, an increasing share of aid costs has had to come from the university's own funds, mostly through tuition.

"That's taking from the rich and giving to the poor," Halstead said. "A lot of universities are doing it, and I think it's a good idea so they can maintain a balance of socioeconomic groups."

Tuition at Georgetown medical school was raised 5.1 percent to $19,600 for next fall. This is the highest figure announced for any medical school in the country, but George Washington, which had the highest medical tuition this year at $18,750, has not yet decided on its fall rate.

Among public colleges, the University of Maryland has announced a 6.6 percent tuition rise, bringing next fall's charge for undergraduates who live in state to $1,420 and for out-of-staters to $3,972. George Mason has raised its in-state tuition 9.6 percent to $1,512. At the University of the District of Columbia, tuition for D.C. residents will rise 40 percent to $462, but it will remain the lowest cost college in the area.

Despite the big price difference between public and private schools, Halstead said, the demand for admission to prestigious private colleges has remained strong. "They're giving an elite education, but family incomes are going up and the federal aid is there," he said, "so they are going to charge what the traffic will bear."