YOU KNOW the TV ad, the one for the United Negro College Fund: "The mind is a terrible thing to waste; donate to the college of your choice." It's the first week of classes in a new academic year at the University of the District of Columbia. That's an occasion to consider the prospects for that kind of youngster, talented but poor, in this city.

UDC was formed in 1976 by a merger of the District's three public college -- D.C. Teachers College, Federal City College and Washington Technical Institute. This new university deserves strong community support. But how far should it go? For example, District taxpayers spend $6,065 for each student at the university -- more than any state except Alaska spends for higher education. UDC's subsidy from the District government during the 1979-80 academic year was 91 percent above the national average of $3,173 per student. It isn't necessary to be among UDC's critics to ask the question: is the university spending too much money?

The answer is a qualified yes. The cost of educating a student at UDC will come out high in national comparisons with other public colleges. One reason is the low tuition -- just $199 this fall. Another is that UDC's students are mainly low-income residents of the District with mediocre high school records who are poorly prepared for college-level courses. That makes small, remedical classes and counseling services a necessity for their academic survival. But the evidence so far is that even with that assistance few students ever reach the junior or senior level; nearly two-thirds of the university's current students are freshmen. The enrollment has been declining, and the average student is taking few courses.

Third, efforts to reduce UDC's costs are partly hampered by the large number of faculty and administrators whose high pay and positions are protected under the law that established the university. In a recent article in this newspaper, Lawrence Feinberg noted that UDC offered 11 different beginning French courses in the 1979-80 catalog even though most classes had fewer than 10 regular students. Worse, the ratio of administration to students is unacceptably high.

All of these factos may explain the university's high costs. But because some are unavoidable for good reason, UDC has a special obligation to cut down where it can. There are several ways to achieve that goal. Raising the tuition up to levels comparable with nearby states seems the most obvious. That in no way implies a retreat in community support of the university -- or students' access to it. There are several federal loan and grant programs available to college students in need of financial aid.

It is wrong in principle that UDC, amidst clear evidence of overstaffing, should be exempt from budget cuts at a time when funds for the city's public schools are being sharply reduced. Higher education is important, but hardly more important than the school system from which its students come. College education is getting more expensive. UDC's high dropout rates and redundant staffing are a threat to the public support that it will need for the years ahead. The challenge now is to provide a college atmosphere in which serious students can complete the serious work they begin.