HERE IS an image: a welfare mother has moved to the area where she lives to get the highest welfare benefits available. She is fat, happy and probably pregnant, with a gaggle of untended children already scrambling around her. In front of her house is a golden Cadillac, the one she gave her beer-drinking boyfriend. For many people who have worked for what they have, this image is surely a source of great resentment. Surveys show that even though people believe in helping the poor through welfare, they also regard welfare cheats and the foul-ups in the welfare system as so upsetting that they don't want to support the welfare system. But that image of the typical person on welfare has always been overblown -- and just how overblown is the subject of a report by the Greater Washington Research Center.

According to the report, the average monthly payment in Aid to Families, with Dependent Children (AFDC) was $230 in 1978, an increase of 13 percent since 1970. In the same eight years, the Consumer Price Index rose by 68 percent. The number of people in what are sterotyped as "baby-breeding welfare families" actually declined from four to three people between 1970 and 1977. During the same period, the number of people in all households in the greater metropolitan Washington area was falling at less than half that rate.

Also, despite variables in payments, there is little movement between the District, Maryland and Virginia. The biggest change in any area's welfare population, according to the report, was in the Maryland portion of the region, where welfare recipients declined from 24 to 21 percent of welfare residents in the metropolitan area. In addition, welfare payments by local governments have stabilized, having risen by only 3 percent since 1975. The absence of any rise in payments results in welfare families' receiving only half of what the Bureau of Labor Statistics estimates they should have to make ends meet. In addition, the number of welfare recipients in the area is decreasing at a rate of over 15,000 cases per month.

In the early 1970s, the welfare caseloads increased drastically. With that increase came increased fraud and other problems. But that time has passed. Yet in the District, a lack of concern still is reflected; no increase in welfare payments is planned for next year. In the past few years, there have been 5 percent increases while the cost of living has risen at a rate of more than 10 percent. Now the new 5 percent increase for next year has been removed for budgetary reasons. But to refuse poor people with children this slight increase -- only 5 percent -- in the face of the inflation is a mean and pointless economy.