A caption on page F1 in yesterday's real estate section reversed the identifications of Clara Morgan and Sandra Alexandra.

Although Washington, D.C., has one of the nation's strictest rent control laws, Lavonda Williams and her three small children are facing a tripling of their rent over the next few years.

Rent control doesn't apply to Williams' case, because she lives in public housing. The large rent increases--for Williams and millions of welfare mothers and food stamp recipients like her--are part of President Reagan's plan to cut the federal budget.

Williams' rent for her apartment in the East Capitol Dwellings project in Northeast Washington at the District-Maryland line will rise from $46 to an estimated $147 a month.

"It's going to mean less food," Williams said. She now pays about $35 a month more for food than her $125 food stamp allotment covers.

The administration's fiscal 1983 budget would raise rents for families living in locally run public housing and in so-called Section 8 subsidized housing by changing the rent contribution formula in a number of ways, primarily by including the value of food stamps as income.

In addition to these rent increases, the administration has proposed a more radical shift in the way it will subsidize housing for low income persons in the future. As part of a move away from building low income housing, the administration wants to put about 106,000 families on a "voucher" system that would provide them with a set subsidy and leave it to them to choose whatever apartment they can find in the private sector.

Now, the tenant's payment at public housing or a Section 8 building is determined by family size and income. The federal government pays Section 8 landlords whatever it takes to bring that payment up to a median "fair market rent." At public housing, the federal government now pays operating subsidies for maintenance of the projects operated by local housing authorities.

If a family like Williams' were in the proposed new voucher program, the head of household would receive an estimated $298 subsidy toward rent for a three-bedroom apartment of her choice and would have to pay the rest herself. Last year the median rent of a three-bedroom apartment in the Washington area was $422 a month.

While the administration's proposals soon will be the subject of intense debate in hearing rooms on Capitol Hill, it is already being seriously discussed in the living rooms at East Capitol.

Lavonda Williams sits on a sofa next to her neighbor, Clara Morgan, with three other East Capitol residents as they contemplate what the rent increases could mean for them and their families.

The walls of Morgan's neat living room are covered with framed family photographs. The bookcase contains a complete set of World Book encyclopedias, ceramic figurines and two games, Monopoly and Exploring Mathematics. The women's conversation rolls through anger to resignation to humor.

"I've been robbing Peter to pay Paul," says Grace Stewart, whose 17-year-old daughter and baby grandson live with her. "There is no way we can make it." She now receives $299 in AFDC and $158 in food stamps for the three of them. Her rent is $23 and utilities run about $114 a month.

These women are not the welfare queens that Ronald Reagan has portrayed in his speeches as driving Cadillacs and unwilling to work. All five women are trying hard to make ends meet.

For about two years the group has worked on developing a plan for managing janitorial services at the run-down public housing complex in the expectation of obtaining a contract from the District housing department. The contract has not come through so they have no salaries, but the women say the project has kept them from looking for other work.

Three of the group have tried to further their education. Williams says she needs to take only two more classes to earn a degree in mortuary science from the University of the District of Columbia. She figures she could earn about $14,000 a year and get off welfare once she finishes, but for now she cannot afford to go back to school.

Stewart says she was studying at the Brook-Wein Business Institute but had to quit in 1979 because she and her daughter became seriously ill.

Sandra Alexander, the mother of nine children, five who still live with her, was in occupational and industrial training but said she had to quit to take care of the younger ones. She says she now is terminally ill and must have X-ray therapy five days a week.

Caroline Gantt was recently laid off from her job at the D.C. housing department but is waiting to see if the janitorial contract comes through before looking for another job.

The five women take a defiant attitude toward the inclusion of food stamps in the income calculation.

"We're going to pay the rent increase with food stamps. If they don't take it the stamps , they are going to have a whole lot of people down there" at the housing department protesting, Stewart said. "They don't have a choice."

"Probably the single most severely cut part of the budget is in housing assistance," said Robert Greenstein of the Center on Budget and Policy Priorities, which is fighting deep benefits cuts in the budget. The changes in the contribution formula would mean "a doubling or tripling of rent for a lot of people," he said.

Lavonda Williams' case is a typical example of how these proposed changes would affect an individual family, because most have female heads of household with two or three small children, according to housing assistance experts.

Besides her food stamps, she receives $366 in Aid to Families with Dependent Children. Williams' family of four lives in a three-bedroom unit at the East Capitol Dwellings, and she about $124 a month in utilities. Her $46 monthly rent is 25 percent of her income, adjusted for family size and not including food stamps, minus a $15 utility allowance, under the current federal formula.

Under the budget plan, her rent contribution would rise to 30 percent of her income--which would include food stamps--over the next five years. It is unclear what will happen to the utility allowance, which now covers only a fraction of her true utility costs.

The increase to 30 percent already has been approved by Congress, but the administration's plan would double the yearly increase from a maximum 10 percent to 20 percent for those currently getting aid. For new recipients, the 30 percent rule would go into effect immediately.

Most of the proposed new-housing vouchers are intended to go to families currently in the Section 8 housing program, but some people in public housing also may get them if their projects are demolished or otherwise abandoned and they are forced into the private housing market. The East Capitol Dwellings are supposed to be rehabilitated, but Williams and her neighbors question whether it will get done because the project depends on federal Housing and Urban Development funds, which may be in jeopardy.

If Williams were included in a voucher program, the payment would be calculated differently than under the current system, and it is impossible now to determine how much she would pay.

A "payment standard" equal to the "40th percentile of the median rent" in the area would be established for the three-bedroom apartment required under federal standards for her size of family. (The payment standard is a reduction from the fair market rents used in current assistance formulas, which equal the median in the area). From this amount, 30 percent of the recipient's adjusted income would be subtracted to determine the amount of subsidy.

The 40th percentile of median rent in the Washington area for a three-bedroom apartment this year is $428 a month. Cranking in the rest of the calculations, a family like Williams' would get a subsidy of $298 a month. The family then would have to find its own apartment and pay the difference not covered by the federal subsidy.

The administration says housing vouchers will be a more efficient means of providing assistance and will give recipients the incentive and flexibility to find the best housing value. They could end up paying less rent if they bargain well, the administration argues.

But low income housing experts say that shortages of rental housing, particularly in urban areas, will make it virtually impossible for those receiving assistance to compete effectively for the small supply of moderately priced apartments.

"The reports we get from housing counselors is that current fair market rents aren't high enough for people to find decent housing" under current programs similar to the voucher idea, said Cushing Dolbeare, president of the National Low Income Housing Coalition. The fair market subsidy standard is being reduced under the new proposal.

"Some poor families would probably feel they had no choice but to move out of subsidized housing and live in cheap substandard housing so that they can clothe their children and meet other needs, or drop out of the food stamp program so that they can afford to pay the rent," states an analysis by the Center on Budget and Policy Priorities on rent increases.

At the East Capitol Dwellings, the women in Morgan's living room already have made a number of hard choices. As they wind up their discussion with a mixture of realism and panache, their feelings seem to be summarized by the inscription on an plaque sitting on the coffee table:

"God grant me the serenity to accept the things I cannot change, the courage to change the things I can, and the wisdom to know the difference."