Ronald Reagan, who has promised to scuttle cost-inflating federal regulations, might do well to study the Case of the Vanishing Bathtub. It's a tale of how even such modest deregulation as easing a few housing-construction rules can consume an entire political stint in the capital.

President-elect Reagan pledged during his campaign to cut "excessive and unnecessary government regulations which impede the production of houses or add substantially to their cost." As it happens, President Carter's Department of Housing and Urban Development, after nearly a four-year effort, is just about to do something along those very lines. HUD will soon publish in final form a new, simplified rule book governing construction of houses purchased with government-backed mortgages.

Among other things, HUD is eliminating requirements that builders furnish towel bars in the bathrooms, closets in the bedrooms, and shelves in the linen closets. It is tossing out a requirement that balconies and roof decks have railing at least 42 inches high. And it is junking rules that dictate what sort of trees and shrubs must be provided for landscaping.

Builders can still include all of these things, but they no longer will have to. And they will be able to omit the currently mandatory bathtubs and put in shower stalls instead. The thinking is that consumers have enough sense to decide for themselves whether they want tubs or showers, and they don't need Washington regulating the shrubbery.

The revisions could help would-be home buyers who find prices soaring out of their reach. The new rules will allow builders to put up somewhat smaller, cheaper houses. HUD estimates that just reducing its minimum sizes for rooms and lots will allow a $4,100 saving in putting up the smallest allowable house.

Builders, however, say the changes are too modest to produce extensive cost cuts. The relaxes rules will "allow the designer to take advantage of some economies," says Eric Marten, chief engineer for Ryan Homes Inc. But the National Association of Home Builders, which wants HUD to scrap even more rules, says it sees little if any savings.

The total volume of the HUD rule book is being slashed by about 40 percent, to just over 70 pages of fine print. But most of the shrinkage comes from eliminating lengthy quotes from other rule books, not from reductions in the regulations themselves.

Although this rule-book revision was begun soon after Jimmy Carter took office in 1977, by the time the regulations go into effect there will be a new President (and a new HUD secretary).

One reason for the slow pace was he, inside HUD, some officials staunchly resisted rewriting the housing-construction rules. People involved in the often-acrimonious haggling say that many in the department simply didn't accept the idea that home buyers needed less protection. Eliminating the bathtub requirement "really seemed to set some people off," says an official who took part in some of the negotiations.

The process began in 1977 when President Carter appointed a Task Force on Housing Costs, which eventually urged a cutback in regulations. That took until mid-1978.

Another year was consumed in writing a proposed new rule book. "This is only one of many things we were working on," a HUD official explains.

Finally, a year was taken up by internal "clearance," in which one set of HUD bureaucrats pretty much demolished the deregulation that another set had proposed.

The result was a deadlock. By mid-1980, the proposed new regulations had been extensively compromised. For example, a requirement for a coat closet by the front door, axed in an early revision, had been put back. "When the product finally got to me, it was not very satisfactory," recalls HUD Secretary Moon Landrieu. "We had got back virtually to where we had started from."

Landrieu says he then issured some command decisions, ordering the original deregulation proposals to be essentially reinstated. Out went the coat-closet requirement. "I made the decisions myself," he says. "It was the only way it could be resolved."

Could a determined Reagan administration move such things along faster, perhaps by issuing command decisions from the start? Perhaps. "We can move like a whip" if necessary, declares one HUD official involved in the drafting of the bathtub rule. "It only takes five minutes to burn the rule book." But while incoming administrations inevitably vow to cut through the bureaucratic morass, the federal bureaucracy has shown that it has ways to resist those who would undo its handiwork.

The rules originally were written just after World War II to protect consumers from shoddy housing. In those days, local building codes didn't often apply to homes. The standards for homes financed with loans backed by the Federal Housing Administration and the Veterans Administration became, in effect, a national building code for residential construction and a blueprint for the suburbs that mushroomed during the 1940s and the '50s.

Housing officials say the one-house, one-bathtub rule made more sense in the 1940s, when 45 percent of American homes had no or only partial plumbing facilities. And in fact, with the rule book in effect, the quality of American housing increased notably. By 1960, only 13 percent of U.S. homes lacked some or all plumbling fixtures.

But today fewer than 3 percent of houses lack full plumbing facilities. Most new homes exceed HUD's minimum standards, and most localities have residential building codes based on uniform regional model codes.

(About 25 percent of new-home sales are covered by government-backed mortgages and thus subject to the HUD rules.)

HUD's new rule changes haven't produced a peep of protest from consumer groups. The only consumer organization that commented on the proposals, Rural America, said the regulations should be reduced even more to allow cheaper housing.

The group's housing expert, David Raphael, says HUD's requirement for plumbing vents at least 4 inches in diameter is wasteful because smaller vents would do. He also says the agency's scaled-back requirement that bedrooms have at least 70 square feet of floor space is still too high and would have added at least $1,000 to the cost of a model home that the group built in Mississippi. The home has two bedrooms of 60 square feet each, he says, and they were "totally adequate for one or two children per bedroom."

The regulations that Secretary Landrieu wants abolished haven't found many defenders among 38 organizations that submitted comments on the proposals. Most comments were from industry associations seeking even more deregulation, except where their self-interest is involved. The builders, for example, want HUD to require less concrete, while the Portland Cement Association wants it to require more.

The only group flatly opposing deregulation is the AFL-CIO, which denounces the HUD plan as "a definite retrogression in American housing standards." The labor federations say buyers who seek VA or FHA financing often are first-time buyers who can't expect to know what features to look for. "There would be a tendency for a reduction of standards without reductions of prices," it warns.

So far, though, no complaints have been filed by two presumably affected industry groups -- the makers of bathtubs and of rubber ducks.