Taxable private property acreage in the District of Columbia has shrunk almost 24 percent in the past 40 years, yielding to an ever expanding federal government and such tax exempt entities as universities and foreign embassies, according to city land records.

The decline, which has shown signs of leveling off at least temporarily in recent years, has eroded the city tax base, deminished the already limited space available for private housing and helped drive up the price of homes to record levels, say officials of the D.C. Property Assessment Administration.

According to their figures, taxable land in the city shrank from 17,989 acres in fiscal 1935, the earliest year for which figures are available, to an estimated 13,749 acres for the current fiscal year -a drop of 23.6 percent.

As private lands have been gobbled by the government, universities, embassies, churches, Metro, Streets, freeways and other exempt properties, taxable acreage has declined from 44.8 percent of the District's total land surface in 1935 to 34.2 percent today.

Despite what appears to be a temporary lull. this trend is "undoubtedly going to keep going on because this up by the government. universities, embassies churches, Metro, streets. is the federal city," says Donald R. Beach, the District government's chief assessor.

"It raises problems in financing for the city," he said. "It simply means there is less property available to generate revenues."

"A lot of storefront churches are buying up adjacent lands," he said. ". . . Universities are all expanding . . . We're losing buildings (in the private sector), making a tighter housing demand . . . and that drives prices up."

All told, the city's 40,146 acres (62.75 square miles) of land surface has a total assessed value estimated at $20.9 billion with a potential for generating $382.3 million in taxes at the current rate of $1.83 per $100 of assessed value.

But since almost two-thirds of the land is exempt from taxation, the city is expected to realize only about $194.3 million in property taxes in fiscal 1979. The annual federal payment - now pegged at a possible maximum of $300 million - is designed to compensate for revenue losses in this uniquely federal city, not only for untaxed federal land but for other limitations on the city's taxing authority such as restrictions on income and sales taxation of military and diplomatic personnel.

The continued shrinkage in taxable Private property makes it difficult to maintain tax levels sufficient to meet annual budgets, despite inflation in the real estate market, says Beach. The D.C. Tax Revision Commission has recommended several alternative sources including a requirement that currently exempt properties likes churches and embassies pay 10 percent of what they would be billed if they were taxable. The proposal has been resisted by many political leaders in the city.

Lawrence Woodwell, review supervisor in the assessor's office, said that many old estates and "mansion type dwellings" that once generated huge taxes are no longer supportable by private families and have been purchased by foreign governments as embassies and chanceries, removing them from the tax base.

A prime example is the 22-acre Firenze estate bordering Rock Creek Park at Broad Branch Road NW, purchased by the Italian government in December 1976 for $4.3 million from the Polly Logan family.

The wooded estate and 40-room mansion are now officially assessed at only $2.36 million, District officials say the $4.3 million sale price may have been inflated and not typical of comparable properties.

If it were not exempt as an embassy-chancery complex, it would generate $43,188 in taxes per year, even at its current assessment.

The expanding federal government, however, has put a much bigger dent in the private taxable property of the city.

The new J. Edgar Hoover FMI building, for example, replaced an entiref 5-acre plot of revenue-generating shops, liquor stores, restaurants and other outlets in the downtown block bounded by Pennsylvania Avenue and Ninth, 10th and E streets NW.

Assessors say it is impossible to estimate what the block would generate in taxes today if it still consisted of private retail businesses, but the present mamoth FBI building and its grounds are officially assessed at $140 million. If the FBI paid taxes, it would owe the city $2,562,000 a year.

The federal government as a whole now occupies nearly one-third of the District of Columbia - 32.1 percent of the land area, excluding an unknown number of streets and alleys also titled to the federal governmet, according to land records.

Included are the Mall, Capitol, Washington Monument grounds and surrounding enclaves of government office buildings, plus Rock Creek Park, Bolling Field, St. Elizabeths Hospital and numerous other properties totaling 12,373 acres, a growth of almost 2,000 acres since 1935.

The District government occupies a much smaller amount - 1,375 - and has grown by only about 330 acres since 1935.

Private exempt properties - embassies, churches, universities, libraries, cemeteries and hospitals - occupy 2,362 acres, a growth of 784 acres since 1935.

Street and alley rights-of-way take up a combined total of about 9,787 acres - nearly 25 percent of city's land surface. With the construction of freeways downtown and new residential streets in the outer areas, right-of-way space has increased more than 900 acres since 1935.

This trend has slowed in recent years, however, with the near saturation in road development, the moratorium on freeway construction and the closing of numerous alleys for realestate assemblies. CAPTION: Picture 1, The 900 block of Pennsylvania Avenue NW was filled with taxable private retail businesses in this 1968 photo. The Washington Post; Picture 2, Today the J. Edgar Hoover FBI Building occupies the block. If taxable it would bring in $2.6 million a year. The Washington Post; Charts 1 and 2, no caption; The Washington Post