The real estate tax increases imposed in Northern Virginia last week underscore, once again, the need to analyzethe reasons for rising government costs and the need to come up with the most equitable tax structure possible to pay for them.

In Alexandria and Arlington, property tax bills of typical homeowners, those with homes close to bthe median value, were increased by about 6 or 7 percent. In Fairfax County, typical residential real estate tax bills were increased abput 4 percent.

This means that many Arlington and Alexandria residents will again see a larger portion of their incomes going for the costs of services provided by state and local governments.

The increase may be small in comparison to those ofreceny years, but in those receny years there was an enormous rise in the share of personal income paid to the governments closest to home.

In Fairfax, the rising incomes of typical homeowners probably will offset the property tax increases and maintain something like the present split between the share of income individuals keep and share taken by county and state.

However, the Fairfax taxpayer is justified in wondering why there is a tax increase at all. Fairfax, as opposed to Arlington and Alexandria, is still a growing jurisdiction. It is always reasonable to hope that the addition of new residents, business and construction will pay for the increasing costs of government. Once again in Fairfax, this did not happen.

Only in Prince William County, the fourth most populous jurisdiction in Northern Virginia, is there cause for celebration. The Board of Supervisors continued the present real estate tax rate and there was no reassessment. This means tax bills will remain unchanged and that increased county spending will be paid for with the growth in tax revenues from new residents, houses, buildings and businesses.

Not everyone in Prince William thinks this is a good thing. There was a significant lobby, chiefly parents of school children, who wanted a tax increase.

State Sen. Charles J. Colgan (D-Prince William), a former county supervisor, monitored these pleas with some awe. "I was amazed at the number of people demanding higher taxes for the schools," he said. but Colgan thinks the board did the right thing and points out that tax-payer joy in Prince William may soon be tempered by a three-fold increase in water and sewer bills.

Back in the inner suburbs, an office-holder who has been living with the political consequences of high real estate taxes for 10 years in Sen. Wiley F. Mitchell Jr. (R- Alexandria), who was vice mayor of the city before being elected to the state Senate in 1973.

During those 10 years the tax bill on a median-priced home in Alexandria has at least doubled, and now is about $1,100 a year, or $90 a month on a payment.

This remarkable increase has come despite a surge in revenues from sales taxes, enarted in the mid-1960s, and despite revenues form new and increased taxes on utility bills, automobiles, gross business receipts, motel room occupancy and even ambulance use. Many of these taxes were levied in an effort to keep real estate taxes down.

Mitchell believes in the cause of homeowning real estate taxpayers and has a healthy respect for their political clout. Many of his constitutents are tenants, but of homeowners he says, "They probably are the most active and influential segment of the taxpaying constituency."

So this year Mitchell introduced a bill that would have permitted Alexandria and other cities and counties to tax commercial properties, and indirectly their office and paprtment tenants, at a rate up to 25 percent more than the homeowner rate.

He said the bill was justified by the disproprtionate increases in homeowner assessments, which have been skyrocketing along with market values, while commercial property assessments, keyed to landlord profits, have remained relatively stable. The bill passed the Senate but was relegated to a property tax study by the House.

The Mitchell bill was one of those legislative efforts going on in Virginia and other states to disengage the often illogical connection between tax biurden and the value of the house you live in.

"Fundamentally," he said in an interview, "all these debates over the real estate tax come down to the question of how do you pay for the cost of local government ... The fair market value of the house you live in is clearly not an equitable means of apportioning the cost of government."

Mitchell can recite all the inequities of the real property tax, including the often overlooked fact that higher income homeowners are able to pass on a larger share of their property tax increases to the federal and state governments through deductions froim progressive income taxes. In the end, however, he believes that property tax relief may require broad government changes.

If it cannot be achieved through restructuring the property tax itself, he said, it may take a combination of new local option taxes for cities and counties and greater assumption of local government costs by the state.

If all else fails, he said, it may come to imposition of a statutory or constitutional ceiling on state and local government spending increases. "I'm not prepared to say that I wouldn't support such a device." he said. "There are people in Virginia talking about such a proposal now, and they are not unreasonable people."