Virginia's liquor board has suggested that its stores in the Washington suburbs be permitted to sell whiskey and other spirits at lower prices than at stores downstate in order to compete with the discount prices available at many stores in Washington and Maryland.

In testimony before a legislative committee in Richmond, state Alcoholic Beverage Control Board chairman Archer L. Yeatts Jr. recommended also that some private retail stores in areas remote from state-owned ABC stores be permitted to sell liquor on an "agency" basis.

For the first time in years, Yeatts told the House General Laws Committee, ABC profits declined from 1981 to 1982, showing that "obviously state ABC stores are not capturing their share of . . . sales" to Virginians. The proposal for lower prices in the Washington area, where many consumers buy supplies in discount stores of the capital, seems sure to draw protests from downstate legislators who regard it as a subsidy of affluent Northern Virginians.

Moreover, the ABC Board's own figures seem to belie the idea that Northern Virginians shun making their purchases in state-owned stores. Statistics reported by a board spokesman yesterday showed that, in the last fiscal year, stores in Northern Virginia -- which has 19.9 percent of the state's population -- produced precisely 20 percent of the sales of distilled spirits.

That's 1.79 million of the statewide sales of 9.36 million gallons, producing revenues of $54.1 million of the statewide total of $270.5 million.

There is a precedent in at least one state -- Maine -- of a state liquor monopoly lowering prices to compete with an adjacent state. To meet the cheaper prices at New Hampshire's store near Portsmouth, just across the river from Maine, the Maine Legislature in 1973 authorized its own state ABC store at Kittery to cut prices by 10 cents a fifth below New Hampshire's. Maine bar owners, who originally took advantage of the cut, since have been prohibited by law from buying at the cut rates. Maine also considers the use of "agency" stores in remote towns a success, spokesman Bob Tilson said.