Doctors, bookkeepers, barbers, refrigerator engineers and scores of others who do business in Arlington County will collectively be paying $1.4 million less in taxes next year as a result of cuts made yesterday by the County Board.

Arlington, which imposes some of the highest business taxes in Northern Virginia, is one of a number of Virginia jurisdictions under orders from the state to reduce gradually its several categories of business-tax rates.

Under a complicated formula set by state law, the county was obligated to cut about $1.1 million in taxes for 1986. But board members decided to slash another $350,000 as a signal to the business community that it may accelerate its schedule for cuts and reduce some rates below state ceilings.

"Our goal," said board member Albert C. Eisenberg, "is to try to do better than we're required to do under state law."

Last year, the county collected $15.8 million in the taxes, known as the business, professional and occupational license taxes, said Anna Lee Berman, director of the department of management and finance.

But because of the county's rapidly expanding commercial base and the planned opening of several new developments in the next year, including shopping centers in the Ballston and Shirlington neighborhoods, the county should collect at least $16.3 million from the taxes next year, she said.

The board's action came after it heard testimony yesterday from several business owners, the Chamber of Commerce and members of its fiscal affairs advisory committee and economic development commission who lobbied for larger cuts in some rates than those County Manager Larry J. Brown had proposed.

The speakers said that Arlington's rates put them at a competitive disadvantage with neighboring jurisdictions.

The complaints were particularly strong from the hotel and parking lot industry. For each $100 in gross receipts, hotels must pay the county 82 cents. Next year the rate will be 65 cents, still well above the state ceiling of 36 cents.

The parking lot tax of $4 per $100 of receipts was lowered to $3.95, still above the state rate of 36 cents.

Businesses, said Stephen Caruthers of the Chamber of Commerce, feel "a sense of frustration and being taken for granted."

Board member Ellen M. Bozman said she wanted the county to study the overall impact of taxes on businesses and residents. Citing real estate taxes and the personal property taxes on equipment that businesses pay, she said: "When you look at one tax, you're really not looking at the entire tax burden."

Among other reductions made yesterday was one to reduce the minimum annual filing fee for firms doing less than $4,000 in business annually from $25 to $10. The reduction is expected to affect those licensed to conduct a small amount of business at their homes, such as free-lance writers and consultants.