Following the lead of Fairfax and Prince George's counties, the Montgomery County Council this week approved for the first time a $60,000 appropriation for advertising the county's amenities to prospective businesses.

The county plans to hire an advertising agency with part of the money and will begin placing ads in trade journals and developing handouts, according to James F. Giegerich, director of the county office of economic development.

"All these counties have been spending big on advertising," Giegerich said. "This is our first year for an advertising budget."

Fairfax County, for instance, has a New York public relations firm and an advertising agency handling some of its business and last month county officials went to New York to carry its message to the world. Fairfax's economic development authority has an $800,000 budget and spends about $500,000 of it on advertising.

Prince George's County recently embarked on a campaign in its economic development marketing division to attract more business.

In the District a business and economic development agency was created in an attempt to stop businesses from moving out and create incentives for the influx of firms.

"We haven't done enough to compete with other counties," Montgomery County Executive Charles W. Gilchrist told reporters several weeks ago.

"Fairfax County has an enormous budget," Giegerich said. The Montgomery economic development agency has a regular budget of $60,000 which will increase to $120,000 for next year with the next appropriation.

With homeowners across the country professing their desire for lower property taxes, many are increasing their efforts to bring in business to relieve the homeowners' tax burden.

In 1972 and 1973 in Montgomery County, commercial and industrial contributed about 26 percent of the jurisdiction's tax revenues, Giegerich said. "Now, it's only about 14 percent," Giegerich said. "We'd like to see it in the 20's."