Lower lease rates and increased leasing activity could lead to a shortage of office space in Fairfax County by the end of 1982, according to a study just released by the Fairfax County Economic Development Authority.

The county has a total of 18 million square feet of office space, of which about 912,000 square feet are available for lease. The study said that an average of 113,000 square feet has been leased each month so far this year. About 1.2 million square feet is under construction, mostly in the Baileys Crossroads, Fairfax West and Tysons Corner areas.

"If leasing activity continues at its present level, 2,411,515 square feet more than the space immediately available and under construction will be absorbed by the end of 1982," the study said.

Lease rates in Fairfax County are about half the rate for comparable office space in downtown Washington. The range is from $10 to $15 a square foot for new office space. The study said rates would not pass the $20 level before 1983.

The Washington law firm of Anderson and Pendleton has moved into its new offices at 1000 Connecticut Ave. NW. Leasing for the 4,100-square-foot space was arranged by the Smithy Cos.