Falling stock prices usually give investors a sinking feeling, but Geico Corp. stockholders should benefit from a decline in the price of the company's shares, according to securities analysts.

That's because the price decline has prompted Geico officials to authorize purchase of 500,000 of its common shares, a move which will increase the earnings per share for the remaining stock.

The decision to accelerate reduction in the number of outstanding common shares was made after the company withdrew its friendly bid to acquire the remaining shares of one of its subsidiaries, Government Employees Financial Corp. (Gefco). The $11 a share offer to acquire the remaining 33 percent of Gefco stock was withdrawn after some of the subsidiary's minority shareholders rejected the bid as too low.

When the offer was made on May 19, Gefco stock was trading at $7.50 a share bid and $8 a share ask.

"We were surprised the offer was rejected because we thought it was a fair price," said Geico public affairs director Robert W. Jackson. "Some of the minority shareholders felt the company was worth more than we felt it was worth."

Geico can be expected to make another bid for the remaining Gefco shares, according to securities analysts. The acquisition would make all Geico subsidiaries wholly owned and would save between $100,00 and $200,00 a year in administrative and filing fees, Jackson said.

Other Geico subsidiaries acquired in the last three years include Criterion Insurance Co., a standard risk automobile insurer acquired in January 1980, and Equitable General Insurance Co., acquired for $5.6 million in cash on April 1. Equitable General sells both automobile and homeowners insurance.

Geico found itself in a highly favorable liquidity position after the sale of Government Employees Life Insurance Co. last December for $90 million.

Geico is currently awaiting regulatory approval for its bid to acquire Garden State Life Insurance Co. The bid includes $2.5 million in cash and $7.5 million in 15-year debentures.

Since 1979, Geico has retired more than 14 million, or 40 percent, of its common stock. Financial difficulties had forced Geico to increase the number of common shares and equivalents--stock convertible into common--from 17.7 million shares in 1975 to a high of 34.2 million in 1977. The company now has 20.3 million common shares and equivalents outstanding.

Company officials say they will continue to retire shares as long as market conditions make purchases attractive.

Geico, which peaked at $27.34 a share on Jan. 4, closed Friday at $22.

"We don't intend to head in the same direction as the industry, and that means we believe in the profitability of our underwriting business," said Jackson. "Most of our profit continues to come from preferred risk automobile insurance, although investment income will also be strong."

In the first quarter, Geico had net income of $16.9 million (82 cents a share) versus $16.4 million (75 cents) for the same period last year, a 27 percent increase.