Geico Corp., the Washington insurance holding company, reported a 22 percent increase in earnings per share from operations during the first quarter of 1979 although business was essentially flat when compared with the same period last year.

In separate reports, Government Employees Life Insurance Co. reported an 8 percent decline in profits from the first quarter while the Rouse Co., a columbia real estate development firm, listed higher operating earnings and announced an increased dividend.

Geico, the holding company for Government Employees Insurance Co., reported operating profits after taxes (not counting tax benefits related to earlier losses and gains or losses from investment transactions) of $14.9 million in the recent quarter (44 cents a share) compared with $13.2 million (36 cents) in the 1978 period.

Total net income of the automobile insurance company's parent firm was $19.8 million (58 cents a share) compared with $20.6 million (58 cents) a year earlier. Net income includes tax benefits that boosted earnings by $4.9 million and $76 million in the first quarters of 1979 and 1978, respectively.

Written premium volume for Geico, at $142 million in the recent quarter, was essentially unchanged from last year and Chairman John Byrne said yesterday that although sales to new customers continue to improve steadily, growth remains slower than planned.

Geico suffered a sharp increase in collision and property damage settlements in the first quarter, because of higher replacement and repair parts costs. But there were offsetting factors: a reduction in accident frequency, fewer policies in force and fewer polices assigned under state laws for consumers unable to acquire insurance in the open market.

Geico board members, meanwhile, have authorized purchases from time to time up to 1 million common shares or equivalent, in the open market.

Government Employees Life Insurance Co., in which Geico Corp. is now the major investor, reported first quarter earnings dipped to $1.95 million (43 cents a share) from $2.12 million (47 cents) a year ago.

Net investment income rose 14 percent to $2.9 million and sales of individual life policies rebounded substantially-up 21 percent to $48 million. As of March 31, the firm had policies in force totaling $2.36 billion, an increase of 2 percent from one year earlier

Rouse Co. earnings from operations before non-cash charges rose 43 percent in the first quarter to $2.66 million from $1.86 million a year ago. The firm's dividend rate has been increawed to 7 cents a share quarterly from 5 cents in previous periods.

Revenues rose to $24.7 million from $23.6 million while net income declined to $773,000 from $1.8 million-reflecting a $1.3 million one-time gain from foreign currency translations in the year-earlier period.

rChairman James Rouse and President Mathias DeVito said all divisions showed strong gains in the 1979 quarter, with retail sales at the company's shopping centers up 5 percent and "strong" April sales indicated.

A new Tallahassee mall, Governor's Square, is scheduled to open during the summer. A mall in Austin, tex., is being expanded and construction has started on new shopping centers in downtown Baltimore and Santa Monica, Calif.

Planning Research Corp., a large professional services company in Washington, reported a 22 percent decline in earnings for the third fiscal quarter ended March 31. President John Toups said the lower profits reflected a loss on the sale of a division and establishment of reserves to cover possible losses from business in Iran.

Although revenues rose to $65 million, from $57 million, earnings fell to $949,000 (14 cents a share) from $1.2 million (18 cents). Nine-month earnings rose to $3.87 million (56 cents a share) from $3.48 million (51 cents) as sales rose to $595 million from $158 million.

The third-quarter after-tax operations included a $3.2 million gain after selling a London computer software firm, Logica; a $598,000 loss from selling a European division; and a loss of $2.5 million to cover losses from Iranian operations where PRC had contracts with the ousted government.

PRC also announced receipt of a $1.5 million, 30-month contract to provide engineering support and assist in development of Navy systems.