Geico Corp. and its subsidiary Government Employees Life Insurance Co. both reported modest increases in earnings yesterday.

Geico Corp. reported its first-quarter profits increased to $16.4 million (75 cents a share) from $16.2 million (65 cents) and said earnings of Government Employees Life climbed to $1.96 million (44 cents) from $1.94 million (43 cents.)

Premium income for Geico Corp. increased to $164.3 million from $159.4 million for the quarter while investment income was up 8.4 percent to $19.9 million from $18.3 million.

MCI Communications Corp. reported a 62 percent increase in revenues and a 58 percent jump in profits for the fiscal year ended March 31.

Revenues of the Washington long-distance phone service firm increased to $234.2 million from $144.3 million and earnings climbed to $21.1 million (24 cents a share) from $13.3 million (20 cents).

MCI Chairman William McGowan said the number of MCI customers increased seven-fold from 40,000 to 280,000 due to a national advertising campaign launching MCI's residential marketing program.

The $2.4 million cost of that program was largely written off during the fourth quarter, when MCI profits increased to $7.9 million (11 cents) from $5.2 million (10 cents). Fourth quarter revenues climbed to $71.8 million from $43.4 million.

Consolidated Rail Corp., the government experiment in railroading, which the Reagan administration wants to liquidate, yesterday reported the smallest first-quarter loss in its five-year history.

Conrail lost $65.9 million compared with a 1980 first-quarter loss of $95.4 million.

Conrail reported revenues of $1.062 billion for the first quarter of 1981 compared with $1.015.