What was going on when I was born?

Notices of fines totaling $4.2 million have been mailed in recent days to thousands of homes and industries in northern New Jersey in the first concerted campaign by water companies to stop violations of a four-month-old water rationing plan covering six counties. The Hackensack Water Company sent out notices of the largest amount of penalties among the four major suppliers involved - $2.2 million to nearly 7,800 homes and businesses. Newark's Water Department follows with $1.3 million. The payments will go to the state, which has yet to decide how to use them.

After 13 hours of talks, the Government and leaders of the Solidarity trade union movement reported agreement early this morning on two of the three major issues that had caused strikes throughout the country. At a news conference at 4 A.M., exhausted spokesmen for the two sides said they had agreed on a formula for a shortened workweek. While accepting the principle of a 40-hour workweek, the Government would make three out of every four Saturdays nonworking days this year - or one more a month than the Government wanted and one less than the union organization demanded. The exact allocation of the Saturdays to be taken off would be left to the discretion of individual enterprises.

With a rare fervor for a city accustomed to spectacle, New York lionized the freed American hostages yesterday in a torrent of ticker tape, cheers and patriotism. Hundreds of thousands of people lined the confined streets of lower Manhattan as 21 of the 52 Americans who were released from Iran 11 days ago moved up a wind-stung stretch of Broadway in a slow procession of open limousines. By the thousands, people craned from windows and stood perilously on the parapets of buildings that form the canyons of the city's financial district. And as they went from the Battery to City Hall, the former hostages rode a sea of yellow ribbons and vinyl American flags while tape and paper fluttered down upon them.

The Reagan Administration, eager to turn public attention back to the the President's economic program, is unenthusiastic about prolonged investigations of the Iranian hostage crisis, a senior White House official said today. Moreover, Mr. Reagan is determined not to spend political capital winning public approval for the agreement that the Carter Administration negotiated to win the release of the Americans held hostage in Iran for more than 14 months, the official said in an interview. The Administration's position on the hostage issue reflects growing debate in Congress and legal circles over the release agreement. The White House position has been that the Government will meet the main obligations incurred by the Carter Administration, but Mr. Reagan and his spokesmen have carefully avoided any promise that the United States will live up to every detail.

The index of leading economic indicators fell 0.8 percent in December after rising for six straight months, the Commerce Department reported. Most economists regarded the single-month decline in the index, which is designed to forecast future economic trends, as inconclusive. Also, the Labor Department said that productivity - output per worker - fell at a sharp 1.9 percent annual rate in the fourth quarter. (Page 29.) The prime lending rate was cut to 19 1/2 percent from 20 percent by Citibank and United California Bank. The Federal Reserve announced that the nation's basic money supply declined a modest $500 million, adding fuel to predictions that interest rates would continue to decline gradually. (29.)

Jean S. Harris, ending her fourth day on the witness stand today, denied that her intended suicide was meant to be ''a big last act.'' She said: ''I had led a private life and wanted to die a private death.'' Later in the day the prosecutor began his cross-examination. Mrs. Harris is accused of murdering Dr. Herman Tarnower, who she says died in a struggle for her gun. Still testifying under the questioning of her lawyer, Joel Aurnou, Mrs. Harris was asked to explain her ''intentions'' the fatal night of March 10 after a hoped-for ''final'' talk with Dr. Tarnower turned into an argument. The cardiologist had been her companion and lover for most of 14 years.

In the first major internal dispute of the new Administration, Secretary of State Alexander M. Haig Jr., backed by the Treasury Department, began a counterattack today against a proposal for drastic reductions in the foreign aid program proposed by David A. Stockman, President Reagan's budget director. At a meeting involving Mr. Haig, Mr. Stockman and Edward Sprinkle, Under Secretary of the Treasury, Mr. Haig succeeded in postponing until next week a decision on Mr. Stockman's proposal to cut $2.6 billion from the $8.6 billion aid authorization requested by the Carter Administration for the 1982 fiscal year, which begins Oct. 1. Official sources said that the Treasury representative supported Mr. Haig's resistance to the budget cuts. Mr. Haig defended the foreign aid program and displayed messages of concern over the proposed cuts from Western allies and Congressional supporters of foreign aid. The proposed reductions would revoke pledges of aid made by the United States to major international lending agencies, such as the World Bank.

Prime Minister Odvar Nordli, under political attack within his own Labor Party for agreeing to stockpile United States weapons in central Norway, resigned today after five years in office. He cited reasons of health. Mr. Nordli, a strong supporter of the North Atlantic Treaty Organization, to which Norway belongs, announced his resignation at a news conference a day after denying reports that he would quit.

Deputy Prime Minister Leopoldo Calvo Sotelo was designated by Spain's badly divided governing party today as the successor to Adolfo Suarez, who resigned yesterday as Prime Minister. At a meeting that concluded just before dawn, the executive committee of the Union of the Democratic Center assented to Mr. Suarez's nomination of Mr. Calvo Sotelo, a 54-year-old former industrialist who is in charge of economic affairs in the outgoing Cabinet. A number of right-wing members of the executive committee, whose attacks on Mr. Suarez influenced his decision to resign, walked out of the meeting before the vote was taken, protesting the swiftness of the decision. Several appeared concerned that Mr. Calvo Sotelo, who has remained aloof from its squabbles, might exclude them from his new government.

South African forces raided Maputo, the capital of Mozambique, last night, hitting operational headquarters of the African National Congress, a banned movement that has been responsible for a series of sporadic sabotage and small-scale attacks on targets in this country that are symbolic of white power. An army communique issued today said ''numerous'' members of the movement were killed and three ''planning and control'' headquarters destroyed. In Maputo, which was formerly known as Louren,co Marques, diplomats and foreign journalists who were taken to the scene said the headquarters comprised three houses on the outskirts of the city. Eleven members of the African National Congress were reported killed. The body of one South African soldier was left behind by the raiders. A Portuguese civilian was also killed, apparently in crossfire.

Prime Minister Zhao Ziyang of China pledged tonight that Peking would stand by the non-Communist countries of Southeast Asia against foreign aggression. In a speech at a dinner given by Prime Minister Prem Tinsulanonda, Mr. Zhao described Vietnam as a ''regional hegemonist'' and promised that Thailand and the other members of the Association of Southeast Asian Nations could count on China's cooperation for a ''just settlement'' of the Cambodia problem.

President Chun Doo Hwan of South Korea urged American business leaders yesterday to redouble their efforts to strengthen economic ties with his country. About 75 flag-waving South Koreans greeted their President's motorcade at the Waldorf-Astoria Hotel, where a large contingent of Federal security officers mingled with the policemen assigned to guard the freed Amercian hostages who are also staying there. In comments prepared for a dinner given in his honor by David Rockefeller, chairman of the Chase Manhattan Bank, Mr. Chun said that the United States receives 26.3 percent of South Korea's exports and supplies 19.8 percent of its imports.