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LONDON, Jan. 18— The state-owned British National Oil Corporation today proposed to its customers a $3-a-barrel cut in the price of North Sea crude oil. Norway quickly matched the cut, and rumors swirled that some OPEC producers were poised for similar actions.

The anticipated price cut, which follows earlier reductions by the Soviet Union, Egypt, and others, was marginally less than earlier market predictions of between $3.50 and $4 a barrel..

But ever since Saudi Arabia's oil minister, Sheik Ahmed Zaki Yamani, predicted the North Sea action after the Organization of Petroleum Exporting Countries failed to agree last month on a pricing policy, analysts have awaited the development as a major test of OPEC's ability to keep a downward adjustment of prices from accelerating into a free-for-all. Small Impact on Consumers

The North Sea price reductions, by themselves, are expected to have little impact on retail gasoline prices in the United States, but if they are followed by other major producing countries, a continued decline in consumer prices is regarded as certain. Analysts generally calculate that gasoline prices fall 2 1/2 cents a gallon for every $1-a-barrel cut in the price of crude oil. (Page 39.)

The British Government and many economists here have said that a moderate oil price decline would help the world economy, although over-extended oil producers such as Mexico and Nigeria, and the banks that have lent money to them might be hurt. A sharp fall could produce severe financial dislocations.

''The B.N.O.C. move is the first stage and makes it more imminent that OPEC will have to act,'' said David Kern, senior economist at the National Westminster Bank here. ''The key uncertainty remains the behavior of OPEC.''

Immediately after the British announcement, rumors began circulating among traders here that Nigeria is preparing to break ranks with the rest of OPEC by cutting its oil price by between $5 and $5.50 a barrel. Nigerian and the North Sea fields produce comparable grades of high-quality crudes.

Nigerian oil exports have all but halted and production has dropped to about 400,000 barrels a day - about one-fifth its 1980 peak - because the official price of $35.50 has been $2 a barrel higher than official North Sea prices and almost $6 a barrel higher than the prices for North Sea oil available on the open market. ''The markets have already discounted B.N.O.C.,'' said a trader at one of London's main trading houses. ''Everybody is waiting to see what Nigeria does.''

A Nigerian price cut would put intense pressure on other OPEC nations, particularly Libya. In addition, North Sea oil buyers might be encouraged to hold off on accepting B.N.O.C.'s proposal, on the ground that the reduction did not go far enough, industry analysts said.

Indeed, executives of American oil companies, which make up the largest market for North Sea oil, said that with further cuts possible in the next few days, they would be cautious about signing new contracts for British oil at the new level.

(In Kuwait, Oil Minister Ali al-Khalifa al-Sabah said two OPEC members competing with North Sea oil were planning to undercut the new price level by 50 cents a barrel, the Associated Press reported. He was believed to be referring to Nigeria and Libya, and he warned that such a move would deprive them of the right to negotiate within OPEC, according to the report.

(In Caracas, the Venezualan Oil Minister, Humberto Calderon Berti, said his country planned to adhere to the OPEC price structure and would not lower prices independently, Reuters reported.

(A spokesman for the state oil monopoly of Mexico, which is not an OPEC member, said in Mexico City that some price adjustment might be announced in the coming days.)

B.N.O.C.'s price recommendations were made after negotiations with major producers and buyers, but a company spokesman said, ''It will be the middle of next week at least before we see if these cuts are accepted.'' The company effectively sets North Sea prices because it trades about 1.3 million barrels of oil daily, out of 2.2 million produced in the British North Sea oilfields.

Today's proposed cuts would leave the price of the two widely traded North Sea crudes - Brent and Forties - at $30.50 for a 42-gallon barrel. Prices for lower quality crudes would drop below $30. Statoil's price cuts for Norwegian crude would range between $3 a barrel and $3.50 a barrel in order to stay competitive. The proposed cuts would be retroactive to Feb.1.

Brent and Forties crudes have been trading in a narrow range between $29 a barrel and $29.50 a barrel on the spot market, a price at which many refiners say they are still losing money because of the weak demand for petroleum products caused by the recession and a mild winter.

In today's announcement, B.N.O.C. stressed that it was responding to market pressures rather than leading the market downward. The company had carefully laid the groundwork for the move by telexing buyers Monday to tell them it would make a recommendation today and by doing nothing to discourage speculation that the cut would be between $2.50 a barrel and $4 a barrel.

The proposed price cuts would cost the British Treasury about $1.04 billion in lost revenues this year and almost $1.4 billion next year, based on calculations earlier this week.

This is source I found from another site, main source you can find in last paragraph

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