The heads of the seven leading industrial states agreed last night on a package deal to cope with the world's economic problems that President Carter said "exceeded the expectations of all of us."

The two-day summit here among the United States, West Germany, Great Britain, Japan, France, Canada and Italy adopted a general strategy calling for emphasis on growth and reduced protectionism.

But in recognition that economic conditions vary widely among the seven countries, each promised to undertake specific measures that the leaders said would be "mutually reinforcing."

Carter, who has been fighting with Congress to get an energy program passed, included a vague commitment in the communique to raise U.S. oil prices to the world level by the end of 1980.

Both he and aides ducked questions on how he planned to accomplish it, but a White House spokesman said that Carter "has the other leaders convinced."

U.S. officials said that their expectations were exceeded by the "operational programs" that several of the countries said they would put into effect.

They conceded that the total new thrust might not be enough to reduce unemployment in Europe. But if all live up to their commitments, they said the new programs might raise the growth rate of the major countries in Europe over the next 12 months from about 4.0 to 4.3 percent.

The three-key elements of the package, as expected, include the promise by Carter to cut American energy use and pledges by West German Chancellor Helmut Schmidt to try to get a new stimulative program through his legislature and by Prime Minister Takeo Fukuda to reduce the Japanese trade surplus.

In all three cases, the negotiating tactic used to get the agreement was to avoid the details of how each country would achieve its objectives.

"This is not easy," Schmidt said in his concluding remarks, "and some of us have sometimes had to sidestep our difficulties in order to arrive at a conclusion."

Despite a warm round of exchanged compliments in the final declaration before a massed press audience here, there appeared to have been some tough in-fighting during the seasons.

Officials who attended said Schmidt and Fukuda delivered pointed rebukes to Carter on the lack of a U.S. energy policy, and Fukuda, who at previous summits had been nearly silent, spoke up at length.

At one time, they said, Fukuda told Carter that all the world's economic problems were traceable to lack of U.S. action to cut energy imports and to the instability of the dollar. He called for the United States to "put its house in order," the officials said.

While Schmidt has a longtime reputation for being outspoken, this was a new role for Fukuda.

The willingness of both Fukuda and Schmidt to be as blunt with Carter during the summit as they had been publicly was read as sign by some of their colleagues here that they see their economic power in the world growing. As one said, "they've decided it's time to stop being pushed around."

Carter's commitment on energy reduction was, as an aide said, "artfully phrased" to avoid providing a specific road map to his intentions. The communique says that "the U.S. will have in place by the end of the year . . . measures that will result in oil import savings of approximately 2.5 million barrels per day by 1985."

And in order to discourage excessive consumption of oil and encourage the use of coal, "the U.S. remains determined that the prides paid for oil in the U.S. shall be raised to the world level - the end of 1980," the communique said.

Officials refused to elaborate on methods for a achieving that goal, but said they were willing to "take the political heat" if any resulted. The increase would raise gasoline prices at the pump by at least seven cents a gallon.

In summary remarks of his own at the end of the sessions, Carter said that the commitment to a comprehensive energy policy was necessary because "the price of oil is too cheap in our own country."

Officials refused to say that Carter was inplying administrative action to cut imports if Congress failed to pass the final and fifth phase of his energy bill, the oil equalization tax.

Rather, they said, the president had convinced his six summit colleagues by the force of his presentation "that he intended to get it (a 2.5 million barrel reduction) done, and he didn't intend to say how he'd do it."

On the West German side, the commitment to higher growth is non-specific in the sense that Schmidt faces legislative battles within his own administration and in the West German Bundestag over an expansion program. The promise in the communique is that Schmidt will propose "measures up to 1 per cent of gross national product."

That would amount to about $6 billion worth of stimulation, "designed to achieve a significant strengthening of demand and a higher growth rate." A cautionary note in teh communique noted that the precise amount would have to take traditional West German concerns on inflation into account.

The Japanese end of the bargain was in a way more specific than the others. Fukuda said he would take the "temporary and extraordinary step" of keeping the volume of Japanese exports in fiscal 1978, which ends in March 1979, to the same level as 1977.

Special Trade Representatives Robert S. Strauss said that in a private meeting among Carter, Fukuda, and himself, the Japanese prime minister had agreed that the Japanese trade surplus with the United States calendar 1979 would be held to the same figure a in 1978.

Strauss said that Japan would voluntarily put export quota limits on shipments of cars, steel, and TV sets - among other products - to the United States.

"The way things have been going," Strauss said, "their surplus would have been 12 billion dollars without this understanding."

Fukuda, in his wind-up comment, called attention to the low Japanese inflation rate and said his country's problem "is that our balance of payments is in fact too good (and this) . . . has been the focus of much attention by other gentlemen."

He also noted that Japan has a high 7 percent growth rate target and the communique says that in August or September, Fukuda will determine "whether additional measures are needed to meet the target."

American sources took that to mean Fukuda will call a special season of the Japanese Diet if it appears to growth rate is falling below 7 percent.

The pledges by the other countries were as follows:

Canada reaffirmed intentions to push growth and limit inflation, with increases in output up to 5 per cent. That is close to the official Canadian target, but far above realistic expectations in Canada of about 3 per cent. In addition, Canada joined the United States in a pledge to continue to be "reliable suppliers of nuclear fuel within the framework of effective safeguards."

France agreed to increase its GNP rate for 1978 by about 0.5 per cent. Although not in the communique, the French plan is to spend an addition 10 billion French francs on various programs.

Britain, which recently adopted a budget to stimulate GNP by one percent, said it would continue to fight inflation.

Italy promised a 1.5 percent boost by shifting from public spending to stimulation of private investment.

In addition to the deliberately fuzzy commitment on energy, the U.S. part of the "specific" programatic section was a reaffirmation that fighting inflation had become the top U.S. priority. No spefic U.S. growth target for this or next year was mentioned in the communique.

The summit declaration endorsed the "framework of understanding" on the multilateral trade negotiations that was released in Geneva on July 13, noting that some "difficult" issues remained unresolved. It called for successful completion of negotiations by December 15, after rejecting a French effort to water down one part of the Geneva agreement that will tend to curb the use of European Economic Community subsidies to build up agricultural surpluses.

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Attention was devoted to problems of the less developed world - again, with specifics lacking. For example, the rich nations here said that poorer countries "can count on us for an increased flow of financial assistance and other resources." But the only nation stepping forward with a concrete offer was Japan, which said it would attempt to double official development assistance, now one-fifth of one percent of GNP, over the next three years.

There were some issues of presumably great economic importance that the leaders either skirted entirely or dealt with only in passing. Thus, the dollar got only a back-door reference, a sentence on "erratic fluctuations of the exchange markets" which have a damaging effect on confidence. But no new measures for dollar support were announced.

Another topic almost totally brushed off, to the regret of the West Germans and French, was the new European monetary system tentatively put forward by the Europeans in Bremen on July 6.

This plan, which would tie the European currencies tightly together, is viewed by the United States as a potential rival to the dollar and to the International Monetary Fund.

As a result, the communique, instead of incorporating a U.S. blessing that Schmidt and French President Valery Giscard D. Estaing had wanted, merely "took note" and "welcomed" the scheme, and said the European community would keep the United States, Japan and Canada informed of its progress.

Carter and Giscard credited detailed preparatory work with producing a result that they said has a better promise of fulfillment than preceding ones. Giscard added that the leaders "have demonstrated they have the political will to achieve the results they aim at."

The communique said another summit would be held "at an appropriate time next year," presumably in Tokyo, although the site has not been announced. And the leaders announced there would be a follow-up to the Bonn summit in the months ahead so that - in Carter's words, "those commitments made in sincerity are not forgotten, nor abandoned."