High administration officials said yesterday that they are studying a 13-Page analysis of the world's economic problems delivered last week by Prime Minster James Callaghan of Great Britain to President Carter.

Described as "frank without being rude," the paper is the first comprehensive study of the interrelationship of such troubled areas as economic growth, the decline of the dollar, and the needs of developing countries, both American and British sources said.

"It's an excellent paper, and we're taking it seriously," according to an American official, who noted that it would be used in preparing for an economic summit meeting to be held in Bonn in mid-July.

Among other things, the paper stresses the need for increasing aid to poor countries, a theme that also was developed yesterday by President Carter in an address to the Venezuelan Congress in Caracas. The British paper specifically mentioned that Japan, among others, might provide more aid money.

There was no mention in the paper, nor in Callaghan's talks with American officials, of a reported proposal for a five-nation effort, through linked currencies, to stem the decline of the dollar.

British sources said the purpose of the 13-page document was to demonstrate that the world faces "a vortex of malfunctions" and that it may be easier for politicans if all of the economic problems are tackled simultaneously.

Callaghan made clear in talks here in the past few days that he considers it critical that the Bonn summit produce concrete evidence that the seven leading nations can act on key problems in a coordinated way.

He cited, especially, efforts to spur economic growth, reduce energy consumption, cut trade barriers through multilateral agreements, achieve greater stability in currency markets, and maintain long-term capital flows.

He believes that if summit participants act in these areas, the result will be greater than "the sum of the parts," providing a psychological boost to confidence in Western world leadership.

But without concrete results from the summit, Callaghan foresees a slide into trade protectionism.

He implied that, unless there is a concerted effort to encourage expanded world trade, there will be a dangerous tendency for individual countries to limit access to their markets. In passing, Callaghan chided the United States for a recent Proposal to cut wool tariffs by only 2.6 per cent.

On economic growth, the British paper said that each country in position to do so should stimulate economic growth, as partners, to rescue the world fro a debilitations recession.

U.S. sources said the British Paper "Pointed no fingers." But Callaghan noted that, if West German Chancellor Helmut Schmidt sees other nations go along with a coordinated growth program at the summit, he might be more willing to advance German growth targets.

West Germany has set a 3.5 per cent growth target for 1978. Until recently, American officials had been pressing West Germany to raise its growth goals. Now a public truce in mutual recrimination is in force among American and German officials over low German growth rates and the declining U.S. dollar.

The British prime minister, who recently visited Schmidt in Bonn, has made available his good offices to help smooth out misunderstandings between West Germany and the U.S. on economic issues.

Callaghan concedes that many of the same high-growth and antiprotectionist objectives were touted before the London summit in May, 1977, only to lead to disappointing results. He acknowledged there is a certain danger in raising expectations about the Bonn summit. This is not a time for further declarations, but for hard actions, he is known to feel.

Callaghan also suggested to both President Carter and Treasury Secretary W. Michael Blumenthal that the dollar may encounter long-range problems.

He pointed out that the U.S. economy, while strong, is no longer dominant in the world. Moreover, energy requirements are likely to continue to be enormous, perpetuating a trade imbalance. In these circumstances, Callaghan suggested, the dollar might be relieved of some of the burden it carries as a reserve currency for other nations.