Though the West German government enthusiastically welcomed the visit of Vice President Mondale here yesterday, the U.S. delegation left apparently without bridging a fundamental gap in economic philosophies that separates the two fiscal-superpowers.

Eventually bridging that gap is a high stakes business because it is assumed by both Americans and Germans that it will take coordinated efforts by both countries, plus Japan and other major industrialized nations, to steer the west clear of a future recession.

In the view of some economists traveling with Mondale, however, the relatively rich and productive West Germans are not playing a big enough role in helping to stimulate the world's economy.

The Germans, they argue, can afford to pump lots more money into their economy at home so that people here will buy more foreign goods rather than just having foreigners buy ever more German goods.

This, the U.S. economists believe, would be in Germany's own best interest over the long run because it would help reduce unemployment here and in neighboring countries. In turn, this would improve general economic and social stability in nations with weaker economies and help the west avoid slipping into another recession.

The Germans, however, see things differently. They counter that not only are they doing their share among major industralized to help give the global economy a boost, but that their prudent approach to economic growth is one of the few things that has brought whatever measure of stability there is today in the west's economy.

Furthermore, the most important factor in the high stakes debate between the U.S. and its most important ally over the battle against recession, may be the unstated difference in political and public attitudes between the two countries.

Expansionist and re-flationary policies that may work in the U.S. are a very touchy subject in this country, West Germany has the lowest rate of inflation, now under 4 per cent, of any major country and the people have gotten used to it. There are also still long memories here of the 1920s and '30s, when runaway inflation caused the chaos that led to the Nazi regime.

Mondale assured West German Chancellor Helmut Schmidt that the Carter administration's proposed $30 billion stimulus for the U.S. economy "would have no inflationary impact.

The implication was that Bonn's planned $4 billion stimulus programs was not enough and that Bonn could do more without risking inflation.

Schmidt is not so sure.

The basic problem the chancellor faces is whether to tamper with a highly successful economy, one in which one out of every five persons makes a living from export industries.

Higher inflation here eventually could hurt German competitiveness and cost export jobs. It could also cost Schmidt his job, a very important factor in German reluctance to be pressured by the U.S. Schmidt already has been seriously weakened by conservative gains in federal elections last fall and, in the view of experienced politicians, might not survive any significant upswing in the cost-of-living here.