Sure to be high on the agenda when President Carter and Canadian Prime Minister Pierre Elliot Trudeau meet in Washington this week is a discussion of the relative strengths of the U.S. and Canadian economies and what responsibility each nation has to help a seriously faltering international economic situation.

Washington would like to see Canada join the U.S., Japan, and what is so far a recalcitrant West Germany in assuming the burden of the world's "strong" economies by stimulating internal demand and by increasing the flow of imports to pull other nations along.

But Canada, which is this country's largest trading partner and which is dependent on exports to the U.S. for about 14 per cent of its entire gross national product, is running a worrisom deficit of its own and would therefore like a more robust U.S. economy to help it move closer toward the black on trade.

Trudeau arrives for his official state visit on Monday at a time when the Canadian economy is slowing in momentum. Also he is under political pressure to produce results in the wake of the recent electoral triumph in Quebec province of the separatist party - a victory attributed to economic discontent as much as to a desire to secede from the rest of Canada.

Real economic growth in 1977 is now expected to come in at about 3 per cent, according to the latest projection of the Conference Board of Canada, down by 1.5 per cent from the previous estimate and well below both the 5 per cent rate achieved last year and the country's 5.5 per cent long-term growth potential.

Unemployment hovers near 8 per cent. And inflation, while it has been reduced from the double-digit levels of a few years ago, remains nears 7 per cent despite a government wage and price controls policy in effect since late 1975.

The Canadian dollar toward the end of last year lost its premium over the U.S. dollar in foreign exchange markets, experiencing a 5 per cent devaluation that was triggered by the Quebec elections that seemed to cast a shadow over the country's long-term stability.

Perhaps of greater concern is the fact that unit wage costs in manufacturing have risen twice as fast in Canada over the last ten years as they have in the United States, making it cheaper, in many cases, to now locate a factory in this country than in Canada.

Average hourly wages for industrial production workers stood at $7.39 in Canada in 1976 compared with $6.90 in the U.S., according to a study by the U.S. government's Council on Interational Economic Policy. In 1970, by contrast, the Canadian hourly wage was $3.46, below the $4.20 then prevailing in the U.S.

As a result of this reversal, on top of official Canadian government policy to discourage American ownership of Canadian companies, direct ivestment by U.S. citizens and corporations in Canada has slowed considerably.

"In the early 1960s one United States direct investment dollar out of three came to Canada," U.S. Ambassador to Canada Thomas O. Enders observed in a speech last year. "Now it's one dollar out of six."

And preliminary estimates indicate that Canada actually experienced a net investment outflow to the U.S. in 1976 for the first time in many years, as Canadian dollars came pouring into this country seeking investment opportunities.

In 1976 Canada raised more than $9 billion in foreign capital markets, making it the largest international borrower, according to a tabulation by the Morgan Guaranty Bank.

And Canada's balance on current account last year, which includes not only merchandise trade but net income from insurance, shipping, and other services, and all net private and official fund trasfers, was in deficit by about $4 billion and is expected to reach $4.5 billion in 1977.

The later amount would represent about 4 per cent of Canada's approximately $115 billion gross national product, one of the largest deficits in proportion to the size of the economy of any of the major industrialized countries. Which is why Canada would like to see an economic boom in the U.S. pull in more Canadian imports to reduce this total.

While Canada is the world's sixth largest trading nation overall, two-thirds of its exports and imports are with the United States. Canada alone buys virtually as many American goods as the entire European Economic Community. In 1976 exports to the U.S. were about $15 billion while imports were about the same.

To stem the decreasing competitiveness of Canada's economy, Trudeau in late 1975 imposed his wage and price controls program. It has proven quite unpopular with both business and labor. While it seems to have moderated the torrid rate of inflation that was prevalent several years ago, it is also blamed for throttling the country's economic growth.

Recently Trudeau gave indications he is ready to lift the controls, saying there was no chance they would be extended past their scheduled 1978 expiration date and that they could be lifted sooner "if they become intolerable" and "economic conditions are favorable."