In this situation, nothing will happen that is any different from the opening of free trade between any two countries. Each country has a comparative advantage in one or more goods, and will export those goods and import the others. If Canada's onerous regulations are equally onerous for all Canadian industries, the regulations will have no effect on trade patterns. Instead, it will be the same sort of effect as if Canadian labor productivity were 10% lower than US productivity. Whether lower productivity is because of regulations, taxes, or anything else doesn't matter.

If Canada's regulations hit some of its industries harder than others, then it is more likely that Canada will have a comparative disadvantage in those industries. If the regulations were not labor regulations, but pollution regulations, for example, then Canada's high-pollution sectors would tend to shrink and its low-pollution sectors to expand after trade. This is all to the good, of course.

The conventional wisdom is based on the fallacy of confusing comparative and absolute advantage, I think. The naive view is that if Canada has lower productivity in all its industries than the US, then if trade opens up, Canada will produce nothing, and will instead import everything from the US. The fallacy in this is that if Canada produces nothing, it will have nothing to export to the US, and the American sellers will not send anything to Canada. What actually would happen is that Canada would import from the US the goods it has the biggest productivity disadvantage in, and export to the US the goods for which it has the smallest productivity disadvantage. Free trade will benefit some Canadian producers, despite the fact that their productivity is lower than that of their American counterparts.

It would also be true that even if Canada has onerous regulations that hurt its productivity, Canada would benefit from opening up trade with the US. It would actually become easier for Canada to maintain its welfare state, because the country would become richer.

There does seem to be a genuine concern about protecting the welfare state by constraining trade. Is it just ignorance of the idea of comparative advantage, or am I missing something?