I'm sure not what you mean by competing to raise environmental standards. One of the union bosses' prevalent and effective points is that free trade as it currently exists leads to a race to the bottom. It pits workers in different regions and different countries against one another and the same goes for governments who will offer companies tax-incentives to relocate or provide a "good investment climate" which tends to mean "flexible labor markets", i.e. little or no right to organize, and little governmental regulation.
The competition is for whoever can sell the best product for the cheapest price and since with capitalism you get overproduction what you end up with situations like Russia, Brazil, and Japan "dumping" their steel. I would guess true laissez-fair types would be against regulating "dumping", because how can there by unfair competition? The notion of "unfair" business practices always struck me as odd. If some company had the financial means to flood their market with goods that sell below production cost, thereby destroying the competition, shouldn't they be allowed to do so simply because they have the wherewithal, that is, they had earned the right to do so?
Peter