Do low wages lead to high productivity?

United States history is a giant test of high and low-wages on economic growth.  In the north, unlike in Europe, the frontier acted much like a natural version of a minimum wage law: if employers couldn't pay to make the job as good as risking your life on the frontier, employees could leave, so wages were higher than any competitor.  By the economic theory that higher wages for the front-line workers should mean fewer business opportunities, the northeastern United States should have entered the 20th century an economic backwater unable to compete with Europe, and the low-wage slave-and-impoverished-ex-slave South was where the real opportunities for industrialization were.