Please can you describe a plausible 'end game' for price-factor equalisation. I.e. If incomes in each country converge (per skill level) what would the world look like in terms of trade, income distribution etc.
I'm not sure what this end game would look like. If he's asking about an equilibrium in which labor and capital are mobile across borders, then I suspect labor and capital will move toward the regions with the best institutions. This in turn, though, would provide powerful incentives for countries to reform: in order to prevent almost everyone from moving to the United States and Europe, a lot of countries would have to cut taxes and improve provision of basic public services.
In the long run, we would all be richer. In the short run, there would be a lot of disruption. Some of the gains to migrants would come at the expense of high- and low-skill natives. I'm pretty sure the change would be Kaldor-Hicks efficient in that the gains to the winners would be larger than the losses to the losers. Given that high- and low-skill workers are earning an economic rent emerging from barriers to entry into the American labor market, I don't think taxing the winners to compensate the losers would be justified.