What happens when the poor get richer?

I was recently discussing with some friends the issue of increased wages in the developing world. I may be misremembering the conversation, but I think the idea was brought up that higher wages in the developing world could be worrisome for Americans, because we'd have to pay more for the goods we purchase from those countries (whether as final goods or inputs, I suppose). I've heard this sort of argument before. It is related to the idea that we rich nations rely on the labor of poor nations, and without them the whole global capitalist edifice might come crashing down. Once one area becomes rich we "need" to find another poor area. (Taiwan becomes rich, so China starts making plastic toys. China becomes less poor, so Vietnam starts making cheap goods.) This view is actually fallacious, even when stated in less dramatic terms. It is true that a poor country will have a comparative advantage in something vis-a-vis the US, so we will find it worthwhile to trade with them. However, we'd benefit even more if they were richer (almost always, but maybe there's some exception I can't think of).

First of all, higher wages in China does not automatically imply that goods bought from China will be more expensive. Higher wages usually means there has been some productivity gain. The worker gets paid more than before, because he produces more than before. E.g. Maybe he's making twice as many cars per hour as had been before. He might get paid twice as much per hour, and in that case, he's getting the same payment per car. So, the labor cost of building the car has not increased, even though the laborer is getting paid more per hour than before. (Why is he twice as productive now? Maybe he works harder than before. Or maybe he has better tools or knows more.) A simple example can illustrate this. If we should worry about wage increases abroad, we should also worry about them at home. So, someone might say, "Yeah, I'm making ten times more than my great grandfather, but almost everyone else is also making way more than he did. So, I'll just be paying 10 times higher prices. So, I've made no progress." The situation described just now would be true if the entire gain in income were due to inflation (i.e. more dollars chasing the same number of goods.) But in real life, much of the change in income since your great grandfather's time has been due to productivity gains (i.e. is "real" rather than merely "nominal.") In other words, there are more goods being produced per person, and thus there is a higher standard of living and not just higher price levels. I don't mean to say that higher wages never means higher prices, but I think it's generally not a big worry in the long-run.
See the fascinating chart about 40% down the page for historical evidence: http://www.econlib.org/library/Enc/StandardsofLivingandModernEconomicGrowth.html
You can see that even though wages have gone up, we can still buy things more cheaply than before. (I'm assuming most of these goods are produced in large part in high income countries such as the US. It's possible that this is incorrect, but I think my point would hold if you stuck to American goods. If you are skeptical, look up average US income in 1908 and divide it by the price of a Model T. Then divide the average income now by the price of a typical American car--which, in any case, is a way better product than the Model T. You'll get basically the same result the above chart got.)

Second, as people in China get richer, they can buy more of our goods. So, our exports increase, which leads to a higher GDP for the US.

Lastly, as they become wealthier, we can likely expect them to produce more scientific research and more inventions, both of which could benefit us greatly.

Here's an excellent essay on this topic: http://www.economist.com/economics/by-invitation/guest-contributions/important_thing_chinese_productivity_rising