@mrpandaman: Whether or not the US could afford a war with China is a bit of non-issue, considering that the economies of both countries would probably implode at the outbreak of hostilities anyway. Their economies are way too intertwined at this point. Really, the only way the two could sustain a war would be a bizarre agreement where they promise to limit their fight to, say, Korea, while promising to keep trading on the side. Which is obviously impossible. And the world economy would tank anyway due to the loss of the South Korean economy (which would happen even in a limited war with North Korea too, even if they win quickly - South Korea would still be a war zone for weeks to months, which isn't exactly a good thing for affected stockholders)
This as the new MAD doctrine for our time. A nicer one, if you ask me. A total war between the US and China would still be possible, of course, but they would largely have to fight with what resources they already have with limited resupply options. In any case it's unlike either population will stand it for long.
As for affording a war with North Korea I don't think it would be that big of a deal. It would be more similar to the intervention in Libya (which didn't really cost all that much) than Iraq in that ground combat could largely be left to the ROK with the US mainly providing air and naval support. Of course it would be on a much bigger, and costlier, scale and the US would still both be involved on the ground and suffer much higher losses but a large scale US invasion and occupation isn't really necessary unless North Korea turns out to be far tougher than expected. And like I said, any occupation is far better handled by South Korea. In any case the world market crash I mentioned would dwarf any military costs. It might actually cost less to intervene than not to, if it means a greater chance of preserving South Korean industries.
As for the Chinese agreement with North Korea it's nowhere near as ironclad as it sounds. It's quite different to, say, the agreement between the US and Taiwan: the US stands to lose a great deal if they don't follow it since they have several other agreements with other countries that would be questioned, severely harming the US geostrategic objective. Hell, if the US refuses to support an invaded ally the entirety of NATO could be jeopardised.
This is not the case with China. Their relationship with North Korea is rather unique. China doesn't really have military alliances, at most they express mutual security interests in cooperation with other countries - like regarding American activities in Asia. They interact on this level with some big players, like Russia and Pakistan, but it's all rather low profile. Then there's the fact that no-one actually likes North Korea. So while Japan would be concerned if say the US ignored an attack on Taiwan, no one would really care if China ignored North Korea since no one really identifies with them. That's the downside of acting like a rogue state.
And I should probably have mentioned this sooner: the agreement is one of mutual defence. China has no obligation whatsoever to support anything started by North Korea. In fact, Kim Il-sung tried to gain Chinese support for an invasion of South Korea in 1975 but was turned down. And with the strong dislike expressed by China over North Korea's nuclear ambitions, an invasion of North Korea by the West because of them could very well result in China refusing to help because of that fact alone.
China would only enter the war if they felt like it's their only option - as it stands, it really isn't.
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