This is a good way to think about the problem, but it does not necessarily support Krugman's policy preference. He argues that if China appreciated the yuan or if the US slapped a tariff on Chinese exports these would reduce the current account surplus of China. He starts from the macro balances but then comes back to the currency value being the exogenous driving force. He is reading his two equations from the top down. Why does it not work from the bottom up?
Let me start with a proposition: the right way to think about China’s exchange rate is, initially, not to think about the exchange rate. Instead, you should focus on China’s currency intervention, in which the government buys foreign assets and sells domestic assets, on a massive scale.
Although people don’t always think of it this way, what the Chinese government is doing here is engaging in massive capital export – artificially creating a huge deficit in China’s capital account. It’s able to do this in part because capital controls inhibit offsetting private capital inflows; but the key point is that China has a de facto policy of forcing capital flows out of the country.
Now, bear in mind the two basic balance of payments accounting identities:
Capital account + Current account = 0
Current account = Domestic savings – Domestic investment
By creating an artificial capital account deficit, China is, as a matter of arithmetic necessity, creating an artificial current account surplus. And by doing that, it is exporting savings to the rest of the world.
Suppose that China stopped purchasing foreign assets and let the yuan appreciate. Then we are to suppose that Chinese savings will necessarily fall. Presumably this arises because the movement in the exchange rate makes imports more expensive.
But why do we believe that the current account will adjust in this manner. Can't we read the CA equation the opposite way? If Chinese households and corporations want to save over 50% of GDP there will still be an excess of savings over investment (see this article for some evidence on the distribution of Chinese savings by type). So something else must give. What? Presumably the price level. Since net exports fall due to the currency intervention aggregate demand is lower. This puts downward pressure on the price level. This offsets the impact of the currency change on the real exchange rate. China is just as competitive as before.
For a currency surcharge or revaluation to reduce the Chinese current account surplus it has to change the savings/investment balance. It is not clear how that will happen until something changes the desires of Chinese corporations to hoard savings and Chinese households to save. There may be government policies that China can pursue to achieve this, and they would likely improve welfare (for example a retirement system), but it is not at all clear that they will be implemented in response to tough talk from US Congressman about the yuan.