(1) Should the US care about the Euro-Dollar exchange rates?
The world consists only of the United States and Europe, the balance on current account between the USA and Euro-Europe is zero and stays so, and the net credit position of US-residents relative to Europe (i.e. net in dollars) is one trillion dollars, while the net debt position of US-residents relative to Europe (i.e. net in euro) is one and a half trillion euro. At an exchange rate of one dollar per euro the USA are then very heavily a debtor nation while, with a shift to an exchange rate of one half a dollar per euro, the USA have suddenly become a substantial creditor nation. All this was a simple consequence of the denomination of debt instruments in terms of different currencies and the concomitant change in asset prices due to a change in exchange rates - perhaps because of a change in preferences between euros and dollars; and all this had nothing to do with any, perhaps sustained, imbalance in the current account, which by assumption remained nonexistent. All this was the consequence of a simple price change. It is not at all true that the sum of the current account and the capital account of each country have to sum to zero if the two have to be measured differently.
With more than two countries, a further possibility arises: ‘old’ capital assets may be exchanged against each other without a change in the net asset position of the transactor. A Euro-European may, for example, exchange his holding of yen assets against US-dollar assets, which entails a capital movement out of Japan and into the USA, without any change in current accounts and even without necessarily changing capital prices, though an exchange rate change would be likely............