GDP is a measure of output, not welfare: or, HOS meets the SNA

What effect, if any, do changes in the terms of trade have on the level of output (GDP) or welfare? I examine this issue through two versions of a textbook, Hecksher-Ohlin-Samuelson (HOS), two-good model of a small, open economy. In the first version both goods are for final consumption. In the second, one good is an imported intermediate input into the other. In both versions, economic theory suggests that an improvement in the terms of trade raises welfare (consumption) but leaves aggregate output (GDP) unchanged. This follows from a continuous-time analysis using Divisia index numbers. I then show that a national income accountant applying the principles of the 2008 System of National Accounts (SNA) would reach the same conclusions.