Should We Cheer A Sinking Ship?

You pick up the Wall Street Journal and read a headline announcing that the U.S. is headed for another record trade deficit. Remembering that GDP is the sum of Consumption, Investment, Government Purchases, and Net Exports, you fret because the equation Y = C + I + G + (X-IM) (where X is exports and IM is imports) shows that more imports makes GDP go down.

Then you read that a ship containing $12,000,000 in Chinese-made smartphones just sank in the Pacific Ocean.

Should you cheer? Will this sudden reduction in imported smartphones make GDP go up?

No and no, because since they cannot be sold from the bottom of the Pacific Ocean, they cannot show up in Y=C+I+G+NX as consumption spending. Imports will fall by $12,000,000, which means Net Exports will rise by $12,000,000--but consumption also falls by $12,000,000. GDP doesn't change; we're just poorer to the tune of $12,000,000 worth of smartphones no one will ever be able to use.

Inspired by an example in Tyler Cowen and Alex Tabarrok's economics textbook.