It's actually a really interesting question, but also very hard to answer in practice. The positive answer would involve the ability of competitive markets[1] to serve as efficient mechanisms that coordinate the activities of people across the globe to collectively increase wealth/output[2]. With greater total surplus, it becomes relatively "cheaper" [on a societal level] to solve problems like saving the village. (Of course, this leaves out the public goods problem of actually provisioning the village-saving in the case that the villagers don't get lifted up directly by economic growth and buy it for themselves.)

1. https://en.wikipedia.org/wiki/Competitive_equilibrium

2. https://en.wikipedia.org/wiki/Fundamental_theorems_of_welfar...