"Poor little Chinnu lives on one dollar a day"
Cost of Living
If the cost of living in one place is $100 / month, those with the same amount of money will be able to buy more than those who live in places where the cost of living is $1000 / month. $3 a day pretty much guarantees that you'll be homeless in Manhattan.
Getting High
What is interesting is that the more rich people in your neighborhood, the higher the cost of living. The simple fact that the rich can spend more than everyone else means there will be more cash running around chasing the goods that you also want to buy. This raises the local cost of living.
Enabling Domination
This isn't to say that people in Third World countries are much better off than we believe, even if their $3 can go further than a homeless New Yorker's $3. Why aren't they better off?
A strong dollar means those with the most dollars (perhaps the US government or perhaps not) have a lot of purchasing power around the world, especially in those Third World countries. This allows them to buy up the natural resources to produce American weapons instead of local goods, for wealthy corporations to easily bribe any government official they want, to hire the media to push propaganda in any direction they choose, and to make high quality weapons available only to those backed by the wealthy.