I actually did move to a "cheaper country", a couple of years ago! My rationale was simply, "Hell, life's really short why not, for a while?".
London to India, although, I'd hesitate to call India cheap these days, I paid over 800 Rupees (>$11!) for an imported box of Kellogg's Rice Krispies (for the kids, of course! Yes, I do spoil them, I know!).
In my experience, there are four kinds of westerners that move to India (or any other "cheaper country", for that matter):
1. Seconded Expatriates: Those that are sent by their HQ here and live like absolute kings (USD/EUR/GBP salary, massive apartment, private health care plan, private school education subsistence, drivers, cooks, cleaners, etc,).
2. Retirees or those that hold foreign assets/cashflows: (freehold property on rent and/or other domiciled asset/working capital).
3. Those on a year off, traveling or volunteering for an NGO, teaching English, stuff like that.
4. Those that simply fall in love with this country and it's people and see those things that the natives simply don't see.
"Cheaper Country" is a relative term now, and I believe such places only exist, in our imagination given the demands of modern living and how we all now measure either success towards the pursuit of happiness. India is rich in culture, aspiration, knowledge and goodwill to strangers, but it does suffer massively from economic inequality and it still never fails to shock me. I've lost count of the many occasions that I've seen young children, (not at school) on the streets, begging without shoes near the traffic lights and at those same set of lights is a young guy, (20's-30's) driving an Aston Martin, Porsche etc (and that young driver paid close to double in retail value for the car, due to the import duties/luxury taxes etc!). Truth is the this gap is ever widening, around the world and ironically, it even happens in my city, London too, although it's normally, less overt.
It's those things we own, that end up owning us, no matter what country we live in, I suppose.
My two cents, for what it's worth anyway...