If it did India would just reject the patent. Medicines command a special place in market economics and hence all the confusion. For example, there is whole segment of market in India that buys only Ayurvedic products, and there are big cosmetic companies that ensure their product is categorized as Ayurvedic instead of cosmetic.

Medications are not easily ameniable to arbitrage as they are not classified as equivalent goods with regard to customs- special licenses are required (often) to import them.

Plus, there are quality issues with third world drugs (which may or may not be valid) which rear their head when buying sight unseen

> Why not have it cost $500 in both places?

Why are student movie tickets cheaper than general admission? The term for this is 'price discrimination'.

The short answer is because many Indians can't afford to pay $500, and many Americans can afford to pay more than $500.

It's a matter of market clearing prices. A gross oversimplification, but $4 is the price the market can bear. Charging $5 in the developing world isn't much different than charging $500—they just won't sell.

Arbitrage is attempted, but the FDA is pretty good about stopping imports at port. Also, the primary distribution channels are fastidious about not taking goods from other locales so the market is grey/black and not worth the effort in most cases. The people who would buy drugs from India are probably using means-tested assistance programs and can't pay the huge sums insurers can.