However, it's going to cost a lot more than $500 billion to raise per capita GDP by ~7 fold. It'll cost $500+ billion in the first ten years in just welfare support, security, education, infrastructure, disarmament, healthcare, job training.
$50 billion per year in net drag is perhaps even far too low of a number. There are 24 million people in the north. That's a mere $2,000 per year per person. It's going to cost a lot more than that to start bringing them up to speed. I think you could easily spend $2k per person, just on the person - not counting several expensive things I listed previously.
South Korea should plan for $2 trillion over 20 years. They'll intentionally under-shoot the numbers, to avoid freaking out the tax paying public, and the cost will end up ballooning far beyond the public relations numbers.