On Earth, the problem led to a repressive society almost unrecognizable by today's standards. Since the average citizens wished to extend their lives, the world government sought to increase the supply by using condemned criminals to supply the organ banks. When this failed to meet the demand, citizens would vote for the death penalty for more and more trivial crimes. First violent crimes, then theft, tax evasion, false advertising, and even traffic violations became punishable by the organ banks. This failed to solve the problem, as once the death penalty was passed for a crime, people stopped committing it. This resulted in nearly every crime meriting the death penalty. Further attempts to alleviate the problem by declaring certain groups of cryogenically frozen people to be dead in law (the so-called "Freezer Bills") and harvesting their organs also proved to be unsuccessful. The freezer vaults represented a finite supply and therefore were eventually exhausted.
Then you read things like this Al Jazeera story (via Boingboing), and you wonder why Larry Niven isn't more of a household name:
A young woman, posing as a migrant worker from Hebei province, calls a man who has advertised on the website, identified as Mr He.
"I need money," she says over the phone. "Do you want a woman's kidney?"
Mr He asks her age. Twenty-five, she replies.
"Of course we want your kidney."
Mr He tells the woman to travel to Xuzhou city, Jiangsu province, where somebody will be waiting when her train pulls into the station. She'll be given a physical examination and, if she's found to be in good health, Mr He will find a suitable transplant candidate. He says he'll pay RMB 320,000 (50,000 dollars) - a dubious offer, since most kidneys in China sell for around RMB 100,000 (15,000 dollars) - and promises to transfer the money before surgery.
In China, around 1.5 million people require organ transplants, but just 10,000 receive them each year. The vast majority of organs in China still come from condemned prisoners, but new government regulations have reduced the number of organs available for transplant. Meanwhile, few Chinese agree to donate their organs upon death, widening the gap between supply and demand.
I concede that there's a libertarian/free trade argument to be made here, more often applied to egg donation, which is essentially: "You can sell things you own, right, and if your kidney isn't yours, then whose is it? And there are people dying for want of kidneys (and other organs)." The problem is that not everyone knows what their kidneys really do, or what the consequences of giving one away might be - and the organ dealers aren't going to go out of their way to educate sellers.
So, before my fellow techno-libertarians tell me I'm a paternalistic sell-out, either convince me that what's happening in China, and what happened to Hu Jie and thousands like him, is morally optimal, or alternatively that it's only not morally optimal because it's currently a black market. Look at your own positions too - are you ready to legalize all drugs, not to mention do away with all prescription control? That is a far, far less fraught issue than this. And some are ready for that; congratulations, you're consistent. If on the other hand you are not ready for such changes, then you're certainly not ready for legal organ markets.
 I left the part about freezer vaults in for my cryopreservation friends. (You should also see the next Darren Aronofsky movie, with George Clooney.)