From the Washington Post:

nstead of giving priority primarily to patients who have been on the waiting list longest, the new rules would match recipients and organs to a greater extent based on factors such as age and health to try to maximize the number of years provided by each kidney – the most sought-after organ for transplants.
The current system, which dates to 1986, was first based largely on giving kidneys to the patients who matched the organs best, but it evolved to take a first-come, first-served approach made possible by safer, more powerful anti-rejection drugs. Today, the UNOS’s Organ Procurement and Transplantation Network (OPTN) gives priority to patients seeking organs from someone who dies based mostly on who has waited the longest.
The problem is that, in some cases, elderly recipients get organs from much younger donors whose kidneys could have provided far more years of healthy life to younger, heathier patients. Younger patients can receive older or less-healthy organs that wear out more quickly, forcing them back onto the transplant list in a few years.

What about a Market?