Yes, a person has ownership over his or her own body, but this type of ownership should not be allowed to be transferred to any other party.
We should instead look for alternative solutions to the problem of kidney shortages that does not amount to coercion of vulnerable individuals, or to body commodification, which the legalization of kidney sales would entail. "The integrity of the human body should never be subject to trade", and a system is unethical "when it penalizes the weakest people and exacerbates discrimination based on census" and generates "the risk of exploitation of vulnerable donors" (Kishore).
MacKay also states that it would be wrong to tell someone that he has to die from kidney failure because selling a kidney is morally wrong (96). What is morally wrong is telling a poor person that if they want money then they should sell their kidney or remain in poverty. "It's reasonable to assume that rich people are responsible for the poverty that exists in the world, if not directly through their actions (trade policy, colonization etc.) then through their failure to prevent or remedy poverty" (qtd. in Sandel 72). Now, if you first create poverty and then tell poor people that you'll give them money but only if they give you their organs in return, then you add insult to injury. Insisting on the possibility of trade while neglecting the necessity of justice is wrong.
While it is true that most individuals have two kidneys so they can spare one, there is no guarantee that the person really will be able to live with just one kidney - disease or injury later on could be fatal for a kidney donor. This is even more likely with the poor because of their health, behavior and where they live. Besides, who pays if a donor is harmed or developed renal failure of unrelated and theology 15 years later and needs a transplant? .
Organ transplant is a medical device to advance standards of greater social equality rather than exploit people in poverty.