Inelastic demand means that a person really wants a specific amount of something.

When the price changes each individual has a choice: buy or don’t buy. The more inelastic someone’s demand, the less likely a price change will change that person’s purchasing habits. This works in both directions. Consider a healthy person free of cancer. A doctor cuts the price of chemotherapy in half. Is the person much more likely to buy now? Now consider a person with terminal cancer. He believes chemotherapy will save his life. Doctors double the price. Will this man now refuse the treatment?

On the other hand, consider land. How much land will you buy when priced at $500,000/acre? How much will you buy when priced at $5,000/acre?

Essentially the person who spends $500,000 on chemotherapy thinks he would rather have chemotherapy than 5,000 pictures of Benjamin Franklin, 500,000 double cheeseburgers or a new home.

How does one distinguish “necessities” from “luxuries”? For example, man cannot exist without food, but the price of wheat is probably more elastic than the price of chemotherapy. Does this make chemotherapy a greater necessity? Chemotherapy did not exist a few hundred years ago. It is still inaccessible for the vast majority of humans populating the world. Would/should the top priority for such people be to gain this necessity? Do the choices of acting man buying a cell phone in SE Asia support this idea?

Economics must refrain from valuing one thing as more necessary than another in of itself. Value comes from observing the choices acting man makes. Ludwig von Mises:

The teachings of praxeology and economics are valid for every human action without regard to its underlying motives, causes, and goals. The ultimate judgments of value and the ultimate ends of human action are given for any kind of scientific inquiry; they are not open to any further analysis. Praxeology deals with the ways and means chosen for the attainment of such ultimate ends. Its object is means, not ends.
In this sense we speak of the subjectivism of the general science of human action. It takes the ultimate ends chosen by acting man as data, it is entirely neutral with regard to them, and it refrains from passing any value judgments. The only standard which it applies is whether or not the means chosen are fit for the attainment of the ends aimed at.… it is in this subjectivism that the objectivity of our science lies. Because it is subjectivistic and takes the value judgments of acting man as ultimate data not open to any further critical examination, it is itself above all strife of parties and factions, it is indifferent to the conflicts of all schools of dogmatism and ethical doctrines, it is free from valuations and preconceived ideas and judgments, it is universally valid and absolutely and plainly human.
http://mises.org/humanaction/chap1sec4.asp

Ultimate ends are ultimately given, they are purely subjective, they differ with various people and with the same people at various moments in their lives. Praxeology and economics deal with the means for the attainment of ends chosen by the acting individuals. They do not express any opinion with regard to such problems as whether or not sybaritism is better than asceticism.…
Any examination of ultimate ends turns out to be purely subjective and therefore arbitrary.
Value is the importance that acting man attaches to ultimate ends. Only to ultimate ends is primary and original value assigned. Means are valued derivatively according to their serviceableness in contributing to the attainment of ultimate ends. Their valuation is derived from the valuation of the respective ends. They are important for man only as far as they make it possible for him to attain some ends.
Value is not intrinsic, it is not in things. It is within us; it is the way in which man reacts to the conditions of his environment.
http://mises.org/humanaction/chap4sec2.asp

From his point of view the physiologist is right in distinguishing between sensible action and action contrary to purpose. He is right in contrasting judicious methods of nourishment from unwise methods. He may condemn certain modes of behavior as absurd and opposed to “real” needs. However, such judgments are beside the point for a science dealing with the reality of human action. Not what a man should do, but what he does, counts for praxeology and economics. Hygiene may be right or wrong in calling alcohol and nicotine poisons. But economics must explain the prices of tobacco and liquor as they are, not as they would be under different conditions.

There is no room left in the field of economics for a scale of needs different from the scale of values as reflected in man’s actual behavior. Economics deals with real man, weak and subject to error as he is, not with ideal beings, omniscient and perfect as only gods could be.
http://mises.org/humanaction/chap4sec3.asp