When you're young, you expect to have a great deal of time ahead of you. You haven't spent much time yet, and so what remains seems like a fortune in comparison - enough to squander. Think of the way that wealthy children so often turn out despite the best efforts of their parents, their view of the value of money and economic common sense poisoned by having grown up with access to a great deal of money. But before you look down on them or pity them, think of your own situation with respect to the expected time remaining in your life. Your viewpoint on time, life, and the future was poisoned by having what appeared to be a great deal of remaining time, far more than it was easy to compare against what little you had lived to date ... so you valued time poorly.
We are evolved to squander the resources that shower upon us and gather in their piles, while spending a great deal of care, thought, and worry on resources that are scarce. So we care little about air, not so very much more about water, and not at all about time when we are young. But that stock of time diminishes as you grow old, and because there is less of it, it becomes more valuable. This is one reason why people are willing to spend greatly on medical technologies at the end of their lives - and here I am talking only of willingness, not any need to spend more. Aging brings with it degeneration and disease, and the cost of remaining alive and able to enjoy life accelerates with the passing years: the old spend increasingly more than the young because they have to in order to stay in the game. Note that "have to in order to stay in the game" is not the same thing at all as "willing to."
To be old is to live in in the mirror image of youth: time and no money has turned into money and no time. The value of money to an old person is typically less than it is to a young person, and that is nothing more than a measure of how much of the stuff you have: old people are typically much wealthier. The converse is true of remaining time, of which the young have a great deal, whilst the old are time-poor; thus the exchange rate between the time and money is radically different at the opposite ends of life. A young person will give away an hour to gain a small number of dollars, while an old person will spend ten times that sum to gain another hour. A cynic might suggest there is some form of arbitrage to found in this truth of human nature. If you like thinking along these lines, you might look back at past ruminations on the nature of wealth in a past post.
Time is everything. How much have time you spent reading this far? Could you have been doing something more useful, more optimal from your perspective? We make these small evaluations constantly, because time is the most valuable thing we have.
There are always people in the academic world who'd rather spend time looking at factors other than the obvious ones when it comes to aging and economic activity, of course:
Low opportunity cost, weak influence of quality of life in the face of death, the social value of life extension to others, shifting psychological reference points, and hope have been proposed as factors to explain why people apparently perceive marginal life extension at the end of life to have disproportionately greater value than its length. Such value may help to explain why medical spending to extend life at the end of life is as high as it is, and the various factors behind this value might provide normative rationale for that spending.
Upon critical analysis, however, most of these factors turn out to be questionable or incompletely conceived; this includes hope, which is examined here in special detail. These factors help to explain complexity and nuance in the normative issues, but they do not provide adequate justification for spending as high as it often is. In any case, two additional factors must be added to the descriptive explanation of high spending, and they throw its normative justification into further doubt: the "insurance effect" and provider-created demand. Overall, the perception of especially high value of life at the end of life provides some normative justification for high spending, but seldom strong justification, and not for spending as high as it often is.
The trouble begins with a person deciding that an entire clade of people are making systematically incorrect assessments of value despite having access to complete and correct data. Value is subjective, not objective, and it shouldn't be at all surprising that at the end of life there are radical shifts in the value placed by a dying person upon money and time. Note that I don't say "perceived value" - that phrase is just a subtle way of suggesting that the author is correct and the members of the clade are systematically wrong, which is in turn a subtle way of suggesting that value can be objective.
If you have bad or incomplete data, the value you ascribe will probably prove to be unhelpful if you act upon it, but it is still your subjective value: there is no "wrong" or "right" here, just a record of the outcome of a series of actions. People have a way of saying that you valued something wrongly if, by your actions based on that value, you manage to do yourself harm, economic or otherwise. But that really isn't a helpful way to look at subjective value: it is what it is, at any given moment. Either way, I'd argue that when it comes to life, longevity, and medical technology, there's a lot of reliance on bad and incomplete data taking place these days, given the possibilities presented by longevity science and the level of public ignorance of those possibilities. A fraction of people alive today will have the opportunity to live for centuries or longer, but consideration of that possibility is almost entirely absent from their economic calculations.
I suppose I should also mention that this short discussion has nothing much to say in connection with the horrible state of medical economics in the US. Participation in the heavily regulated marketplace for medical technology and services is a pit of horrors for both old and young: everyone suffers from the effects of regulation, lack of accountability for costs incurred, and the general miasma of government-induced systems failure. So arguments based on differential willingness to spend on medicine by age stand apart from that mess.
The neat endpoint to this post, if you want one, is that it can't hurt to think on the value you place on the time remaining in your life expectancy, and to look at whether you are basing both expectation and value on factual data.