Though I initially really liked the resolution to the second story, thinking about it further has made me realize that it's incoherent.
The cambist's answer in the second tale appears to be that life is valued by society's willingness to allow each one to trade life for pleasure, and that because the king is given a greater degree of freedom to trade, it follows that society values his life-time less. (Though even in this view I can't see how one would actually come up with a numerical result.) One flaw in this argument is that society holds freedom as having a value independent from life or pleasure. Another shows up if you imagine the counterfactual case of the king being a health freak: if he used his freedom to eat lots of fresh fruits and vegetables, while the prisoners only got dry bread, he would likely live longer than them -- but the way the cambist defines it, that wouldn't change the respective value of their days of life. Nailing the coffin is the fact that only a prisoner would make such a trade.
I think the question as asked is insolvable, because it doesn't specify perspective. If you asked the king how many days of a prisoner's life he'd trade for one of his own, and a prisoner how many days of his life he'd trade for one of the king's, you'd get different answers, and they'd both be correct; the utility functions simply differ.
Great story, though.
[As a side note, I wonder if there are some characteristics common to arguments that are wrong but in which it's difficult to locate the wrongness. Even though I know that the answer the cambist gave is wrong, and I can provide a counterexample that proves it, I still don't know exactly where it's wrong.]
That's not how I interpreted his argument.
I read it as "According to the actions they take, the king values an additional day of life at 82% of what a prisoner is forced to value an additional day of life at." The rest is explanation that the prisoner is worse off because of the coercion- if they could trade quantity of life for quality of life, they would- and that the marginal value of a day in someone's life is treated very differently from the value of their life in general or other threats. The king doesn't approach alcohol as an assassin that might kill him eight years early, but that's the actual impact on his lifespan.
Available in PDF here, the short story in question may appeal to LW readers for its approach of viewing more things than are customary in handy economic terms, and is a fine piece of fiction to boot. The moneychanger protagonist gets out of several sticky situations by making desperate efforts, deploying the concepts of markets, revealed preferences, and wealth generation as he goes.