| | Tim, since you're an economist, I assume you know the answer(s) to your question, but I'll go ahead and take a shot at it. It may be instructive to some (including me) and entertaining to others.
The easy answer is that the kid would say, "No deal!" and hang on to his $15. Just because someone makes ridiculous demands doesn't mean others must accede to them.
So you could change the scenario to make it one where the kid can't say no. That's what Scott D. did above. Say the guy has insulin that he doesn't need for himself, the kid's a diabetic, and the kid doesn't have any insulin of his own. Under "normal" conditions, the kid could again say, "No deal!" and find someone else to sell him insulin at a more acceptable price.
But since we're assuming that the guy and the kid are on a desert island, then I guess we're assuming as well that there's no other source of insulin than this guy. Then, depending on how much time the kid has to live, he can (1) try to negotiate a better deal, (2) grant the guy his wish, or (3) grab the insulin and run. I think that, in this context, choice (3) is moral when the kid's need becomes dire (or when it becomes clear that the guy won't change his mind). The guy is being immoral by making an impossible demand. My view of this situation would be exactly the same if the guy demanded just one penny for the insulin, while knowing all along that the kid has no money at all, and the guy steadfastly refused to accept anything else. By sticking to an impossible demand, the guy is choosing the path of death when he could, at no cost to himself (he doesn't need the insulin, and there's no one else to trade it to), choose the path of life.
OK, so what if the guy made a demand that was not impossible but very aggressive (e.g., "become my servant for 10 years at a salary of 10 cents a day")? The moral course for the kid would be to say whatever he needed to say to get the insulin in time to survive and then to perform the agreement only to the extent that he (the kid) thinks is appropriate under the circumstances. This is a desert island with 2 people, not a market. They are both trying to survive: each should do what he needs to do to keep himself alive, each should do what he can to keep the other from dying (if it doesn't entail a material risk to himself), and where possible they should try to work together to come up with better solutions than either could have managed alone.
BTW -- For more on price theory (but not on desert islands), I highly recommend Thomas Sowell's Basic Economics.
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