Infinite Value?


Last night my professor claimed that there was no amount of money that he would accept in exchange for losing his arm.  I think he may have even said his value for his arm was “infinite”. 

If this is what he meant, I have trouble believing this to be true.  If so, it would suggest that he would pay me any amount of money if I threatened to cut his arm off.  The expected value of losing infinite value is certainly worse than all of the money in his bank account.  Or, for example, it would imply that he never leaves the house because of the small, but very real, risk of losing a limb in some freak accident.  It wouldn’t be worth it.


12 Responses to “Infinite Value?”

  1. Jason Says:

    I beleive he said infinite to the point of still having food and shelter. So it is finite. Lets say said proffessor makes 100k. If it requires (in DC) 35000 for him to feed and shelter his family. That means “infinite” in his case is 65k. So while a superlative was used he used infinite in a finite way.

    Me you ask? I definately would put a price on my arm. It would depend on a few things though. How much of my arm would be taken? I definately would require more compensation if you cut it above the elbow rather than below, as with the shoulder (an oddly spelled/looking word don’t you think?). I’m not sure the exact number but somewhere above a million and bellow a billion (though I think I could be persuaded to give it up for more than a billion too ;)) Think of what I could do with all that dough, end poverty in Aledo, TX as well as providing for all my future children and grand chilldren and so on with education and a solidified foundation for survival.

  2. Jason Says:

    What should be considered as well is the endowment effect. People often value something they have more than they would be willing to pay for the same Item. EX: I’m willing to pay $5 for item x but would require $6 to give it up. So in said proferssors case he is only willing to pay up the the amount to which he’d have enough for food in order to save his arm if forced, but would require more to voluntarily give up his arm.

  3. Eli Says:

    I think that he could be telling the truth. He did not say that he received infinite utility from his arm—only that no amount of money would induce him to make the trade. Suppose that his MU of money is diminishing sufficiently rapidly to make his total utility from infinite money converge. In this case, as long as he gets more utility from his arm than the difference between this converged utility of infinite wealth and his utility of current wealth, then he would not make the trade. He might still go out of the house and risk losing his arm, because he might get utility from running errands or going to work. In other words, this is not so much a claim about the value of his arm as it is about the value of money.

  4. Stewart Says:

    Is not the distinction between calculated risk and compensated certainty? For example, it is possible that my family, my friends, and my loved ones will be annihilated in a nuclear holocaust. This would suck. The possibility exists but they do not live in bunkers. I would not trade their lives for any amount of money. I do not see an inconsistency with an absolute aversion to certainty of loss.

  5. Stewart Says:

    Isn’t another possibility that when a failure to trade occurs, we assume the price to be infinite? Functionally infinite, not platonically infinite?

    EDIT: fixed a typo but!=not

  6. kebraks Says:

    Everyone has interesting comments, but if our good Professor did say that he valued his arm infinitely, as my post assumes, would he then be acting in discord with his statement?

  7. Eli Says:

    Not necessarily. What if he also values leaving the house infinitely? He also indicated that you couldn’t pay him enough to do jail time, so this may be the case. How do you make trade-offs between two things that you value infinitely? Obviously, I don’t know, but I do know that observed behavior would not contradict such preferences.

  8. kebraks Says:

    Interesting. That seems to raise the question of what “infinite” really means. Does it mean anything or is it “operationally meaningless” like “need”?

    Infinite is defined as “unbounded, unlimited”. This seems to suggest that one couldn’t value everything infinitely, because there are bounds such as scarcity, which require trade offs. But if some things can be valued infinitely, it seems to suggest that there is no margin at which you would substitute away from it. Maybe, by definition, you can’t infinitely value two things that require any trade offs with each other.

  9. Jason Says:

    I’d say if he valued his arm infinitely and thus would take no payment for it then he would never have to do anything that increased utility as you can’t go up from infinity. If I derive infinite utility from a a rock. As long as I have the rock it is functionally meaningless to do ANYTHING else as all it is doing is costing me time away from my rock. If he values having his arm infinitely then why read, sleep, have a family, teach, etc. as it isn’t increasing his utility. infinite utility derived from something is a functionally meaningless phrase. I understand what he means though, he values it so much that the chances of someone paying enough for his arm aren’t reasonably possible, even though it exists. If you look at the horizon while in west texas on a flat road, the road seems infinite, though it isn’t, the same is with the value of the arm.

  10. Eli Says:

    I think you would have to apply L’Hôpital’s rule.

  11. Stewart Says:

    My argument:

    Given infinite funds I doubt I could pay any of you to kill yourselves. That being the case, it does not follow that until the end of your days you will hide in a bunker.

  12. kebraks Says:

    L’Hôpital’s rule can fail to work depending on the behavior of the derivative in the limit.

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