Does Anyone Truly Know Their Reservation Price?

(Originally written on April 14, 2011)



The idea of a reservation price has always worried me. I don't know how many times I've played out some scenario in my head of how a certain situation might go if two particularly stubborn people, with all the time in the world to spend, are haggling over a price. For simplicity I like to assume it's just a gallon of milk.

I myself just bought a gallon of milk a few hours ago, for $3.98. And it just leads me to wonder… they say "everyone has a price" and some people think that this literally applies to everyone and everything. I won't necessarily argue against that position, it's rather complicated and emotion-centered (which makes it wildly difficult to actually debate with anyone who isn't willing to approach it rationally as a simple though experiment) but there are some things that I'd really, really like to say I wouldn't take anything for. To throw out one of the more extreme examples, killing some designated person for, say, twelve billion dollars (yes, very extreme case). I want to say that I would just flat-out turn this down, regardless, even if I was somehow guaranteed immunity from the law. But I think it's worth pointing out that twelve billion dollars (or some other similarly INTENSE amount of money) is not an easy thing to comprehend fully, to genuinely grasp the implications of, not to mention that the value of a human life is most likely an even more difficult concept to consider in any practical value, so I just end up dismissing the thought altogether. I default to "NO WAY!!!" and I hope everyone else would too…

(If the idea offended anyone…. my apologies. But I find that developing an extremely extreme case is usually the best way to help reconcile some conflicting idea in my head. Not to trivialize the life of a fellow human in any way, but to point out that the question is pretty much meaningless in some cases because there is way too much at stake for some spontaneous decision to be made.)

Anyway… some guy is staring at a gallon of milk on the shelf at some small, local, privately-owned grocery store. He doesn't like the price. He is frowning. The tag says "$7.49". He frowns for so long that the owner comes over and offers assistance. By the way, the guy's name is Arthur Dent. Arthur complains about the price of the milk, and the owner apologizes and says that… I don't know, there's been a shortage at the farm that supplies him and he has to temporarily raise the price of milk. Arthur keeps protesting and says that Walmart has gallons of milk for $3.98. And the owner is like "WELL GO TO WALMART THEN!!!" No, just kidding. But the owner can at best lower the price to whatever it is he paid for it. And of course he doesn't want to… and of course Walmart is not going to suffer extreme price fluctuations like this poor shop owner will (at least in this simulated ideal world). And of course Arthur can drive his whiny self over to Walmart and pay a "guaranteed low price." But I doubt Walmart is even going to consider haggling over the price of a gallon of milk with him. There are thousands of people that are going to be willing to pay whatever the price is (within reason) on any given day, most likely, and Walmart will not even notice that this one sale was lost, I'm sure.

(You're probably thinking "Ideal world??? Yeah right!")

So Arthur has various options at his disposable, the most likely being: 1) go to Walmart and buy it there but, of course, probably spend half the difference in gas just to get there; or 2) HAGGLE.

The first thing that bothers me is this: What is Arthur's reservation price? Obviously $3.98 is a reasonable price to him, and clearly $7.49 is not. At what point in between is he going to be satisfied? Again, I like to take the extremely extreme example and consider this price-hunting in increments of one cent. One measly cent at a time. Would Arthur be willing to pay $3.99? $4.00? $4.01? $4.02? Unless he has some severe aversion to the number "4" he's probably still willing to buy. Fast-forward a little bit and we're at $4.25--still willing? Probably, I imagine. Probably even at $4.50, although there might be a slightly frustrated sigh as he grabs it off the shelf.

Let's assume that, when asked, Arthur decides that at $5.00 he will not buy the milk. This, he proclaims to the world, is his reservation price. On the surface this seems reasonable. I probably wouldn't pay that much (if I had a choice). By the way, I am the shopkeeper. Arthur won't pay me $5.00 for a gallon of milk, that knee-biting jerk, so I drop the price to $4.99. Would he be silly to refuse, if $5.00 was his reservation price? I mean, what's a penny, anyway?! If he doesn't give me the penny he'll probably pull something, his keys, out of his pocket and toss the poor thing over his shoulder in disgust later in the day, anyway. Maybe he still won't buy it, once he thinks it over. So I drop another penny. Is $4.98 reasonable enough? Every time he refuses I drop another penny. At some point he's going to agree (and if it's obvious that he's just refusing in order to get the next penny then the experiment is useless--I should point out that both people are being completely honest here. …Yes. The world is ideal in my head. I know… crazy…).

So maybe he finally agrees to the price of $4.75. This is now his (revised) reservation price, as he clearly hadn't considered carefully enough. Now, naturally, I would like to get every penny I can out of this stingy idiot (I am exaggerating my harshness towards him; after all, we are all stuck in this economy which everyone is so keen to point out "is bad"), and it's my turn to start haggling again. We've established that he's willing to pay $4.75, and maybe I don't feel like this is enough profit for me. So I refuse the deal, and ask if he'll pay $4.76. Is it reasonable to say no? It's a penny more than he would have paid. And if this argument wins him over, and he's ready to give me $4.76, then how about $4.77? It's only a penny more!!! So now we're working our way back up towards $5.00.

At what point do both sides cancel out? For the life of me, I cannot settle this dispute in my head. You can always add a cent, or take off a cent, and who is anyone to make a fuss over this? But you have to, at some point--I think at some point you have to just stamp your foot and say "STOP HAGGLING WITH ME I WILL NOT BUDGE!" Otherwise, the loop will go forever, because one cent is too small an amount to accurately judge against any other (unless you're buying individual tootsie rolls...?). Thankfully, not many (if any) people actually do this. And if anyone ever does, some wise-guy shopkeeper, I'll just be like "Don't even bother with that nonsense, I've already tried!"

But it's interesting... because you could... and it seems to me that the more stubborn of the two is going to win. Or the one in more desperate need. Or the one who can come up with the more convincing argument. Or the one with the gun in his belt. If I, as the shopkeeper, am trying to argue that it's only one more penny out of Arthur's pocket by raising the price a little, and Arthur has every reason to argue that it's only one more penny not going into my cash drawer by lowering the price slightly, then we have come to an impasse. The logic works both ways…

I hope I don't sound like a lunatic. This sort of thing keeps me up at night. :/

But it's fun. This kind of train of thought is just... interesting! And I get tired of arguing with other simulated versions of myself inside my own head…

XD

Posted by Eli Stanley | at 5:27 PM

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