Seth’s got a pretty good post up on the importance of ignoring sunk costs. He makes a couple of mistakes, however, that are worth clearing up.
The Scenario
Seth lays out the following hypothetical:
You have tickets to the Springsteen concert. They were really hard to get. You spent four hours surfing StubHub until you found the perfect seats for $55 each.
On your way into the event, a guy offers you $500 cash for each ticket. Should you sell?
The Answer
The correct answer is “it depends whether or not each ticket is worth less than $500 to you at that moment”. If it is, you sell, if it isn’t, you don’t. This is essentially the answer Seth gives, but he makes a couple of mistakes getting there.
Irrelevant?
Seth writes that “…the amount of time you spent getting the tickets is irrelevant.” This is sort of true. Certainly, the time you spent getting the tickets has no direct bearing on the question of their worth to you at the moment you’re offered the chance to sell them, but their total cost is not an unreasonable proxy for that worth. (This hypothetical is a bit of a special case, in that the value of the tickets to either you or other people is unlikely to change between the time of purchase and the date of the show. Not all cases are like this.) If, for instance, you’d spent $10,000 per ticket (in money, time, or some combination thereof), that would tell us that you probably wouldn’t sell them for $500 apiece.
However, let’s assume that $500 is more than the face value of the ticket, and that you spent no more than face value (totaling up the value of the time you spent finding the tickets, and the cash you paid for them) acquiring them. In that special case, it’s true that their cost tells us nothing about whether or not you are likely to want to accept the offer.
(By the way, to illustrate a computation of a “true” purchase price using Seth’s example, let’s assume you’re a well-compensated marketing consultant, making $120K/yr, buying 2 tickets. Your time has a value of about $60/hr – that’s $120K/year divided by 2000 working hours per year – so the total cost of the tickets is 4*$60 + 2*$55 = $350, or $175/ticket.)
(Yes, the methodology for assigning a marginal value to your time is huge hack.)
Willing to Pay
Seth’s more serious error comes when he writes:
If you wouldn’t be willing to PAY $500 for these tickets (and you weren’t, or you would have)
This doesn’t follow at all. It’s usually the case that goods are valued by their consumers above their price. (Value and price intersect only when the last product of a particular type is consumed; before that, value tends to exceed price. Price never exceeds value; in that case, no transaction occurs.) The purchase price of the tickets (again: including the cost of your time) tells us the minimum value you placed on them at the time of purchase, but not the maximum.
To illustrate the point: Gold trades at about $900/oz. Suppose someone offers to sell you a 1oz gold coin for $100. (I don’t know – they’re crazy.) You’d buy it. But it would be nonsensical to conclude from the purchase price of $100 that the coin isn’t worth, say, $500 to you. You just happened to get a really good deal.
To Be Sure
Overall, Seth’s post is a good one, and he’s right that prices do tell us something about the values people place on things. In general, however, purchase prices only tell us about minimum utilities, not maximums. (Prices tell us about maximums only when people decline to purchase something at a particular price.)
