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Instead of charging $X, why not charge $2X with prob 1/2 and $0 with prob 1/2?

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Re: Instead of charging $X, why not charge $2X with prob 1/2 and $0 with prob 1/2?

#3
The expected value is the same:

(0.5 * 2X) + (0.5 * 0) = X = (X * 1.0)

but perhaps you would be able to attract more customers. I doubt it. While it's certainly true that everybody loves a freebie, no one likes to pay twice for something.

Why not charge X with probability (1-p) and charge zero with probability p? The expected value would be reduced to (1-p) but perhaps you would attract people looking for freebies. More customers is always a good thing, right?

Re: Instead of charging $X, why not charge $2X with prob 1/2 and $0 with prob 1/2?

#5
A clever idea but I worry what happens to the people that miss out. They are either aware they've paid $2X (if you tell them) or they are aware that they've been "ripped off" (you are prepared to give it away for $0 so you must have at least 50% markup. Kind of like jewellery stores putting half price sales on $10-20k diamond rings). Either way you are associating negative feelings immediately and a sense of buyer's regret.

On a practical note, what stops them getting a refund and repurchasing until they get it for free.

Re: Instead of charging $X, why not charge $2X with prob 1/2 and $0 with prob 1/2?

#6
To sell your good a consumer must be both willing and able to pay. Under this system that would be the 2X price since he doesn't know which price he will actually get (if he knew ahead of time, or could back out of the deal after learning the price, you'd always be giving them away).

There's always going to be less people you can afford 2X than X.

Re: Instead of charging $X, why not charge $2X with prob 1/2 and $0 with prob 1/2?

#7
A more common variation of this idea is "Win your purchase free!", with the odds of winning being fairly low, but the price remaining the same.

Car dealerships seem to like this one, and Visa ran a similar contest here in Canada recently (called "Win What You Buy").

The success of this kind of promotion is most likely proportional to the price of your product.

Re: Instead of charging $X, why not charge $2X with prob 1/2 and $0 with prob 1/2?

#9
I think you're interpreting people's irrationality in the wrong way. People are often irrationally risk averse: most people would much rather pay $X with probability 1 than $2X with probability 1/2 and $0 elsewhere. The reason lottery tickets sell is because utility functions are nonlinear. After buying a $1 lotto ticket, they're still poor; they don't miss the dollar. But if they win, suddenly they are rich, which is qualitatively different from being poor. Thus, the calculation is a small but nonzero chance of being rich, vs. the certainty of being poor. Most people don't do the math to figure out just how small.

There's a reason why people indulge "If I won the lottery..." fantasies.

Re: Instead of charging $X, why not charge $2X with prob 1/2 and $0 with prob 1/2?

#10
As omegazero pointed out, there might be a selection bias if you don't do it right -- people will back out if they see they are in the unlucky group of folks who will get charged $2X.

If you make people commit before revealing the amount, the issue is trust: how do customers know that the odds are actually 1/2 that they'll pay $0? How do they know you aren't just charging everyone $2X? You'd have to use some verifiably random bit, which gets complicated. People will smell a scam.

(Speaking of which: are there any commonly used publicly verifiable random numbers, like a die roll, but outside of any party's control? I presume there must be a need for them in a number of situations.)

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