Thursday, September 4, 2008

The Science of Sales

I wasn't born in the US - I moved here soon after I turned twenty. I remember the first time I opened the newspaper on one of the big sales days (I think it was the 4th of July weekend, but it's been a while) - and I saw sales on pretty much everything I could possibly imagine wanting over the next year. I felt really lucky to have this opportunity to buy some cool stuff at "unheard of prices," but as a recent immigrant, I didn't have a fat bank account, and I hadn't cottoned onto the American Way of credit card debt (fortunately, I still haven't!). And then the next holiday weekend came around and it was the same story - sales as far as the eye could see. And then the next, and the one after that.

So, why all the sales? That's a two-part question.

Why would anyone have a sale?

Well, obviously sales draw customers, but if people get to expecting a sale every major holiday, won't they just defer their major purchases until the next holiday? Are all the stores insane?

Turns out the answers are yes (for some people - but that isn't a bad thing) and no, the stores aren't insane.

It all comes down to a form of what economists call second degree price discrimination - allowing people with different levels of price sensitivity to self-identify and buy the right "product" for them. The reason I put the word "product" in quotation marks is because the time at which you buy a given product changes the product. For the elite gamer, for example, owning the latest hot game the day it comes out is more valuable than owning the same game several months later. Similarly, some people want to have that new car, TV, patio set today. Waiting three months just isn't worth what they expect to save when it goes on sale. They're going to go and buy it now, unless the sale is around the corner.

Other people really do want to pay the best price they can for something and they can (and don't mind) waiting to get it. So, they wait for the sales and battle the crowds of like-minded individuals to get that new wide-screen TV, while the less price sensitive people get to sit out the rush and relax on the patio with a cool drink. Or something like that. The ability to relax on the patio while everyone else is out shopping is one of the benefits the less price sensitive people get in return for the higher price they paid for the same product - and they value it more than the people who waited for the sale.

Why does everyone have a sale?

Because if they didn't, they'd lose out on the price sensitive customers (assuming at least one competing store does have a predictable holiday sale), and they don't want that to happen. Would everyone be better off if nobody had a sale? Possibly, depending on the demand curve for the product your store sells. But that isn't what game theorists call a Nash Equilibrium - in other words, even if everyone did best in a world with no sales, in that state any store could increase their profits by having a holiday sale. Turns out that if at least one competing store is having a sale, you'd do better by having a sale than not having a sale (since you'd get some of the price sensitive shoppers instead of none). So, under no condition can you do better than having a sale. Hence the rash of sales.

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