Solving Das XBox Problem

Every year around this time there is a shortage of the hot toy (this year it's the XBox) and economists wonder why the manufacturer doesn't raise price to siphon off demand.  To set the stage remember that the problem isn't why the good is in short supply.  We can explain that with increasing production costs and peak demand (see Tim Harford for more).  The problem is why the firm doesn't raise price to eliminate the shortage. 

The problem appears difficult because we see a) that the quantity demand greatly exceeds the quantity supplied and b) some units are sold at prices well above the selling price and thus we conclude c) $500 bills must have been left on the ground.  The conclusion, however, is false.  The key is to recognize that the shortage is largest when most people are not willing to pay much above the market price.

Take a look at the figure on the right.  Note that any price below the equilibrium price will generate a larger shortage for demand curve Da than for demand curve Db.  (Ignore the left tail on Da for the moment).

But this means that a large shortage is not a sign that manufacturers could make lots more money by raising the price - in fact, it is a sign of the opposite.  Raising prices even a little would reduce the quantity demanded a lot and would generate only marginally more revenue.

Does the fact that some XBoxes are being sold for high prices on Ebay mean that the firm could sell lots of units at those prices?  Not at all.  Relative to total sales only a few are being resold and not surprisingly these go to the gamers with the very highest values.  The resale market manages to pick off some of the people on the left tail of the Da demand curve but, absent price discrimination, the firm could not sell to these buyers without greatly restricting the quantity demanded and reducing profits.  Note also that the fact that most people with an XBox won't sell it for a price above what they paid is just the endowment effect - the firm could not sell at those prices.

Once we realize that a large shortage does not imply $500 bills on the ground explaining the shortage becomes much easier.  Small menu costs, small errors, or small values of maintaining consumer loyalty or generating "hype" (but see below) can all make it optimal or near-optimal to have a shortage.

Comments are open.  In the extension I explain why the usual explanation, a shortage generates hype, is not very convincing.

The usual explanation, a shortage generates hype, doesn't make much sense.  First, as Tim Harford also points out hype can be generated by high prices as well as by shortages.  Very high end luxury items, for example, like Lamborghini's are difficult to obtain but also very expensive.  Second, it's implausible that a shortage now could generate such greater sales later as to be worthwhile this is especially true given that Christmas is the peak selling season.  You want hype before not during Christmas.