Thursday, September 08, 2005

 

Tree-stump shaped demand

Some points from the argument between Tim Worstall and Jesse Taylor over "price-gouging".
To recap: John Stossel made an argument, with a hypothetical example, to the effect that if you pay a high price for some essential, you should be glad that the price was set high, because had it been set low the vendor would have already sold out and you wouldn't have it at all.

Jesse Taylor attacked this argument as "odious".

Tim Worstall then nominated Jesse Taylor as an "Economic Idiot"

After that, things started to get unfriendly.

The sides are so far apart in their unstated assumptions that they appear quite unable to comprehend each other. After much pondering, however, I think I understand Taylor's claim that the seller is "artificially encouraging scarcity".

The model Taylor is using is that a buyer is going to buy a bottle of water over a two-day period. If he buys it on day one, he will be willing to pay p1 for it. If he is unable to buy it for p1 on day one, by day two he will be desperate, and willing to buy it for p2, where p2 > p1. The seller is only able to get p2 for the bottle by not selling it on day one. Therefore, he is "artificially encouraging scarcity" -- he isn't just profiting from the scarcity (the price of p2 on day 2), he's caused it by having withdrawn from the market on day 1.

The root error, as usual, is denying the law of demand - Taylor is (implicitly) claiming that the only people who will buy less water if the price increases are poor people who are not able to buy sufficient for their needs.

In what I call the "tree-stump" model of demand, the quantity demanded by an individual of a good is given by the formula

max( n, w / p )

Where p is the price, n is the amount the individual "needs", and w is the amount the individual can afford to spend.

[ I call it "tree-stump" for it's shape - it's a poor description, but I can't think of a better one. ]

Given this model of demand, the only reason total demand decreases when the price increases is that some people cannot afford as much as they need.

Another implication of this model is that there is no optimum price for the seller. As the price increases, revenue increases, until everyone in need is paying everything they can afford for whatever they can get.

I think Taylor and the critics of "gouging" are assuming that demand is approximated by this model, at least for some essential goods. Under this model, controlled prices would not restrict supply, but would redistribute some of it from richer buyers to poorer buyers.

The important way in which this model is in error, (apart from ignoring the effect of competition among sellers), is in the flat part. I might "need" two bottles of water a day to maintain reasonable health. Normally, however, I might drink eight. If the water is at "normal" price, I'll probably buy and drink those eight. If it is increased, I will buy less. Arnold Kling addressed this point recently in a very similar argument over pricing of health care.

Now it might be that Taylor sees this as just another form of gouging: that if I am greedily drinking water to keep comfortable, while others are suffering, that is just as bad as the high prices that would have dissuaded me from doing it. If that is the case, then what he is asking for is not simply for vendors to sell at the normal price to whoever turns up first, but for goods to be deliberately allocated, by sellers and potential buyers, to the needy. In an extreme emergency, that is a very desirable outcome, (as opposed to more stable situations, in which the issue of encouraging greater production comes to dominate) but denunciations of "gouging"are not nearly sufficient to achieve it - for every vendor selling the good there are probably many buyers who would willingly consume more than they need if the price were low enough.

This has got long, but I think it's necessary to try to understand the errors of these people, rather than just calling them idiots. Apart from anything else, they have shown in the comments at Tim's that they can at least equal our powers of vituperation: we're going to have to resort to rationality. Also, they're too plentiful to dismiss.
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