There is a legend about the last king of the Romans, Tarquin. An old witch came to Tarquin, and offered to sell him nine books of prophecy at an exorbitant price. Tarquin laughed at the offer. The witch burned three of the books, and then offered to sell him the remaining six for the original price. Tarquin refused again.
The witch burned three more books and offered to sell Tarquin the three books that were left for the original price that she had demanded for nine. This time Tarquin was scared that he might be losing something precious, and bought the remaining three books for the price that the witch asked. What sort of demand curve is that?
Chris McMahon, by e-mail
Dear Mr McMahon,
Forget the demand curve; this is a two-player negotiation over the division of economic surplus. Tarquin was always willing to pay a high price but hoped to get a bargain. The sibyl ("witch" is such an uncouth label) responded with a supply constriction designed to drive up the price.
Tarquin might have thought that the sibyl had just one rival buyer, and if each buyer wanted only one trilogy, that would be a supply glut. Once there was only one trilogy available for two buyers, Tarquin knew he was in a serious auction and made a pre-emptive offer.
Another possibility is that the sibyl was dealing with the so- called durable monopoly problem. Tarquin knew that the sibyl might sell him an expensive trilogy, and then come back later with a cut- price offer to buy a second or third. By destroying two trilogies, the sibyl enabled herself to make a credible, take-it-or-leave-it offer. Forward-thinking stuff, but then, she was flogging prophecies.