King-Davenant Law

The English Mercantilist Charles D'Avenant (1699) provided a schedule (from data he credits to Gregory King), relating the price of corn to the "defect in the harvest".  By relating the decline in supply to the resulting price, the first modern demand schedule was ostensibly outlined.  D'Avenant's passage in full is the following:

It is observed that but 1/10th the defect in the harvest may raise the price 3/10ths, and when we have but half our crop of wheat, which now and then happens, the remainder is spun out by thrift and good management, and eked out by the use of other grain; but this will not do for above one year, and would be a small help in the succession of two or three unseasonable very destructive, in which many of the poorest sort perish, either for want of sufficient food or by unwholesome diet.

We take it that a defect in the harvest may raise the price of corn in the following proportions:

Defect        raises the price                    above the common rate
1 tenth        ...............                           3 tenths
2 tenths       ...............                           8 tenths
3 tenths       ...............                           16 tenths
4 tenths       ...............                           28 tenths
5 tenths       ...............                           45 tenths

So that when corn rises to treble the common rate, it may be presumed that we want above one-third of the common produce; and if we should want five-tenths or half the common produce, the price would rise to near five times the common rate.

(Charles D'Avenant, 1699, Essay on the Probable Means of Making a People Gainers in the Balance of Trade, as reprinted in C. Whitworth (1771), editor, Political and Commercial Works of William D'Avenant LLD, Vol. II, p. 224-5)

We can depict the King-Davenant data graphically as follows.  Normalizing average price at 1 and average quantity at 10, we can thus construct a simple relationship from the above data:

  This is commonly credited to be the first econometric estimation of the "Law of Demand".  The original source in King's work has never been found, so many economists have credited this to be D'Avenant's own construction and estimation.

W.S. Jevons (1871: p.157) tried to fit the King-Davenant observations the following non-linear function form:

p = a/(x-b)n

where x is quantity of corn and p the price of corn, a choice dictated by his desire that the curve approach the axes asymptotically.  Jevons writes "An inspection of the numerical data shows that n is about equal 2, and assuming it o be exactly 2, I find that the most probably values of a and b are a = 0.824 and b = 0.12" (Jevons, 1871: p.157), or approximately:

 p = 5/[6(x-(1/8))2]

Years later, P.H. Wicksteed (1889) would take Jevons to task for supposing that the curve should not cut the axis.  Instead, Wicksteed proposes a third-degree polynomial with the following parameters:

60p = 1500 - 374x + 33x2 - x3

would fit the data with a "vraisemblence which is truly remarkable" over the range of the data considered (Wicksteed, 1889 [1910: p.738]).