Did Adam Smith make a calculation error in Chapter XI of Book I?

Question

Excerpt from Chapter XI of The Wealth of Nations (emphasis mine):

The money-price of wool, therefore, in the time of Edward III, was to its money-price in the present times as ten to seven. The superiority of its real price was still greater. At the rate of six shillings and eightpence the quarter, ten shillings was in those ancient times the price of twelve bushels of wheat. At the rate of twenty-eight shillings the quarter, one-and-twenty shillings is in the present times the price of six bushels only. The proportion between the real prices of ancient and modern times, therefore, is as twelve to six, or as two to one.

If my math is correct, the proportion is four to one, not two to one.

If 6 bushels cost 21 shillings, then 12 bushels cost 42 shillings, and 42 divided by 10 is ~4.

Did Smith make an error here?

Answer 1

What you have calculated (based on Smith's data) is the ratio of the money price of wheat in Smith's time to its price in the time of Edward III (14th century). The same result could be obtained more directly by dividing the former (28 shillings per quarter) by the latter (6 shillings and 8 pence per quarter) (see note).

From the extract (and ignoring the first sentence for the time being) we can infer the following consistent set of ratios, in each case expressed as number in Edward III's time to number in Smith's time:

Ratio of money price of wheat $\,6.66 : 28 \approx 1:4$

Ratio of money price of wool $\,10:21 \approx 1:2$

Ratio of real price of wool in terms of wheat $\,\dfrac{10}{6.66} \Big/ \dfrac{21}{28} = \dfrac{3}{2} \Big/ \dfrac{3}{4} = 2:1$

However, the ratio for the money price of wool as calculated above ($1:2$) is quite different from that in the first sentence of the extract ($10:7$). The explanation for this difference lies in the following passage which comes just before the OP's extract:

There are many authentic records which demonstrate that ... about 1339 ... [the] price of ... twenty-eight pounds of English wool was not less than ten shillings of the money of those times, containing, at the rate of twenty-pence the ounce, six ounces of silver ... equal to about thirty shillings of our present money.

If thirty shillings is taken as the money price of wool in the 14th century, the ratio to its price in Smith's time becomes $30 : 21 = 10 : 7$.

This does however suggest that the passage as a whole is, if not in error, then at least inconsistent in switching between two standards of value, namely, silver and wheat.

Note
In old English money 12 pence equals 1 shilling. Thus 6 shillings and 8 pence is almost a quarter of 28 shillings and exactly two-thirds of 10 shillings.