For comparison with mainly agrarian pre-industrial societies, it is possible to derive estimates of X from figures in the Maddison Project Database, which contains estimates of real per capita GDP at various historic dates for various countries. For the UK / England, for example:
$$\frac{\text{UK Per capita GDP 2010}}{\text{UK Per capita GDP 1720}}=\frac{23777}{1703}=14$$
For the US and predecessors:
$$\frac{\text{US Per capita GDP 2010}}{\text{US Per capita GDP 1720}}=\frac{30491}{900}=34$$
However, such figures should be treated with extreme caution for various reasons:
- The data underpinning GDP only began to be routinely collected in
the mid 20th century following the work of Kuznets. Earlier
figures, however carefully researched, are inevitably estimates and
unlikely to be very accurate.
- Even if accurately measured, GDP is subject to many well-known limitations
as a measure of welfare (see for example here). One limitation
which is perhaps especially significant when making
comparisons over long periods of time is the exclusion of unpaid household work. Ordinary
people in the 18th century, living rurally as most of them did, are unlikely
to have had either the opportunities or the means that people have today to
pay for others to do their cooking, cleaning, laundry, etc.
- Many countries have changed in size and area. It isn't clear, for example,
whether the US figures for 1720 relate to the whole of the current area of
the US (and so include the economies of Native Americans), or whether they
just include the regions then settled by Europeans.
- A further pitfall would be to interpret these figures as estimates of growth
in productivity arising from improved technology and capital accumulation. Even the low living standards of the 18th
century were achieved with much lower population densities than today,
implying on average much more land suitable for agriculture per person. So it can be argued that the figures under-estimate productivity growth.