Smith disagrees with you on poverty
This is actually slightly more nuanced than your usual posts, Worstall, though I find both your view and that of Lanchaster questionable.
Smith discusses, at length, the basis for wages, the impacts of a sub-living-wage pay on the economy, and the effects on overall welfare of increasing that of the poorest of society.
It's also interesting to note how he defines poverty, in his passage describing the poor of China. It's not on the basis of their monetary wealth, income, or spending, but on the quality of their life:
"The poverty of the lower ranks of people in China far surpasses that of the most beggarly nations in Europe. In the neighbourhood of Canton, many hundred, it is commonly said, many thousand families have no habitation on the land, but live constantly in little fishing-boats upon the rivers and canals. The subsistence which they find there is so scanty, that they are eager to fish up the nastiest garbage thrown overboard from any European ship. Any carrion, the carcase of a dead dog or cat, for example, though half putrid and stinking, is as welcome to them as the most wholesome food to the people of other countries."
That is: poverty isn't a wage, it's a standard of living. And it absolutely is relative.
Smith describes income, "the real recompence of labour", again, in terms of what it gains: "the real quantity of the necessaries and conveniencies of life which it can procure".
And as to increasing the lot of the poor:
"Is this improvement in the circumstances of the lower ranks of the people to be regarded as an advantage, or as an inconveniency, to the society? The answer seems at first abundantly plain. Servants, labourers, and workmen of different kinds, make up the far greater part of every great political society. But what improves the circumstances of the greater part, can never be regarded as any inconveniency to the whole. No society can surely be flourishing and happy, of which the far greater part of the members are poor and miserable. It is but equity, besides, that they who feed, clothe, and lodge the whole body of the people, should have such a share of the produce of their own labour as to be themselves tolerably well fed, clothed, and lodged."
Yes, the post-Industrial Revolution period has increased the average wealth of many. Gregory Clark of UC Davis notes though, in his book "A Farewell to Alms" that the average income of those in the poorest nations of the world has actually _fallen_. "There walk the earth now both the richest people who ever lived and the poorest."
So that $1.25/day wage is actually somewhat worse than was the case in historical times. People with so little access to resources then would already be dead.