Florence in 1427. The people at the top of the ladder are members of the city's powerful guilds, while those at the bottom are beating, cleaning and washing raw wool.
Fast-forward almost 600 years and while the jobs may have changed, the people have not. The very same families are still on top.
Researchers at the Bank of Italy have used surnames (which are relatively region-specific) as a proxy to inspect the fortunes of Florentine families since the 1427 census.
They found that the top five earning surnames in 2011 were also the elites six centuries ago, when they were lawyers or members of the wool, silk or shoemaker guilds. The researchers found evidence of dynasties in some elite professions such as banking and law.
That is not to say there was no mobility. Lower-class people had a fairly good chance of rising to a higher position, but there seemed to be a "glass floor" that stopped the upper classes from sliding to the bottom.
Florence is not unique. Studies (often using rare surnames to track families through generations) have found similar stories in countries as varied as Sweden and China. In Britain, the effect seems to last about six generations before finally petering out.
So what? Why should we care if a "glass floor" protects the rich from becoming poor, so long as the poor can become rich? Until recently, we have not cared very much. But now we might not have a choice.
There is a difference between relative and absolute mobility. Relative mobility measures whether you end up on a different rung of the income or social ladder from your parents. It is a zero-sum game: if someone moves up, someone else has to move down.
Absolute mobility simply measures whether you end up better off than your parents, regardless of what happens to everyone else. Over the course of the 20th century, absolute mobility increased in many countries as economies expanded and household incomes rose.
The shape of developed economies also changed: an increase in professional and managerial roles (which happened alongside the expansion of higher education) created extra room at the top.
Ms Marion Kimberley, a 72-year-old Brit I interviewed last year, was one of many to ride this wave. Her mother would cry with worry when the rent was due. Ms Kimberley was the first in her family to go to university, and remembers her father's excitement when her first job as an academic came with a higher salary than his.
But times are changing. Global growth has slowed sharply since the financial crisis. There is evidence that the latest generation may not be richer than their parents. If "room at the top" is no longer growing, social mobility starts to look more like that zero-sum game, in which upward mobility requires downward mobility too.
What stops people moving down?
A study by the LSE's Centre for Analysis of Social Exclusion compared the fortunes of British children born in 1970 who had performed well or badly on cognitive tests when they were five years old. The low-attaining children with rich parents were doing better in the labour market by the age of 42 than those with poor parents. The rich bright kids did better than the poor bright kids, too. The study concluded that a powerful mix of factors was helping children of the wealthy to succeed, from social capital to private school and access to higher education.
To boost relative mobility, you would need to unpick those privileges - or find a way to control for them - so the brightest could rise to the top, regardless of their backgrounds. That is tricky.
It is hard to disentangle someone's "pure talent" from his acquired advantages in a fair way. Some universities and employers are trying. British company Rare has a product that uses data analysis to put candidates' achievements in the context of their backgrounds.
It is also politically treacherous. When the British civil service suggested this month that it would take into account candidates' schools and backgrounds, Lord Waldegrave, the provost of Eton College, threatened to resign as the Conservative Party Whip in protest against what he saw as discrimina- tion against the privately educated.
These are early skirmishes in a fight over how to divide a cake that is barely growing. Either we find a way to revive productivity and growth, or we accept the alternative: that if we want more poor kids to climb up, we need more rich kids to slide down.
THE FINANCIAL TIMES