There's been discussion of inequality and social mobility lately, e.g. Tyler Cowen says:
Here is the latest, by Emmanuel Saez and co-authors... Here is one key sentence:
...we find that short-term and long-term mobility among all workers has been quite stable since the 1950s.
...In [Saez'] view a constant level of mobility means that no force is offsetting ongoing inequality. ... I believe he would likely read his own paper as support for ... concern with income inequality. He would not read his work as reason to dismiss the mobility issue. My view differs, as I worry about mobility -- can a hard-working person get ahead? -- but I do not worry about inequality per se, nor do I require of mobility that it overturn a particular level of inequality.
There may be a connection between mobility and inequality. Dan Andrews and Andrew Leigh find that countries that are more unequal are also countries where social mobility is lower:
More Inequality, Less Social Mobility by Andrew Leigh: Dan Andrews and I have a short paper out on the relationship between inequality and intergenerational mobility (aka social mobility). By contrast with the view that inequality is offset by more income mobility across generations, it turns out that in more unequal countries it is actually harder to move from rags to riches (or vice-versa). ...
We’re pretty sure that we’re the first to test for a statistically significant relationship between the two variables, but our results do accord with other studies that have shown that there is less intergenerational mobility in the US than in the Scandinavian countries.
Here's the abstract, introduction, and conclusion to the paper:
More Inequality, Less Social Mobility, by Dan Andrews and Andrew Leigh: Abstract We investigate the relationship between inequality and intergenerational mobility. Proxying fathers' earnings with using detailed occupational data, we find that sons who grew up in countries that were more unequal in the 1970s were less likely to have experienced social mobility by the late-1990s.
I. Introduction A common view among citizens of large industrialized countries is that economic inequality is fair, provided there are equal opportunities. At the same time, there tends to be a belief that equal opportunity norms are violated when the degree of intergenerational mobility is low and family background exerts a strong influence on children's income in adulthood. It is therefore reasonable to think that inequality may be more acceptable in a society with a high level of social mobility. Despite this important conceptual nexus between social mobility and inequality, the literatures on inequality and intergenerational mobility have largely developed in isolation from one another. That very little is known about the association between inequality and intergenerational mobility stands in contrast to the burgeoning literature on the consequences of inequality for variables such as economic growth, health and political behavior. To the extent that other studies have looked at the relationship between inequality and social mobility, the analysis has been descriptive, or focused around the question of 'American exceptionalism'. We know of no previous study that has formally tested the hypothesis that there is a relationship between a country's level of inequality and the degree of intergenerational mobility.
From a theoretical perspective, the relationship between inequality and intergenerational mobility is unclear. One possibility is that when inequality between parents increases, intergenerational mobility will fall because it is easier for rich parents to buy their children educational advantages that less well-off parents cannot afford (Burtless & Jencks 2003). But as Solon (2004) argues, this effect will be undermined to the extent that children from less advantaged backgrounds disproportionately benefit from public programs. Another channel through which inequality might affect intergenerational mobility is via the demand for redistribution. In more unequal societies, the median voter will tend to lie further below the mean income and may have a stronger preference for redistribution (Alesina & Glaeser 2004). Conversely, if higher inequality increases the political influence of the wealthy – perhaps through campaign finance contributions – then the scope for government to institute progressive policies may narrow (Burtless & Jencks 2003). Finally, higher inequality might reduce intergenerational mobility to the extent that it leads to segregation along income lines, resulting in adverse peer effects for children from low-income families (Durlauf 1996).
IV. Conclusion Using cross-country data, we find that sons who grew up in more unequal countries in the 1970s were less likely to have experienced social mobility by 1999. Across countries, our estimates suggest that a 10-point rise in the Gini coefficient is associated with a 0.07-0.13 increase in the intergenerational earnings correlation. Moving from rags to riches is harder in more unequal countries.
 In 1991, almost all adults in West Germany, Britain, and the United States, and a majority of adults in Japan, agreed with the statement "It's fair if people have more money and wealth, but only if there are equal opportunities." (Jencks & Tach 2006).