Well, I just got Capital in the 21rst Century and started in on it. It looks exciting, but I confess to being puzzled by the claim that r>g means that inequality grows inexorably. We have the capital share = r (K/Y), and K/Y in the long run equal to s/g (These are Picketty's "fundamental" equations) where g is the sum of population and per capita output growth rates and s is the net saving ratio . Nothing to quarrel with there. But then the capital share in the long run will be (rs)/g. Then if r and g are constant ( and s as well) -- the capital share remains constant whether r>g or r< g. What am I missing?
Krugman had a blog post where he spells out Picketty's argument that a decrease in g will increase r/g and thus the capital share: r will fall by less than g if, as Picketty argues, production is CES and the elasticity of substitution is greater than 1. That makes sense, but this will be so whatever the initial level of r is relative to g, whether above or below unity.