Should the rich be taxed more?

Larry Elliott writes about the findings of a recent paper looking at tax systems.

The paper, from John Hatgioannides of the Cass business school, Marika Karanassou of Queen Mary University and Hector Sala of the Universitat Autònoma de Barcelona and IZA in Bonn, argues that the rich are paying a lower share of their income and wealth than they were previously and this isn't fair. 

The problem is that in absolute terms, they are paying a greater proportion of total taxes than before, but the fact is that relative to their incomes. they are paying less. 

The question is, is this fair? Is it efficient? And is it equitable?