Tackling inequality

Larry Summers posits that we need to do better, and issues a few warnings:

Government must be careful that it does not facilitate increases in inequality by rewarding the wealthy with special concessions. Where governments dispose of assets or allocate licences, there is a compelling case for more use of auctions to which all have access. Where government provides insurance implicitly or explicitly, premiums must be set as much as possible on a market basis rather than in consultation with the affected industry. A general posture for government of standing up for capitalism rather than particular well-connected capitalists would also serve to mitigate inequality. 

We can all easily grasp the concept of income inequality, but has anyone actually considered the implausibility of income equality? Would we rather the gap were smaller, but everyone – including the already poor – poorer, or would we prefer that the gap be larger, but everyone generally better off?