Concerns for horizontal equity impose constraints on the optimal tax problem. The public would not accept a tax on height because it would seem unfair to tax more a taller person than a shorter person with exactly the same economic means. However, the public fully accepts that taxes should be based on income, which measures economic welfare or need closely, with the idea that it is less painful for a rich person than for a poor person to give up $1. Therefore studying the constrained utilitarian problem using a tax based solely on income and not based on extraneous characteristics such as height makes the most sense and can usefully inform the tax policy debate. That's what economists have done (including myself) since the famous contribution of James Mirrlees in 1971.
I'd recommend Greg develops a model explaining why people care about horizontal equity -- that'd be a useful contribution."
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