Equal sacrifice taxation

We axiomatically characterize the family of equal sacrifice rules for the problem of fair taxation: every agent with positive post-tax income sacrifices the same amount of utility relative to his/her respective pre-tax income. In contrast to the result in Young (1988), our family of rules allows for asymmetric and “constrained” versions of equal sacrifice. When we add the requirement that an agent's tax burden must not decrease when their income increases, then this is equivalent to assuming that every agent's utility function is concave. When we add the requirement that a tax rule be independent of scale, then this is equivalent to assuming that every agent has the same constant measure of relative risk aversion. In addition, as a special case of our family of rules, we derive a tighter result than Young (1988) by showing one of his axioms is unnecessary.