This paper examines the tax implementability of allocations based on Foley's (1967) concept of fairness as no-envy (or envy-free) and its alternatives. An allocation is tax implementable if there exists a tax schedule under which the allocation is realized as a result of agents' optimization. Tillmann (1984) and Bös and Tillmann (1985) showed that the class of fair allocations that are income tax implementable is quite limited. This paper examines the implementability of fair allocations by a tax schedule that depends on labor supply and gross income ((y,l)-implementability), whose availability is supported by Dasgupta and Hammond (1980), Tillmann (1989), Kolm (1997), Beaudry and Blackorby (1997) and others. A relevant incentive constraint is perishability of abilities, where agents can exert a lower ability level than they actually possess. We first show that in any economy, every envy-free allocation is (y,l)-implementable. On the other hand, we can show that perishability of abilities results in the impossibility of (y,l)-implementability of the egalitarian equivalence (Pazner and Schmeidler (1978a)), the l*-equal budget allocation (Kolm (1996, 1997), Maniquet (1998)), and the balanced-envy allocation (Daniel (1975)). Among them, a special form of the egalitarian equivalence examined by Fleurbaey and Maniquet (1999) and others is (y,l)-implementable in a class of preference-skill distributions where the lazier agent has the higher skill.
