The Proportional Solution in a Permit Sharing Problem

A permit sharing problem is represented by countries, each of whom owns a technology that emits pollutants such as GHGs to produce output and privately owns a certain amount of permits. The permits are treated as the only input and are regarded as perfectly transferable among the countries, unlike regular factor inputs such as labor or capital. First, we axiomatically characterize a series of solutions called the pro- portional solutions. We hypothetically separate countries into two groups, permit contributors and technology contributors, and identify solutions un- der which countries receive rewards systematically according to the two types of contribution they provide (Separation Principle). Two other main axioms (NART and NARP), saying that no group of countries bene t from rearranging their contributions of technologies or permits among themselves, are used in characterizing the proportional solutions. Second, we introduce another axiom called Voluntary Participation to the solutions of sharing the surplus produced beyond the autarky economy output. This addition of Voluntary Participation leads to an interesting result; the surplus must be shared equally between the two groups, the per- mit (input) contributors and technology contributors. Hence the equal share proportional solution is uniquely characterized.