Efficiency and Fairness in the Walrasian Mechanism

We consider fair allocation problems of dividing a social endowment of infinitely divisible goods among agents with equal rights to these resources. The first objective of this paper is to describe the implications of the three axioms (population monotonicity, resource monotonicity, and welfare domination under preference replacement) on the Walrasian mechanism from equal division. In a pure exchange economy, the Walrasian mechanism from equal division fails to satisfy resource monotonicity and welfare domination under preference replacement with homothetic preferences. Next, we impose three distributional criteria (equal division lower bound, no envy, and no domination) on general economic problems of fair division and investigate whether each criterion is compatible with the Walrasian mechanism from equal division. We mainly find that (i) in the absence of substitution effects the transfer paradox occurs if and only if the preference replacement paradox occurs and that (ii) in the presence of substitution effects in demand, the preference replacement paradox may occur even when the transfer paradox does not.