Algebraic Theory of Pareto Efficient Exchange

We study pure exchange economies with symmetries on preferences up to taste intensity transformations. In a 2-person, 2-good endowment economy, we show that bilateral symmetry on each utility functional precludes a rectangle in the Edgeworth box as the location of Pareto optimal allocations. Under strictly quasi-concave preferences, a larger set can be ruled out. The inadmissible region is still larger when preferences are homothetic and identical up to taste intensity parameters. Symmetry also places bounds on the relations between terms of trade and efficient allocation. The inferences can be extended to an n-person, m-good endowment economy under generalized permutation group symmetries on preferences. JEL classification: D51, D61, C60