Efficiency invites divide and coercion in the age of increasing returns to scale

In the presence of (at least locally) increasing returns to scale tech- nologies, the paper asks the question: does there exist an economic system which implements Pareto efficient allocations and respects the voluntary participation principle? To answer this question, the paper formulates an economic system as an allocation rule under economies with non-convex production possibility sets, and proposes a few weaker axioms to represent the voluntary participation principle. Then, the paper shows that any Pareto efficient allocation rule satisfies none of the axioms of the voluntary participation principle. The result suggests that pursuing Pareto efficiency in the presence of increasing returns to scale technologies leads to a dictatorial allocation rule, or forces someone to participate in the economic system without any guarantee of a minimal living standard.