Here we reconstruct the Proportional Solution for Economies with both public and private ownership of productive assets, proving the existence of a competitive equilibrium assuming non-monotonic utility and actors behaving with envy. With a possibility for excess at no additional cost, our aim is to provide a mechanism under which envious individuals, competing for a commonly pooled resource, can reach a stable equilibrium. In other words, we derive a proportional solution with envious agents in a pure exchange economy.
Richard Johnson (Wed,) studied this question.
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