Abstract
An amount of income can be obtained jointly by m agents, the ith agent's share of income being θ i. The income and the utilities of each agent are functions of the state of nature. Each agent has a probability measure over the states of nature. An efficient proportional distribution is one which is (1) Pareto optimal and for which (2) the expected proportion of income agent i recieves divided by θ i is independent of i. It is shown that if the attitudes are strictly concave then there exists exactly one proportional distribution scheme. Furthermore, in special cases, each agent expects to recieve an income that exceeds his share.
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