I. Ex ante and ex post optimum, 81. — II. Consumers and commodities, 83. — III. Consumer choice and the subjectivity theorem, 85. — IV. Necessary conditions for ex post Pareto optimum given Arrow optimum, 88. — V. Production, 89. — VI. Efficiency, 91. — VII. Economies where the necessary conditions for Arrow optimum to imply ex post Pareto optimum are sufficient, 93. — Table of notation, 94.
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Ross M. Starr (1973) studied this question.