I. Introduction, 533. — II. The Arrow-Debreu models of consumer and entrepreneurial choice under uncertainty, 534. — III. Consumer choice under uncertainty, 538. — IV. Entrepreneurial choice under uncertainty, 543. — V. The existence of a competitive equilibrium under uncertainty, 547. — VI. Concluding remarks, 553. — Appendix, 556.

[In this paper we give necessary and sufficient conditions such that a decision maker who operates in a world in which finitely many states of nature can occur has an increasing, strictly concave utility function U(.) and a subjective probability measure P(.) and such that he chooses among acts with uncertain outcomes according to the expected value of U(.) (with respect to P(.)) which they offer him.]