The Expected Utility Hypothesis

The Expected Utility Hypothesis
In standard consumer theory, the preference function over commodity
bundles is typically assumed to have certain mathematical properties but is typically not hypothesized to take any specific functional
form, such as the Cobb-Douglas or Constant Elasticity of Substitution
form. Specific functional forms are typically only used when absolutely necessary, such as in empirical estimation, calibration, or testing.
In contrast, the standard theory of choice under objective uncertainty
typically does assume (or does assume axioms sufficient to imply) a specific functional form for the individual’s preference function
over lotteries, namely the objective expected utility form VEU(x1, p1;...; xm, pm) = U(x1) ⋅ p1 + … + U(xm) ⋅ pm for some von Neu-mann-Morgenstern utility function U(⋅). Mathematically, the characteristic
features of this functional form are that it is additively separable in the distinct (xi, pi) pairs, and also that it is linear in the probabilities. The term “expected utility” arises since it can be thought of as the mathematical expectation of the variable U(x) (the individual’s “utility of wealth”) if wealth x has distribution P = (x1, p1;...; xm, pm). The literature
on choice under uncertainty has generated a number of theoretical results linking the shape of the utility function to aspects of the individ-ual’s attitudes toward risk, such as risk aversion or comparative risk aversion for a pair of individuals. Excellent discussions of the foundations
and applications of expected utility theory can be found in standard
graduate level microeconomic texts such as Kreps (1990, Chapter 3), Mas-Colell, Whinston, and Green (1995, Chapter 6), and Varian (1992, Chapter 11).