Simon Grant, Monti, Martin Osherson, Daniel

The classical theory of preference among monetary bets represents people as expected utility maximizers with nondecreasing concave utility functions. Critics of this account often rely on assumptions about preferences over wide ranges of total wealth. We derive a prediction of the theory that bears on bets at any fixed level of wealth, and test the prediction behaviorally. Our results are discrepant with the classical account. Competing theories are also examined in light of our data.

Surplus sharing with coherent utility functions

We use the theory of coherent measures to look at the problem of surplus sharing in an insurance business. The surplus share of an insured is calculated by the surplus premium in the contract. The theory of coherent risk measures and the resulting capital allocation gives a way to divide the surplus between the insured and the capital providers, i.e. the shareholders

Walrasian Solutions Without Utility Functions

SUMMARY: This note reviews consumers’ preference orderings in economics and shows that irrationality is a poor explanation for apparent violations of some axioms of order. Apparent violations seem to be better explained by the fact that consumers’ utility functions, if they exist at all, might not even belong to the class of quasi-concave functions. However, the main task of markets is the determination of equilibrium price vectors. The note shows in addition that, in Walrasian structures, quasi-concave utility functions are unnecessary for the determination of equilibrium price vectors.Walrasian structures, preference orderings, irrationality, utility functions, and equilibrium price vectors

Power Risk Aversion Utility Functions

This paper introduces a new class of utility function -- the power risk aversion.It is shown that the CRRA and CARA utility functions are both in this class. The implications of the PRA utility functions are explored in the context of growth theory. In particular, it is found that economies facing a common real interest rate do not necessarily grow at the same rates if they start with different levels of capital stock. Thus diversity in growth performance across countries occurs even if these countries have access to perfect international capital markets. Potential applications of the PRA in asset pricing are considered.Power Risk Aversion, Growth, Asset Pricing

WALRASIAN SOLUTIONS WITHOUT UTILITY FUNCTIONS

This note reviews consumers’ preference orderings in economics and shows that irrationality is a poor explanation for apparent violations of some axioms of order. Apparent violations seem to be better explained by the fact that consum-ers’ utility functions, if they exist at all, might not even belong to the class of quasi-concave functions. However, the main task of markets is the determination of equilibrium price vectors. The note shows in addition that, in Walrasian structures, quasi-concave utility functions are unnecessary for the determination of equilibrium price vectors.Walrasian structures preference orderings irrationality utility functions and equilibrium price vectors.

Identities For Homogeneous Utility Functions

Using a homogeneous and continuous utility function that represents a household's preferences, this paper proves explicit identities between most of the different objects that arise from the utility maximization and the expenditure minimization problems. The paper also outlines the homogeneity properties of each object. Finally, we show explicit algebraic ways to go from the indirect utility function to the expenditure function and from the Marshallian demand to the Hicksian demand and vice versa, without the need of any other function, thus simplifying the integrability problem avoiding the use of differential equations.Identities, homogeneous utility functions and household theory.

Bounding the CRRA Utility Functions

The constant-relative-risk-aversion (CRRA) utility function is now predominantly used in quantitative macroeconomic studies. This function, however, is not bounded and thus creates problems when applying the standard tools of dynamic programming. This paper devises a method for "bounding" the CRRA utility functions. The proposed method is based on a set of conditions that can establish boundedness among a broad class of utility functions. These results are then used to construct a bounded utility function that is identical to a CRRA utility function except when consumption is very small or very large. It is shown that the constructed utility function also satisfies the Inada condition and is consistent with balanced growth.Utility Function; Elasticity of Marginal Utility; Boundedness

Bounding the CRRA Utility Functions

The constant-relative-risk-aversion (CRRA) utility function is now predominantly used in quantitative macroeconomic studies. This function, however, is not bounded and thus creates problems when applying the standard tools of dynamic programming. This paper devises a method for "bounding" the CRRA utility functions. The proposed method is based on a set of conditions that can establish boundedness among a broad class of utility functions. These results are then used to construct a bounded utility function that is identical to a CRRA utility function except when consumption is very small or very large. It is shown that the constructed utility function also satisfies the Inada condition and is consistent with balanced growth.Utility Function; Elasticity of Marginal Utility; Boundedness