This paper describes a parametric family of utility functions for decision analysis. The parameterization is obtained by embedding the HARA class in a four-parameter representation for the risk aversion function. The resulting utility functions have only four shapes: concave, convex, S-shaped,...

In this note, we consider an economy with heterogeneous agents, differing by their time preference rate and by their beliefs. We show that at the Pareto optimum, the representative agent exhibits interesting behavioral properties. More precisely, starting from a standard model with expected...