Calculation of Price Equilibria for Utility Functions of the HARA Class

We explicitly calculate price equilibria for power and logarithmic utility functions which--together with the exponential utility functions--form the so-called HARA (Hyperbolic Absolute Risk Aversion) class. A price equilibrium is economically admissible in the market which is a closed system. Furthermore it is on the one side individually optimal for each participant of the market (in the sense of maximal expected utility), on the other side it is a Pareto optimum and thus collectively optimal for the market as a whole. KEYWORDS Risk exchange, Price equilibrium, Utility function, Pareto optimality, Risk aversion.