A solution to the monopolist's problem when demand is iso-inelastic

Economic theory does not provide a solution to the monopolist's price setting problem when the demand curve faced is isoelastic with elasticity smaller than or equal to one. In the present paper it is argued that this is no longer true when uncertainty about demand and risk aversion of the monopolist are admitted. In particular it is shown that a monopolist with constant relative risk aversion r facing an expected demand curve with constant elasticity ε may be seen as behaving like a standard monopolist facing a demand curve having elasticity (1+r)ε.