A value function that explains the magnitude and sign effects

Two of the anomalies of the exponentially discounted utility model are the 'magnitude effect' (larger magnitudes are discounted less) and the 'sign effect' (a loss is discounted less than a gain of the same magnitude). The literature has followed Loewenstein and Prelec (1992) in attributing the magnitude effect to the increasing elasticity of the value function and the sign effect to a higher elasticity for losses as compared to gains. We provide a simple, tractable, functional form that has these two properties, which we call the simple increasing elasticity value function (SIE). These functional forms underpin the main explanation of the magnitude and sign effects and may aid applications and further theoretical development.