Optimal Discounting with Negative Consumption

Noor and Takeoka [3] propose a generalization of the discounted utility, called the costly empathy representation, where a current self empathizes future selves at cognitive costs and optimally chooses a discount function for each consumption stream. This model accommodates several anormalies of the discounted utility including the magnitude effect, the common difference effect, preference for increasing sequences, and so on. In the present study, we extend the costly empathy representation to an intertemporal choice environment with negative consumption utilities. This extension allows for distinction between gains and losses relative to a reference point and explaining anormalies of the discounted utility such as the sign effect.