The amount-based deformation of the q-exponential discount function: A joint analysis of delay and magnitude effects

The magnitude effect is one of the main anomalies shown by people in the context of intertemporal choice. Thus, the main objective of this paper is to provide a general procedure to obtain a general discount function able to explain this paradox. By this methodology, we will to mathematically deform time in a discount function, more specifically to multiply the variable “time” by a certain power of the reward amount. However, in most cases, the existing literature presents some ad hoc discounting models to describe a unique anomaly. In order to solve this limitation, we will apply the former methodology to the q-exponential discount function introduced by Cajueiro (2006). In this way, we will obtain a mathematical setting able to jointly explain the delay and the magnitude effects, depending on the values of parameters q and α involved in the model. Moreover, another advantage of this amount-based q-exponential function is its convergence to the time-deformed exponential, hyperbolic and linear discounting, depending on the value of q in the joint interval (−∞,1)∪(1,+∞).