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

*Salvador Cruz Rambaud*,
*Isabel María Parra Oller* and
*María del Carmen Valls Martínez*

*Physica A: Statistical Mechanics and its Applications*, 2018, vol. 508, issue C, 788-796

**Abstract:**
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,+∞).

**Keywords:** Econophysics; Intertemporal choice; Discount function; Magnitude effect; Dynamic inconsistency (search for similar items in EconPapers)

**Date:** 2018

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**Persistent link:** https://EconPapers.repec.org/RePEc:eee:phsmap:v:508:y:2018:i:c:p:788-796

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