Delay and Interval Effects with Subadditive Discounting Functions

Delay effect appears as an anomaly of the traditional discounted utility model according to which a decrease of the discount rate is performed as waiting time increases. But, in this description, it is not clear if the benchmark (that is to say, the reference instant in the assessment process) or the discounted amount availability is fixed or variable. In this way, other authors use the term common difference effect (and immediacy effect, when the first outcome is available immediately) and this expression at least does implies a variable discounted amount availability. Read introduces another different effect, the interval effect: longer intervals lead to smaller values of the discount rate r. Taking into account the parameter δ (geometric mean of the discount factor), the interval effect implies larger values of δ. In this paper we try to clarify the concepts of delay and interval effect and we deduce some relationships between these concepts and certain subadditive discounting functions.