Hursh Steven R, Schwartz Lindsay P
Institutes for Behavior Resources.
Psychol Addict Behav. 2023 Feb;37(1):37-56. doi: 10.1037/adb0000848. Epub 2022 Jun 30.
A simulation using a two-commodity demand model, with time as the constraint, replicated the primary findings from delay discounting experiments and introduces explicit terms for time elasticity and cross-price substitution into the delay discounting paradigm.
A two-commodity temporal demand equation based on Hursh and Silberberg (2008) and Hursh (2014) was used to emulate delay discounting experiments. The own-price and cross-price demand curves intersected and plotting those indifference points emulated the usual hyperbolic discount function for substitutes. Simulations examined delay discounting in relation to (a) time elasticity of demand, (b) substitution between the delayed and immediate alternatives, and (c) amplitude of demand for the delayed alternative.
The simulated discount functions with substitutes were hyperbolic. The discount rate was a direct function of increasing time elasticity and substitutability of delayed alternative demand, shifting the function toward an exponential model. Amplitude of demand for the delayed alternative was inversely proportional to discount rate and supported a hyperboloid model with a power function of time (Killeen, 2015; Rachlin, 2006). The emulation of cross-commodity discounting involving drugs points to amplitude and persistence of time-dependent demand and cross-commodity substitution as primary factors.
This report describes the first general model of time-dependent demand and delay discounting. The model implicates cross-commodity substitution as a potential factor in delay discounting. In the context of substance use disorder, the model underscores the importance of defining the properties of multicommodity demand (time elasticity, substitution, and amplitude) specific to the commodities and context. (PsycInfo Database Record (c) 2023 APA, all rights reserved).
使用一种双商品需求模型进行模拟，以时间作为约束条件，重现了延迟折扣实验的主要发现，并将时间弹性和交叉价格替代的明确术语引入延迟折扣范式。
基于赫什和西尔伯格（2008年）以及赫什（2014年）的双商品时间需求方程来模拟延迟折扣实验。自身价格和交叉价格需求曲线相交，绘制这些无差异点可模拟替代品通常的双曲线折扣函数。模拟研究了与以下方面相关的延迟折扣：（a）需求的时间弹性，（b）延迟和即时替代品之间的替代，以及（c）延迟替代品的需求幅度。
带有替代品的模拟折扣函数呈双曲线型。折扣率是延迟替代品需求的时间弹性和可替代性增加的直接函数，使该函数向指数模型转变。延迟替代品的需求幅度与折扣率成反比，并支持一个具有时间幂函数的双曲面模型（基林，2015年；拉赫林，2006年）。涉及药物的跨商品折扣模拟表明，时间依赖性需求的幅度和持续性以及跨商品替代是主要因素。
本报告描述了第一个时间依赖性需求和延迟折扣的通用模型。该模型表明跨商品替代是延迟折扣中的一个潜在因素。在物质使用障碍的背景下，该模型强调了针对特定商品和情境定义多商品需求属性（时间弹性、替代和幅度）的重要性。（《心理学文摘数据库记录》（c）2023年美国心理学会，保留所有权利）
