Objective: 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.
Method: 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.
Results: 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.
Conclusions: 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).