A Two‐Parameter Exponential‐Demand Formula with a Behavioral Momentum Normalization: A Novel Method to Characterize the Reinforcing Effectiveness of Drugs
Authors: de Moura Fernando Barreto , Walton Jay , Lima‐Filho Paulo , Bergman Jack , Kohut Stephen John 
Published: June 2021

Application of behavioral economic principles to the characterization of drugs of abuse has yielded compelling evidence for a relationship between price (P) and consumption (Q). In turn, a quantitative assessment of this relationship provides a metric for comparing the reinforcing effectiveness (α) of various drugs, and demand analysis may provide a screening mechanism to evaluate candidate medications for the management of substance abuse. However, discordance between the α values for some drugs in nonhuman subjects and their reinforcing effectiveness in humans (e.g., high α avalues and high rates of abuse of nicotine) suggests that previous demand equations may require further refinement. In the present work, demand equations were derived to try to more accurately reflect the contribution of behavioral momentum‐ evident in resistance to vehicle extinction‐ to the calculation of reinforcing effectiveness. Resistance to extinction conceivably may influence demand curve elasticity, especially at higher prices. Here, demand curves were derived from intravenous self‐administration data obtained with four psychomotor stimulant drugs using a logarithmic model modified from the Hursh‐Silberberg (2008) exponential equation with a two‐parameter fitting algorithm for consumption versus price. The new algorithm reduces the three free parameter model to a two free parameter model by interpolating data at the minimum fixed ratio (FR) and at the breakpoint pB (i.e., the FR where Q=0). The augmented model takes the form:
urn:x-wiley:08926638:media:fsb2fasebj2019331supplement80512:fsb2fasebj2019331supplement80512-math-0001where QFRLdenotes consumption at the lowest evaluated FR and pB denotes the breakpoint price. A strategy was tested for developing a single parameter classification scheme for fitted models using the parameter α as a measure of elasticity of the demand curves. The strategy normalizes behavioral momentum as measured by data for vehicle self‐administration. More specifically, if Q(P) denotes the demand curve for a particular drug, the discounted demand curve, Qd(P), is defined by:
urn:x-wiley:08926638:media:fsb2fasebj2019331supplement80512:fsb2fasebj2019331supplement80512-math-0002where Qs(P) denotes the demand curve generated by vehicle. To test this approach, two doses of cocaine, 3,4‐methylenedioxymethamphetamine (MDMA), methylenedioxypyrovalerone (MDPV), and methcathinone (MCAT) were examined in rhesus monkeys (N=4). Using the Hursh‐Silberberg (2008) exponential formula, a rank‐order of reinforcing effectiveness of cocaine>MDPV>MCAT>>MDMA was established, and reinforcing effectiveness did not vary as a function of dose. However, in the Two‐Parameter Exponential‐Demand formula, a rank‐order of cocaine (large dose)>MDMA=MCAT>MDPV (large dose)>MDPV (small dose)>cocaine (small dose) was established. These results suggest that behavioral momentum may influence demand elasticity in a dose‐dependent manner, and α values derived in the augmented model may differentiate drug effects that contribute to price‐consumption relationships in a pharmacologically sensitive manner.Support or Funding InformationDA002519, DA039306, and HMS‐ Livingston AwardThis abstract is from the Experimental Biology 2019 Meeting. There is no full text article associated with this abstract published in The FASEB Journal.