SRH 6 07

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Published on February 14, 2008

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Exponential Demand and Essential Value: Exponential Demand and Essential Value June 2007 Steven R. Hursh, Ph.D. Institutes for Behavior Resources, Inc. and Johns Hopkins University School of Medicine srhursh@ibrinc.org 410-752-6080 Behavior Analysis and Economics: 2 Behavior Analysis and Economics Shared interest in a definition of value of reinforcers or utility of commodities. Each has devised methods to assess value and the behavior to acquire valuable commodities. What can we learn by comparing behavioral and economic approaches to value? Consider various definitions of value……. Consider Three Forms of Value: 3 Consider Three Forms of Value Scalar Value: size of a reinforcer or commodity Constrained Value: size of the reinforcer combined with the cost to obtain it Essential Value: importance of the commodity to the subject, similar to intrinsic value. “a dollar versus a dime”. a “super economy size” versus a “travel size” “meat and potatoes” versus “popcorn and a movie” Behavioral Economics gives us a way to distinguish between these three forms of value, and Gives us a way to measure & compare essential values. Behavioral Economic Method Basic metric is daily consumption, not response rate: 4 Behavioral Economic MethodBasic metric is daily consumption, not response rate Standardized metrics for scalar and constrained value Give the subject control over daily level of reinforcement or consumption – closed economy. Generally, control constraint with ratio schedules of reinforcement so cost is independent of behavior. Evaluate total consumption as a function of constrained value – map a demand function. Determine the form of the demand function and its slope across qualitatively different reinforcers. Compare commodities in terms of the parameters of the demand function. Typical Demand Curves : 5 Typical Demand Curves The slope - “elasticity”- is a reflection of essential value. Exponential Shape of the Demand Curve in Semi-log Coordinates: 6 Exponential Shape of the Demand Curvein Semi-log Coordinates Demand curve General exponential form between log Q and price: 7 Demand curveGeneral exponential form between log Q and price log Q = log(Q0)+ k(e-Q0C -1) C = Cost in responses or time of each reinforcer Q0 = maximum consumption at zero price  = rate of change in consumption k = scaling constant for range of the exponential log Q0 – k = minimum consumption Function fit to consumption data without normalizing. Q0 represents the level of demand.  represents the essential value of the reinforcer or change in elasticity with price. Q0 x C represents the “real price” to defend maximum consumption and automatically “normalizes” the estimate of essential value, . The Demand Curve and Response Output Function Exponential form in double log coordinates: 8 The Demand Curve and Response Output FunctionExponential form in double log coordinates Most demand curves in this review conform to this shape, with R2 that average .96 (.89 to .99). Exponential Rate Constant () is similar for two scalar examples of the same reinforcer: 9 Exponential Rate Constant () is similar for two scalar examples of the same reinforcer Data from Hursh, S. R. Raslear, T. G., Shurtleff, D., Bauman, R. and Simmons, L. (1988) A cost-benefit analysis of demand for food. Journal of the Experimental Analysis of Behavior, 50, 419-440. Variations in Exponential Rate of Change () with Increases in Substitution: 10 Variations in Exponential Rate of Change () with Increases in Substitution Exponential Demand Across Species and Reinforcers: 11 Exponential Demand Across Species and Reinforcers Essential Value is Independent of Dose Consumption and Responding for Multiple Drug Doses : 12 Essential Value is Independent of DoseConsumption and Responding for Multiple Drug Doses Ko, M.C., Terner, J., Hursh, S., Woods, J.H., and Winger, G. (2003) Relative reinforcing effects of three opioids with different durations of action. J. Pharmacol Exp Ther 301, 2. Many scalar values (doses) yet a single rate constant Essential Value is Independent of Potency Higher two doses (and lowest dose) of each drug have the same rate constant.: 13 Essential Value is Independent of Potency Higher two doses (and lowest dose) of each drug have the same rate constant. Effects of Drug Treatment Antagonist caused change in scalar value of one morphine dose, not the essential value of morphine : 14 Effects of Drug TreatmentAntagonist caused change in scalar value of one morphine dose, not the essential value of morphine Quantitative Distinctions in Abuse Liability Comparison of drugs based on rate constant, : 15 Quantitative Distinctions in Abuse LiabilityComparison of drugs based on rate constant,  Slide 16: Data from Lea, 1978 Summary of Pmax Values Exponential Demand Equation: 17 Summary of Pmax ValuesExponential Demand Equation Advantages of Demand Curve Approach for Assessment of Abuse Liability: 18 Advantages of Demand Curve Approach for Assessment of Abuse Liability Provides a conceptual framework that ties assessment of abuse liability to the larger context of the economics of drug abuse policy. Provides a consistent and simple method for assessment. Provides a method that is both dose and potency independent. Provides a quantitative approach that returns a single parameter that reflects the essential difference among drug reinforcers that is based on a consideration of responding across an entire range of constraint. Thank you: Thank you Steven R. Hursh, Ph.D. Institutes for Behavior Resources and Johns Hopkins University School of Medicine srhursh@ibrinc.org 410-752-6080 The Essential Value of Reinforcers

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