Exponential Demand Simulation Tool
Reed, Derek D.
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Operant behavioral economics investigates the relation between environmental constraint and reinforcer consumption. The standard approach to quantifying this relation is through the use of behavioral economic demand curves. In log-log coordinates, the operant demand curve illustrates the degree of elasticity in reinforcer consumption (participants accessing the reinforcer, frequency of reinforcers consumed, proportion/percentage of reinforcer access, etc.) across increasing costs (fixed-ratio requirements, monetary costs, probabilistic delivery costs, time/effort costs, etc.). Hursh and Silberberg’s (2008) exponential model is the leading contemporary approach to modeling this demand relation. This simulation tool permits the user to visualize how different levels of initial consumption (Q0), ranges of consumption (k), and rates of change in elasticity (alpha) affect the shape of the demand curves and its associated work function.
This Microsoft Excel tool allows the user to insert their specified values of Q0, k, and alpha into green cells. As data are entered, Pmax (dotted blue vertical line) and Omax (dotted red horizontal line) will automatically be calculated according to the Exact Pmax equation from Hursh, 2014.In the columns below the instructions, Consumption and Work are calculated as a function of Unit Price cost and user-specified Q0, k, and alpha parameters.The Elasticity column calculates elasticity between unit prices. Shaded gray cells indicate inelasticity (slope is > -1.00, such that a one log unit increase in price is associated with a less than one log unit decrease in consumption). Shaded yellow cells indicate elasticity (slope is < -1.00). Note that the shift from gray to yellow occurs at a cost that closely approximates Pmax (cost cell shaded blue; due to rounding, pmax may not always be exactly associated with a slope of -1.00). Use the split screen to scroll through the cells.The calculator does not plot the Demand or Work functions when consumption is so low that the Work curve begins to increase at high unit prices. The calculator will return a #N/A in the below consumption and work cells when this happens. Note that some Pmax values that do not exactly match a slope of -1.00 will return a #N/A for some Consumption and Work cells associated with costs immediately following Pmax.
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