# Analytical *P*_{MAX} Calculator

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The Analytical *P _{MAX}* Calculator is a web-based tool for examining the elasticity of demand for reinforcers. This calculator streamlines the determination of unit elasticity (i.e., slope = -1) using a simplified interface. Both Approximate and Analytic

*P*measures are provided.

_{MAX}**In Preparation:**

Gilroy, S. P., Kaplan, B. A., Reed, D. D., Hantula, D. A., & Hursh, S. R. (In Prep). An Exact Solution for Unit Elasticity in the Exponential Model of Demand.

*P*_{MAX} Calculator

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This calculator uses several methods to evaluate models of operant demand (see Hursh & Silberberg, 2008) to determine a point where one log-unit increase in price corresponds to a one log-unit decrease in consumption, *P _{MAX}*. This can be done using numerical approximations or through more computationally-exhaustive iterative methods, using the first order derivative.

To calculate *P _{MAX}* here, you must paste the fitted Q

_{0}, alpha, and K parameters from the model of demand into the spreadsheet component (in their respective columns). Once entered, simply press the "Calculate" button to apply calculation the Analytical

*P*. Additionally, the Approxiate

_{MAX}*P*will also be outputted in the spreadsheet component, in its respective column.

_{MAX}Optionally, you may preview a sample of a exemplary data by pressing the "Load Sample Data" button and then pressing "Calculate". This will let you view the differences between the Approximate and Analytical *P _{MAX}*.

Calculate

*P*_{MAX} Output Logs

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The *P _{MAX}* Calculator uses the following tools to function: