In this notebook I want to experiment with some basic models for price elasticity estimation in the simple context of a simple sku across multiple stores and regions. The motivation is to have a concrete example of the elasticity models presented in the Chapter 11: Big Data Pricing Models of the book Pricing Analytics by Walter R. Paczkowski.
Elasticity Definition
Here I provide a very succinct definition of elasticity (there is a vast literature on this topic, see the reference above). The elasticity of a variable \(y(x, z)\) with respect to another variable \(x\) is defined as the percentage change in \(y\) for a one percent change in \(x\). Mathematically, this is written as \[ \eta = \frac{\partial \log(y(x, z))}{\partial \log(x)} \]
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