Mathematical Definition
The definition of elasticity is based on the mathematical notion of point elasticity. In general, the "x-elasticity of y", also called the "elasticity of y with respect to x", is:
The approximation becomes exact in the limit as the changes become infinitesimal in size. The absolute value operator is for simplicity – generally, depending on context, the sign of the elasticity is understood as being always positive or always negative. However, sometimes the elasticity is defined without the absolute value operator, when the sign may be either positive or negative or may change signs. A context where this use of a signed elasticity is necessary for clarity is the cross-price elasticity of demand — the responsiveness of the demand for one product to changes in the price of another product; since the products may be either substitutes or complements, this elasticity could be positive or negative.
Read more about this topic: Elasticity (economics)
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