Elasticity (economics)

In economics, elasticity is defined as the proportional change of a dependent variable divided by the proportional change of a related independent variable at a given value of the independent variable. Elasticity is a factor in the operation of the law of supply and demand. The concept was introduced by Alfred Marshall and is explained with great clarity in his Principles of Economics

Price elasticity of demand

The best-known application of the concept of elasticity is to the effect of a price change on the demand for a marketed product. Supposing that Q is the quantity of a product that would be bought by by consumers when its price is P, and that - to take an artificially simple linear case - Q is related to P by the equation:

$Q=-AP+B$

- then the elasticity of demand, E, for the product is given by:

$E=(dQ/Q)/(dP/P)$, or

$E=(dQ/dP)(P/Q)$,

- where dQ and dP are small changes in the values of Q and P.

It can be shown that, for the simplified linear example,:

$dQ/dP=-A$ so that $E=-A(P/Q)$

- and E will vary in value with different values of P and Q because as P increases the fraction P/Q will increase.

The terms "elastic" and "inelastic" are applied to commodities for which E is respectively numerically (ie ignoring the sign) greater or less than 1. If the elasticity of demand for a product is greater than 1, a price increase will lead to a fall in the amount PQ spent on the product, because demand Q will fall more than the rise in P. Conversely, if its elasticity is numerically less than 1, a price rise will result in a rise in the amount spent on it.