Elasticity (economics)/Tutorials

Elasticity of Demand (an example of the algebra of elasticity)

Supposing that Q is the quantity of a product that would be bought by consumers when its price is P, and that 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.

Cross elasticity of demand is defined as above in algebraic terms, except that Q is the quantity of one of the products that will be bought when P is the price of the other.