As noted previously, the elasticity of one variable, say A, with respect to another, say B, is given by

Since the percentage change in any variable can be approximated as the ratio of the change to the initial (or final or any intermediate) value, we can rewrite this definition as

Thus, price elasticity can be calculated as

Other elasticities are defined analogously.

Cross elasticity (of demand) is a measure of the responsiveness of quantity demanded of one commodity (X) to price changes of another (Y):

If X and Y are substitutes, _XY > 0. If they are complements, _XY < 0.

Income elasticity (of demand) is a measure of the responsiveness of quantity demanded to income (I) changes:

For normal goods, _I > 0; for inferior goods, _I < 0.

The more necessary is a given normal good from the point of view of households, the lower will be its income elasticity. Necessary (or income-inelastic) goods are those (normal) goods for which quantity demanded increases proportionately less than income increases (0 < _I < 1). Luxury (or income-elastic) goods are those (normal) goods for which quantity demanded increases proportionately more than income increases (_I > 1).

Elasticity of supply is a measure of the responsiveness of quantity supplied to price changes:

Since supply curves are upward sloping, and have the same sign. Thus, 0. The actual value of will depend on the nature of the costs of production in the industry under consideration.

Find out more on the derivation of demand elasticity from Stats Canada

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