The ratio of the proportional change in the relative quantities of two goods demanded to the proportional change in their relative prices. Let px and py be the prices of goods X and Y, and qx and qy be the quantities demanded. The elasticity of substitution, σ, is defined asThe minus sign is included to make σ positive. The better substitutes any two goods are, the higher the σ between them. For perfect substitutes σ is infinite. Where σ > 1, as a good gets relatively cheaper it takes a larger share of total expenditure. If σ < 1, as a good gets relatively cheaper it takes a smaller share of total expenditure. If σ = 1, the two goods take constant shares of expenditure whatever their relative prices. The elasticity of substitution can be written in terms of marginal utility using the relation px/py = Ux/Uy.
Elasticity of Substitution