## Quick Reference

The ratio of the proportional change in the relative quantities of two goods demanded to the proportional change in their relative prices. Let *p*_{x} and *p*_{y} be the prices of goods *X* and *Y,* and *q*_{x} and *q*_{y} 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 *p*_{x}/*p*_{y} = *U*_{x}/*U*_{y}.

Elasticity of Substitution

*Subjects:*
Economics.