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 as

The 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. If 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.