The property of production or utility functions such that the ratio between proportional changes in relative prices and proportional changes in relative quantities is always the same. A CES function may be written
y = k[δ(x1)ρ + [1−δ](x2)ρ]1/ρ
where y is output or utility, x1 and x2 are inputs, and k is a constant. The ratio of proportional changes in relative quantities to proportional change in relative prices is the elasticity of substitution, σ = 1/(1 − ρ); if 1 > ρ > 0, then σ > 1 and the goods are good substitutes; if ρ < 0, then σ < 1 and the goods are poor substitutes. The Cobb–Douglas function is the limiting case corresponding to ρ = 0; in this case σ = 1.