## Quick Reference

(CES)

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(*x*_{1})^{ρ} + [1−δ](*x*_{2})^{ρ}]^{1/ρ}

where *y* is output or utility, *x*_{1} and *x*_{2} 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.

*Subjects:*
Economics.

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