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A process displays '''constant returns to scale''' when increasing all [[input]]s by a factor of ''s'' leads to an increase in output by the same factor.  In [[economics]], this is in terms of the [[production function]] of the process &mdash; for instance, that of a [[business]], [[company]], or economy as a whole.  Mathematically, if the function is <math>F(\vec{x})</math>, where <math>\vec{x} \in \bold{R}^{n}</math> is a vector of inputs, constant returns to scale are characterized by <math>F(s\vec{x}) = sF(\vec{x})</math>, where <math> s > 0 </math>.

'''Constant returns to scale''' are displayed by processes when all [[input]]s are increased by a factor of ''s'' and outputs increase by the same factor.  In [[economics]], this is in terms of the [[production function]] of the process &mdash; for instance, that of a [[business]], [[company]], or economy as a whole.  Mathematically, if the function is <math>F(\vec{x})</math>, where <math>\vec{x} \in \bold{R}^{n}</math> is a vector of inputs, constant returns to scale are characterized by <math>F(s\vec{x}) = sF(\vec{x})</math>, where <math> s > 0 </math>.

A function displaying constant returns to scale is [[homogeneous]] of degree one, and by Euler's Theorem can be written as:

A function displaying constant returns to scale is [[homogeneous]] of degree one, and by Euler's Theorem can be written as: