Constant returns to scale

Formal definitions

In a more general set-up, for a multi-input-multi-output production processes, one may assume technology can be represented via some technology set, call it ${\displaystyle \ T}$, which must satisfy some regularity conditions of production theory. In this case, the property of constant returns to scale is equivalent to saying that technology set ${\displaystyle \ T}$ is a cone, i.e., satisfies the property ${\displaystyle \ aT=T,\forall a>0}$. In turn, if there is a production function that will describe the technology set ${\displaystyle \ T}$ it will have to be homogeneous of degree 1.