In mathematics, a homogeneous function exhibits multiplicative scaling behavior, which implies that its value is multiplied by a power of that factor if all of its inputs are multiplied by that factor.
For instance, consider a two-variable homogeneous real-valued function. and is a real-valued function that fulfills the requirement for some constant and all real numbers The constant is called the degree of homogeneity.
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The underlying homogeneous functions are included in the homothetic class of monotonically increasing homogeneous production functions. The firm's isoclines, including the long-run expansion path, would be straight lines from the origin if the production function is homogenous.
The isoquants of the homothetic production function are identical to those of the underlying homogeneous function, but in most cases have distinct quantity indices.
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