Euler's homogeneous function theorem facts for kids

Euler's theorem is one of the theorems Leonhard Euler stated: There are certain conditions where a firm will neither make a profit, nor operate at a loss. The theorem is also known as Euler's homogeneous function theorem, and is often used in economics.

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  A homogeneous function is not necessarily continuous, as shown by this example. This is the function f defined by f(x,y)=x if xy > 0 and f(x, y) = 0 if xy \leq 0. This function is homogeneous of degree 1, i.e. f(\alpha x, \alpha y) = \alpha f(x,y) for any real numbers \alpha, x, y. It is discontinuous at y = 0, x \neq 0.