Euler's homogeneous function theorem
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.[1][2]
Euler's Homogeneous Function Theorem Media
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, that is, f(s x, s y) = s f(x,y) for any real numbers s, x, y. It is discontinuous at y = 0, x \neq 0.
References
- ↑ 2.6: Euler's Theorem for Homogeneous Functions (in en). Physics LibreTexts (2017-01-25). Retrieved 2021-04-12.
- ↑ Elghribi, Moncef. Homogeneous functions: New characterization and applications (in en). Transactions of A. Razmadze Mathematical Institute 171 (2) (2017-08-01). p. 171–181. doi:10.1016/j.trmi.2016.12.006.