Define Production Function. Distinguish between Short Run and Long Run production Functions.

A Production Function is a technological relationship between physical inputs and physical outputs of a good which shows the maximum outputs that can be produced with combination of inputs.

Mathematically, the Production Function can be written as:

Q_x = f(F₁, F₂,F₃...F_n)

Where Q_x is the physical output of commodity X and F₁ ... F_n, are the physical inputs required in the production of output X.

Difference between Short Run and Long Run Production Function are:

Long Run Production Function	Short Run Production Function
It is a constant proportion type production function in which factor ratio remains constant, no matter what the level of output is.	It is a variable proportion type production function in which factor ratio changes with change in the level of output.
Output is sought to be increased by increasing the appiication of all factors	Output is sought to be increased by increasing the application of one variable factor only.
Scale of production tends to change with the change in the level of output.	Scale of production remains constant, even when the level of output changes.
Long period production function is studied with reference to'Returns to Scale'.	Short period production function is studied with reference to 'Returns to a Factor'.