A firm produce $q$ amount of output using $x₁$ amount of factor 1 and $x₂$ amount of factor 2.

Match List-I with List-II

List-I	List-II
(A). Cobb-Douglas Production Function	(I). $f(tx_1, tx_2) > t \cdot f(x_1, x_2)$
(B). Constant returns to scale	(II). $f(tx_1, tx_2) < t \cdot f(x_1, x_2)$
(C). Increasing returns to scale	(III). $q = x_1^\alpha x_2^\beta$
(D). Decreasing returns to scale	(IV). $f(tx_1, tx_2) = t \cdot f(x_1, x_2)$

Choose the correct answer from the options given below:

The Cobb-Douglas Production Function is given by $q = x_1^\alpha x_2^\beta$, which matches with (III). This is a specific functional form that relates output to inputs through exponents alpha and beta.

Constant returns to scale occurs when scaling both inputs by a factor t results in output also scaling by exactly t. Mathematically, this is expressed as $f(tx_1, tx_2) = t \cdot f(x_1, x_2)$, which matches with (IV).

Increasing returns to scale happens when scaling inputs by factor t produces an output increase greater than t times the original output. This is shown as $f(tx_1, tx_2) > t \cdot f(x_1, x_2)$, matching with (I).

Decreasing returns to scale occurs when scaling inputs by factor t results in output increasing by less than t times. This is represented by $f(tx_1, tx_2) < t \cdot f(x_1, x_2)$, matching with (II).

Therefore, the correct matching is: (A) - (III), (B) - (IV), (C) - (I), (D) - (II).