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 |…

The Cobb-Douglas Production Function is given by $q = x_1^\alpha x_2^\beta$q=x1α​x2β​, 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 $f(tx_1, tx_2) = t \cdot f(x_1, x_2)$f(tx1​,tx2​)=t⋅f(x1​,x2​), 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 $f(tx_1, tx_2) > t \cdot f(x_1, x_2)$f(tx1​,tx2​)>t⋅f(x1​,x2​), 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 $f(tx_1, tx_2) < t \cdot f(x_1, x_2)$f(tx1​,tx2​)<t⋅f(x1​,x2​), matching with (II).

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