is the following function increasig decreasing or constant i

is the following function increasig, decreasing or constant in scale, and why?

Is the following function increasing, decreasing or constant in scale, and why? F (A, B, L) = Min [Root L, A + B)]

This is exhibiting decreasing returns to scale (DRS).

A function shows DRS when, if we change all inputs by N times, the output also changes N times. Let\'s test it here by doubling L, A & B all.

New function: F* = Min [(2L)^0.5, (2A + 2B)]

F* = Min [(2)^0.5 (L)^0.5, 2(A + B)]

F* = Min [1.41 x (L)^0.5 , 2(A + B)]

This is less than double of F (Since 1.41 < 2)

So, the function shows DRS.