Consider the following production functions.
(a) F (K, L) = √ KL
(b) F (K, L) = K2 + L 2
(c) F (K, L) = K^αL ^1−α where 0 < α < 1
For each production function, determine whether the production function demonstrates constant returns to scale, increasing returns to scale, or decreasing returns to scale for some factor z > 1.