3. [20 points] Consider the following two production functions:
$q(K, L) = K^\alpha L^\beta$
$q(K,L) = K^\alpha + L^\beta$
Suppose that $\alpha = 1$ and $\beta = 1$
(a) Does production function 1 have increasing, constant, or diminishing returns to scale? Explain.
(b) Does production function 2 have increasing, constant, or diminishing returns to scale? Explain.