Recall that a Cobb$-$Douglas production function has the form P $=$ cLK with c$,,>0.$Economists talk about increasing returns to scale if doubling L and K more than doubles P $,$ constant returns to scale if doubling L and K exactly doubles P $,$ decreasing returns to scale if doubling L and K less than doubles P $.$What conditions on the sum $+$ lead to $($a$)$ constant returns to scale?$($b$)$ decreasing returns to scale?Fully justify your answers mathematically.