$(3pts)$ Recall that a Cobb$-$Douglas production function has the form

$P=c{L}^{}{K}^{}$ 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.