$1$ CES production

Consider $a2-$input, $1-$output production technology with production function

$f(z)=(z_1^r+z_2^r{)}^{\frac{}{r}}$

for known constants $r0$ and $>0.$

Show that $fis$ a homogeneous function, and identify the degree $of$ homogeneity.

Using your answer $to$ the previous part, show that the cost function satisfies $C(q)=$

$K*q^{}$ for some constants $K,>0,$ and characterize $.(You$ should not need $to$ solve

the cost minimization problem $to$ answer this part.$)$

Characterize $Kas$ a function $of$ the input prices $w_1,w_2>0by$ solving the cost mini$-$

mization problem.