Suppose that the production function is the following:

Yt $=$ A$$K

$1$

$$

t $+(1)$N

$1$

$$

t $$

$$

$1$

:

It is assumed that the parameter $$ C $0$ and $0<<1.$

$($a$)$ Prove that this production function features constant returns to scale.

$($b$)$ Compute the $$rst partial derivatives with respect to Kt and Nt$.$ Argue

that these are positive.

$($c$)$ Compute the own second partial derivatives with respect to Kt and Nt$.$

Show that these are both negative.

$($d$)$ As $1,$ how do the $$rst and second partial derivatives for this pro$-$

duction function compare with the Cobb$-$Douglas production discussed

in the text?