Suppose that the production function is the following:

Yt = A[K_t^1/ + (1 )N_t^1/]^/1

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

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

(b) Compute the first 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 first and second partial derivatives for this pro-

duction function compare with the Cobb-Douglas production discussed in the text?

(e) Does this function satisfy the assumption that labor and capital are essential goods in production process? If so, then for what values