Derive the cost function for the given production function

Question

Problem

Let a firm's production function be z=f(x,y)=x^ay^b

where z is the output level and x and y are factor inputs and a and b are exogenous parameters, a,b>0. Prices on factors are given, p_x and p_y and the product price is p.

a) Show that this production function exhibits constant returns to scale if a+b=1, increasing returns if a+b>1 and decreasing returns if a+b<1

b) Derive the cost function for this production function

c) Derive, using the Envelope Theorem, the Shephard's Lemma for this production function.

Explain, and show workings, thank you.

The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.