Derive the cost function for the production function

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Reference no: EM132152117

Question: 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.

Please explain, and show workings.

Reference no: EM132152117

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