3. Consider the following production function:
q = f(Z1,Z2) = Z?$^{1/4}$Z?$^{1/2}$
Assuming that the price of the output is p and the prices of inputs are w? and
W?, respectively.
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a) State the firm's profit maximization problem.
(2 marks)
b) Derive the firm's factor demand functions, Z? and Z?.
(10 marks)
c) Derive the firm's supply function.
(3 marks)
d) Derive the profit function.
(3 marks)
e) Verify Hotelling's lemma for q(w,p), Z?(w,p) and Z?(w,p)
(6 marks)