Question Four Consider the following production function: y = f(z)=z¼/^z/2. Assuming that the price of the output is p and the prices of inputs are w, and w₂ respectively: (a) State the firm's profit maximization problem. (2 marks). (b) Derive the firm's factor demand functions for z; and zo. (10 marks). (c) Derive the firm's supply function. (5 marks). = 2. (d) Derive the firm's profit function. (3 marks). an (e) Verify Hotelling's lemma for q(w, p), z₁(w, p) and z₂(w, p). (6 marks). az (f) State the firm's cost minimization problem. (2 marks), (g) Derive the firm's conditional factor demand functions. (8 marks). (h) Derive the firm's cost function. (4 marks). Cond: 69 Porat funct