1. Consider a firm with the following production function LYDpleasef(z1,z2,z3)=z1+min{z2,z3} The market prices for all goods are positive, i.e. p>0,w1>0,w2>0, and w3>0. (a) Show that this production function exhibits decreasing returns to scale. (b) State the profit maximization problem. What does part (a) imply about the solution to PMP? (c) Can the producer choose inputs such that z2=z3 if she tries to maximize her profit? Explain your answer. (d) Derive the producer's output supply q(p,w) and input demand z(p,w). When deriving, clearly state the optimality conditions (FOCs) you used to derive the output supply and input demand. Does the producer use all inputs in production? [Hint: Keep in mind your answer to the previous part. Given the answer to the previous part, is the production function non-differentiable?] 1. Consider a firm with the following production function LYDpleasef(z1,z2,z3)=z1+min{z2,z3} The market prices for all goods are positive, i.e. p>0,w1>0,w2>0, and w3>0. (a) Show that this production function exhibits decreasing returns to scale. (b) State the profit maximization problem. What does part (a) imply about the solution to PMP? (c) Can the producer choose inputs such that z2=z3 if she tries to maximize her profit? Explain your answer. (d) Derive the producer's output supply q(p,w) and input demand z(p,w). When deriving, clearly state the optimality conditions (FOCs) you used to derive the output supply and input demand. Does the producer use all inputs in production? [Hint: Keep in mind your answer to the previous part. Given the answer to the previous part, is the production function non-differentiable?]