2. Answer ALL parts of the question a) A firm has the production function Q=10 +0.25 In(2X) + 0.6 Z where X and Z are variable inputs. Derive the "marginal product" of X and Z by taking the partial derivatives of the production function. (10 marks) b) Using your results in (a) complete the following table (8 marks) X Z Q Marginal Marginal Product of X Product of Z 2.00 2.00 2.00 3.00 3.00 2.00 3.00 3.00 c) Take the second order derivatives (including the cross partial) of the production function. What do their signs tell you? (8 marks) d) Using the results in the table above, a 50% increase in all inputs results in what percentage of an increase in the output? What does this imply about the returns to scale (over this region) for the production function above? (4 marks) 2. Answer ALL parts of the question a) A firm has the production function Q=10 +0.25 In(2X) + 0.6 Z where X and Z are variable inputs. Derive the "marginal product" of X and Z by taking the partial derivatives of the production function. (10 marks) b) Using your results in (a) complete the following table (8 marks) X Z Q Marginal Marginal Product of X Product of Z 2.00 2.00 2.00 3.00 3.00 2.00 3.00 3.00 c) Take the second order derivatives (including the cross partial) of the production function. What do their signs tell you? (8 marks) d) Using the results in the table above, a 50% increase in all inputs results in what percentage of an increase in the output? What does this imply about the returns to scale (over this region) for the production function above? (4 marks)