Question 11 (10 points) [10 marks] The production function of a competitive firm is described by the equaon y = 4x11/2x21/4 1. [2 marks] If x2 is currently 81, how much x1 is needed to produce y units of output? Derive an expression for the marginal product of 1:1. 2. [3 marks] Denote the factor prices of x1 and x; in dollars per unit as P1 and P2 respectively. In the short run x2 = 81. Derive the short run total cost function as a function of output and the prices of inputs. In addition, derive the short run marginal and average cost functions. What are xed costs? 3. [2 marks] Suppose P1 = 1, P2 = 3 and the price of output, Py = 5. Determine the prot maximizing level of output, y*, and associated optimal demand for x1*. Determine prots at y* and label as 3*. 4. [3 marks] In the long run both factors are variable. Determine the lowest cost choices of x1 and x2 for producing the optimal short run 32* which you found in part (3) above. Denote these input choices as ff and 3. Determine prots given if and f5, and label as 7?. Explain why if is higher or lower than::*