Suppose you manage a firm and are planning to produce 2 goods, X and Y. Your production engineers have provided you with the following spreadsheet showing a portion of the multiproduct expansion path (least-cost combination of inputs to produce various output levels) with the required inputs grouped into two broad categories, where L represents the labor input and K represents the capital input. Multiproduct Expansion Path Multiproduct Total Cost LTC L K X Y 0 0 0 0 1 6 4 0 2 11 8 0 1 10 0 6 2 25 0 12 1 10 4 6 2 32 8 12 a. If your firm faces input prices of $25 per unit of labor and $50 per unit of capital, construct the multiproduct cost function by computing the missing values in the spreadsheet. b. If you anticipate that the long-run demand for X is 4 units and the long-run demand for Y is 6 units, are there economies of scope for your firm? Explain. c. Suppose a new long-run forecasts expects the demand for X and Y to be 8 and 12 respectively. Are there economies of scope for your firm? Explain. d. If your firm is already producing 4 units of X, what is the marginal cost of adding 6 units of Y to your output? How does this cost of 6 units of Y compare to the same output produced by a single-product producer? Are their economies of scope for the multiproduct production? e. If your firm is already producing 12 units of Y, what is the marginal cost of adding 8 units of X to your output? How does this cost of 8 units of X compare to the same output produced by a single-product producer? Are their economies of scope for the multiproduct production?