Question
Problem 5: Suppose you manage a firm and are planning to produce 2 goods, X and Y. Your production engineers have provided you with the
Problem 5: 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 | |||
L | K | X | Y | LTC |
0 | 0 | 0 | 0 | |
2 | 12 | 4 | 0 | |
4 | 22 | 8 | 0 | |
2 | 20 | 0 | 6 | |
4 | 50 | 0 | 12 | |
3 | 20 | 4 | 6 | |
4 | 64 | 8 | 12 |
a. If your firm faces input prices of $30 per unit of labor and $100 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?
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