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# long-run total cost and long-run average cost

The production engineers at Impact Industries have derived the optimal combinations of labor and capital (the only two inputs used by Impact) for three levels of output: 120, 180, and 240 units of output:
Q L* K*
120 4 20
180 6 30
240 8 50
Q is the output level, L* is the optimal amount of labor to use, and K* is the optimal amount of capital to use. The price of labor is \$100 per unit and the price of capital is \$20 per unit.

1. If the manager of Impact Industries decides to produce 120 units, what will the long-run total cost and long-run average cost of producing 120 units?

2. If the manager of Impact Industries decides to produce 180 units, what will the long-run total cost and long-run average cost of producing 180 units?

3. If the manager of Impact Industries decides to produce 240 units, what will the long-run total cost and long-run average cost of producing 240 units?

4. Are there economies of scale over the output range 120 to 180? Explain briefly.

5. Are there diseconomies of scale over the output range 180 to 240? Explain briefly.

#### Solution Preview

1. To produce 120 units, 4L and 20K are needed, that costs 400 + 400 = \$800. Average cost is 800/120 = \$6.67

2. 6L and 30K are needed which costs 600 + 600 = \$1200. Average cost is 1200/180 = 6.67

3. 8L and ...

#### Solution Summary

long-run total cost and long-run average cost

\$2.19