The production engineers at Impact Industries have derived the optimal combinati
ID: 1212145 • Letter: T
Question
The production engineers at Impact Industries have derived the optimal combinations of labor and capital. These are the only two inputs used by Impact. The following chart shows the combinations of labor and capital for three levels of output. Q is the output level. L* is the optimal amount of labor. K* is the optimal amount of capital. The price of labor is $100 per unit. The price of capital is $20 per unit. Q L* K* 120 5 20 180 7 7 240 12 24 6. 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? Show all calculations. 7. 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? Show all calculations. 8. 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? Show all calculations. 9. Are there economies of scale over the output range 120 to 180? Explain in 25-50 words. 10. Are there diseconomies of scale over the output range 180 to 240? Explain in 25-50 words.
Explanation / Answer
6. 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? Show all calculations
For 120 units, L* = 5 , K* = 20
Total Cost = Pl*L + Pk*K = 100*5 + 20*20 = 500 + 400 = 900
Average Cost = Total Cost/Quantity = 900/120 = 7.5
. 7. 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? Show all calculations
For 180 units, L* = 7 , K* = 7
Total Cost = Pl*L + Pk*K = 100*7 + 20*7 = 700 + 140 = 840
Average Cost = Total Cost/Quantity = 840/180 = 4.66
. 8. 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? Show all calculations
For 240 units, L* = 12 , K* = 24
Total Cost = Pl*L + Pk*K = 100*12 + 20*24 = 1200 + 480 = 1680
Average Cost = Total Cost/Quantity = 1680/240 = 7
. 9. Are there economies of scale over the output range 120 to 180? Explain in 25-50 words.
Yes , there is economies of scale over the output range 120 to 180, as with increase of output, the costs of inputs used is decreasing.
10. Are there diseconomies of scale over the output range 180 to 240? Explain in 25-50 words.
Yes , there are diseconomies of scale over the output range 180 to 240, as the increase in output is less than the increase in the inputs , when inputs are increased.
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