Questions: Plant 1 Plant 2 Plant 3 --------- Output ATC Output ATC Output ATC 10 10 10 15 10 20 20 9 20 10 20 15 30 8 30 7 30 10 40 9 40 10 40 8 50 10 50 14 50 9 What is the long-run average cost of producing 30 units of output? Multiple Choice 7 8 9 10

Plant 1 Plant 2 Plant 3 --------- Output ATC Output ATC Output ATC 10 10 10 15 10 20 20 9 20 10 20 15 30 8 30 7 30 10 40 9 40 10 40 8 50 10 50 14 50 9 What is the long-run average cost of producing 30 units of output? Multiple Choice 7 8 9 10
Transcript text: \begin{tabular}{|c|c|c|c|c|c|} \hline \multicolumn{2}{|c|}{ Plant 1 } & \multicolumn{2}{c|}{ Plant 2 } & \multicolumn{2}{c|}{ Plant3 } \\ \hline Output & ATC & Output & ATC & Output & ATC \\ \hline 10 & $\$ 10$ & 10 & $\$ 15$ & 10 & $\$ 20$ \\ \hline 20 & 9 & 20 & 10 & 20 & 15 \\ \hline 30 & 8 & 30 & 7 & 30 & 10 \\ \hline 40 & 9 & 40 & 10 & 40 & 8 \\ \hline 50 & 10 & 50 & 14 & 50 & 9 \\ \hline \end{tabular} What is the long-run average cost of producing 30 units of output? Multiple Choice \$7 \$8 \$9 $\$ 10$
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Solution

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The question asks for the long-run average cost of producing 30 units of output across three plants. To find this, we need to determine the average total cost (ATC) for producing 30 units from each plant and then calculate the overall average.

From the table:

  • Plant 1: ATC for 30 units = \$8
  • Plant 2: ATC for 30 units = \$7
  • Plant 3: ATC for 30 units = \$10

To find the long-run average cost, we take the average of these costs:

\[ \text{Long-run average cost} = \frac{\$8 + \$7 + \$10}{3} = \frac{\$25}{3} \approx \$8.33 \]

Since the options provided are whole numbers, the closest option to \$8.33 is \$8.

The answer is the second one: \$8.

Explanation for each option:

  • \$7: This is the ATC for Plant 2 alone, not the average across all plants.
  • \$8: This is the closest whole number to the calculated long-run average cost of \$8.33.
  • \$9: This is not the calculated average of the ATCs for 30 units.
  • \$10: This is the ATC for Plant 3 alone, not the average across all plants.

In summary, the long-run average cost of producing 30 units of output is approximately \$8.33, and the closest option is \$8.

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