Questions: In the long run, the firm should use plant size "A" for

To determine when the firm should use plant size "A" in the long run, we need to identify the output levels at which plant size "A" has the lowest Average Total Cost (ATC) compared to plant sizes "B" and "C".

Let's analyze the data provided in the table:

\[ \begin{array}{|c|c|c|c|} \hline \text{Output} & \text{ATC-A} & \text{ATC-B} & \text{ATC-C} \\ \hline 10 & \$6 & \$13 & \$44 \\ \hline 20 & \$5 & \$9 & \$35 \\ \hline 30 & \$4 & \$6 & \$27 \\ \hline 40 & \$5 & \$4 & \$20 \\ \hline 50 & \$7 & \$3 & \$14 \\ \hline 60 & \$10 & \$4 & \$11 \\ \hline 70 & \$14 & \$5 & \$8 \\ \hline 80 & \$19 & \$7 & \$6 \\ \hline 90 & \$25 & \$10 & \$5 \\ \hline 100 & \$32 & \$16 & \$7 \\ \hline \end{array} \]

We need to compare the ATC values for each output level to determine when plant size "A" has the lowest cost.

• At output 10: ATC-A = \$6, ATC-B = \$13, ATC-C = \$44

  • Plant size "A" has the lowest ATC.

• At output 20: ATC-A = \$5, ATC-B = \$9, ATC-C = \$35

  • Plant size "A" has the lowest ATC.

• At output 30: ATC-A = \$4, ATC-B = \$6, ATC-C = \$27

  • Plant size "A" has the lowest ATC.

• At output 40: ATC-A = \$5, ATC-B = \$4, ATC-C = \$20

  • Plant size "B" has the lowest ATC.

• At output 50: ATC-A = \$7, ATC-B = \$3, ATC-C = \$14

  • Plant size "B" has the lowest ATC.

• At output 60: ATC-A = \$10, ATC-B = \$4, ATC-C = \$11

  • Plant size "B" has the lowest ATC.

• At output 70: ATC-A = \$14, ATC-B = \$5, ATC-C = \$8

  • Plant size "B" has the lowest ATC.

• At output 80: ATC-A = \$19, ATC-B = \$7, ATC-C = \$6

  • Plant size "C" has the lowest ATC.

• At output 90: ATC-A = \$25, ATC-B = \$10, ATC-C = \$5

  • Plant size "C" has the lowest ATC.

• At output 100: ATC-A = \$32, ATC-B = \$16, ATC-C = \$7

  • Plant size "C" has the lowest ATC.

From this analysis, we can see that plant size "A" has the lowest ATC for output levels of 10, 20, and 30.

Summary: In the long run, the firm should use plant size "A" for output levels of 10, 20, and 30.