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Sagot :
Let's analyze the data given in the question in order to find the economic profit for the firm:
Given data:
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline \multicolumn{3}{|c|}{Demand Data} & \multicolumn{2}{|c|}{Cost Data} \\ \hline (1) & (2) & (3) & & \text{Total} \\ \hline \text{Price} & \text{Price} & \text{Quantity} & \text{Output} & \text{Cost} \\ \hline \$ 11.00 & \$ 10.00 & 6 & 6 & \$ 61 \\ \hline 9.99 & 8.85 & 7 & 7 & 62 \\ \hline 9.00 & 8.00 & 8 & 8 & 64 \\ \hline 8.00 & 7.00 & 9 & 9 & 67 \\ \hline 7.10 & 6.10 & 10 & 10 & 72 \\ \hline 6.00 & 5.00 & 11 & 11 & 79 \\ \hline 5.15 & 4.15 & 12 & 12 & 86 \\ \hline \end{array} \][/tex]
Step-by-step solution:
1. Determine Revenue for Each Quantity:
- Revenue is calculated as [tex]\(\text{Price} \times \text{Quantity}\)[/tex].
- For each price and corresponding quantity, the revenues are calculated as follows:
- [tex]\( \$11.00 \times 6 = \$66.00 \)[/tex]
- [tex]\( \$9.99 \times 7 = \$69.93 \)[/tex]
- [tex]\( \$9.00 \times 8 = \$72.00 \)[/tex]
- [tex]\( \$8.00 \times 9 = \$72.00 \)[/tex]
- [tex]\( \$7.10 \times 10 = \$71.00 \)[/tex]
- [tex]\( \$6.00 \times 11 = \$66.00 \)[/tex]
- [tex]\( \$5.15 \times 12 = \$61.80 \)[/tex]
2. Determine Profit for Each Quantity:
- Profit is calculated as [tex]\(\text{Revenue} - \text{Total Cost}\)[/tex].
- For each revenue and corresponding total cost, the profits are calculated as follows:
- [tex]\( \$66.00 - \$61.00 = \$5.00 \)[/tex]
- [tex]\( \$69.93 - \$62.00 = \$7.93 \)[/tex]
- [tex]\( \$72.00 - \$64.00 = \$8.00 \)[/tex]
- [tex]\( \$72.00 - \$67.00 = \$5.00 \)[/tex]
- [tex]\( \$71.00 - \$72.00 = -\$1.00 \)[/tex]
- [tex]\( \$66.00 - \$79.00 = -\$13.00 \)[/tex]
- [tex]\( \$61.80 - \$86.00 = -\$24.20 \)[/tex]
3. Identify the Closest Economic Profit to the Provided Choices:
- The calculated profits are:
- \[tex]$5.00 - \$[/tex]7.93
- \[tex]$8.00 - \$[/tex]5.00
- [tex]\(-\$1.00\)[/tex]
- [tex]\(-\$13.00\)[/tex]
- [tex]\(-\$24.20\)[/tex]
The closest profit to the options given is [tex]\( \$8.00 \)[/tex], which is also one of our calculated profits.
Thus, the correct economic profit is:
[tex]\(\$8.00\)[/tex].
The correct answer is:
[tex]\[\boxed{\$ 8}\][/tex]
Given data:
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline \multicolumn{3}{|c|}{Demand Data} & \multicolumn{2}{|c|}{Cost Data} \\ \hline (1) & (2) & (3) & & \text{Total} \\ \hline \text{Price} & \text{Price} & \text{Quantity} & \text{Output} & \text{Cost} \\ \hline \$ 11.00 & \$ 10.00 & 6 & 6 & \$ 61 \\ \hline 9.99 & 8.85 & 7 & 7 & 62 \\ \hline 9.00 & 8.00 & 8 & 8 & 64 \\ \hline 8.00 & 7.00 & 9 & 9 & 67 \\ \hline 7.10 & 6.10 & 10 & 10 & 72 \\ \hline 6.00 & 5.00 & 11 & 11 & 79 \\ \hline 5.15 & 4.15 & 12 & 12 & 86 \\ \hline \end{array} \][/tex]
Step-by-step solution:
1. Determine Revenue for Each Quantity:
- Revenue is calculated as [tex]\(\text{Price} \times \text{Quantity}\)[/tex].
- For each price and corresponding quantity, the revenues are calculated as follows:
- [tex]\( \$11.00 \times 6 = \$66.00 \)[/tex]
- [tex]\( \$9.99 \times 7 = \$69.93 \)[/tex]
- [tex]\( \$9.00 \times 8 = \$72.00 \)[/tex]
- [tex]\( \$8.00 \times 9 = \$72.00 \)[/tex]
- [tex]\( \$7.10 \times 10 = \$71.00 \)[/tex]
- [tex]\( \$6.00 \times 11 = \$66.00 \)[/tex]
- [tex]\( \$5.15 \times 12 = \$61.80 \)[/tex]
2. Determine Profit for Each Quantity:
- Profit is calculated as [tex]\(\text{Revenue} - \text{Total Cost}\)[/tex].
- For each revenue and corresponding total cost, the profits are calculated as follows:
- [tex]\( \$66.00 - \$61.00 = \$5.00 \)[/tex]
- [tex]\( \$69.93 - \$62.00 = \$7.93 \)[/tex]
- [tex]\( \$72.00 - \$64.00 = \$8.00 \)[/tex]
- [tex]\( \$72.00 - \$67.00 = \$5.00 \)[/tex]
- [tex]\( \$71.00 - \$72.00 = -\$1.00 \)[/tex]
- [tex]\( \$66.00 - \$79.00 = -\$13.00 \)[/tex]
- [tex]\( \$61.80 - \$86.00 = -\$24.20 \)[/tex]
3. Identify the Closest Economic Profit to the Provided Choices:
- The calculated profits are:
- \[tex]$5.00 - \$[/tex]7.93
- \[tex]$8.00 - \$[/tex]5.00
- [tex]\(-\$1.00\)[/tex]
- [tex]\(-\$13.00\)[/tex]
- [tex]\(-\$24.20\)[/tex]
The closest profit to the options given is [tex]\( \$8.00 \)[/tex], which is also one of our calculated profits.
Thus, the correct economic profit is:
[tex]\(\$8.00\)[/tex].
The correct answer is:
[tex]\[\boxed{\$ 8}\][/tex]
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