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Sagot :
Let's analyze the given data step-by-step to complete the chart and find out at which output quantity the business firm is experiencing a loss.
First, let's review the provided information:
1. Quantities: 1, 2, 3, 4, 5
2. Prices: [tex]$20, $[/tex]19, [tex]$18, $[/tex]17, $16
3. Total Revenue at each quantity: [tex]$20, $[/tex]38, [tex]$54, $[/tex]68, $80
4. Total Costs at each quantity: [tex]$14, $[/tex]24, [tex]$39, $[/tex]61
Step-by-Step Solution:
1. Calculate the Marginal Revenue:
- Marginal Revenue is the change in total revenue from selling one more unit.
- Marginal Revenue for Quantity 1 is not applicable.
- Marginal Revenue for Quantity 2: \( \[tex]$38 - \$[/tex]20 = \$18 \)
- Marginal Revenue for Quantity 3: \( \[tex]$54 - \$[/tex]38 = \$16 \)
- Marginal Revenue for Quantity 4: \( \[tex]$68 - \$[/tex]54 = \$14 \)
- Marginal Revenue for Quantity 5: \( \[tex]$80 - \$[/tex]68 = \$12 \)
2. Calculate the Marginal Cost:
- Marginal Cost is the change in total cost from producing one more unit.
- Marginal Cost for Quantity 1 is not applicable.
- Marginal Cost for Quantity 2: \( \[tex]$24 - \$[/tex]14 = \$10 \)
- Marginal Cost for Quantity 3: \( \[tex]$39 - \$[/tex]24 = \$15 \)
- Marginal Cost for Quantity 4: \( \[tex]$61 - \$[/tex]39 = \$22 \)
- Total Cost for Quantity 5 is unknown, so Marginal Cost for Quantity 5 is not provided.
3. Calculate the Profit or Loss:
- Profit or Loss is Total Revenue minus Total Cost.
- Profit or Loss for Quantity 1: \( \[tex]$20 - \$[/tex]14 = \$6 \)
- Profit or Loss for Quantity 2: \( \[tex]$38 - \$[/tex]24 = \$14 \)
- Profit or Loss for Quantity 3: \( \[tex]$54 - \$[/tex]39 = \$15 \)
- Profit or Loss for Quantity 4: \( \[tex]$68 - \$[/tex]61 = \$7 \)
- Profit or Loss for Quantity 5 cannot be calculated because Total Cost is not provided.
Now that we have calculated all the necessary values, let’s complete the chart:
[tex]\[ \begin{array}{|l|l|l|l|l|l|l|} \hline \text{Quantity} & \text{Price} & \text{Total Revenue} & \text{Marginal Revenue} & \text{Total Cost} & \text{Marginal Cost} & \text{Profit or Loss} \\ \hline \text{(TR - TC)} \\ \hline 1 & \[tex]$ 20 & \$[/tex] 20 & \text{N/A} & \[tex]$ 14 & \text{N/A} & \$[/tex] 6 \\
\hline 2 & \[tex]$ 19 & \$[/tex] 38 & \[tex]$ 18 & \$[/tex] 24 & \[tex]$ 10 & \$[/tex] 14 \\
\hline 3 & \[tex]$ 18 & \$[/tex] 54 & \[tex]$ 16 & \$[/tex] 39 & \[tex]$ 15 & \$[/tex] 15 \\
\hline 4 & \[tex]$ 17 & \$[/tex] 68 & \[tex]$ 14 & \$[/tex] 61 & \[tex]$ 22 & \$[/tex] 7 \\
\hline 5 & \[tex]$ 16 & \$[/tex] 80 & \$ 12 & \text{N/A} & \text{N/A} & \text{N/A} \\
\hline
\end{array}
\][/tex]
Answering the Question:
From the calculations, the profit or loss is positive for all quantities except quantity 5 where the total cost information is missing. Therefore, the firm is not experiencing any losses for quantities 1 through 4.
Since there are no negative profits (losses) observed in any of the first four quantities, the business does not experience a loss at any of these output quantities.
Thus, the business firm is not experiencing a loss at quantities 2, 3, 4, or 5. Therefore, the correct answer is:
None. (The business does not experience a loss at any of the given output quantities with provided data.)
First, let's review the provided information:
1. Quantities: 1, 2, 3, 4, 5
2. Prices: [tex]$20, $[/tex]19, [tex]$18, $[/tex]17, $16
3. Total Revenue at each quantity: [tex]$20, $[/tex]38, [tex]$54, $[/tex]68, $80
4. Total Costs at each quantity: [tex]$14, $[/tex]24, [tex]$39, $[/tex]61
Step-by-Step Solution:
1. Calculate the Marginal Revenue:
- Marginal Revenue is the change in total revenue from selling one more unit.
- Marginal Revenue for Quantity 1 is not applicable.
- Marginal Revenue for Quantity 2: \( \[tex]$38 - \$[/tex]20 = \$18 \)
- Marginal Revenue for Quantity 3: \( \[tex]$54 - \$[/tex]38 = \$16 \)
- Marginal Revenue for Quantity 4: \( \[tex]$68 - \$[/tex]54 = \$14 \)
- Marginal Revenue for Quantity 5: \( \[tex]$80 - \$[/tex]68 = \$12 \)
2. Calculate the Marginal Cost:
- Marginal Cost is the change in total cost from producing one more unit.
- Marginal Cost for Quantity 1 is not applicable.
- Marginal Cost for Quantity 2: \( \[tex]$24 - \$[/tex]14 = \$10 \)
- Marginal Cost for Quantity 3: \( \[tex]$39 - \$[/tex]24 = \$15 \)
- Marginal Cost for Quantity 4: \( \[tex]$61 - \$[/tex]39 = \$22 \)
- Total Cost for Quantity 5 is unknown, so Marginal Cost for Quantity 5 is not provided.
3. Calculate the Profit or Loss:
- Profit or Loss is Total Revenue minus Total Cost.
- Profit or Loss for Quantity 1: \( \[tex]$20 - \$[/tex]14 = \$6 \)
- Profit or Loss for Quantity 2: \( \[tex]$38 - \$[/tex]24 = \$14 \)
- Profit or Loss for Quantity 3: \( \[tex]$54 - \$[/tex]39 = \$15 \)
- Profit or Loss for Quantity 4: \( \[tex]$68 - \$[/tex]61 = \$7 \)
- Profit or Loss for Quantity 5 cannot be calculated because Total Cost is not provided.
Now that we have calculated all the necessary values, let’s complete the chart:
[tex]\[ \begin{array}{|l|l|l|l|l|l|l|} \hline \text{Quantity} & \text{Price} & \text{Total Revenue} & \text{Marginal Revenue} & \text{Total Cost} & \text{Marginal Cost} & \text{Profit or Loss} \\ \hline \text{(TR - TC)} \\ \hline 1 & \[tex]$ 20 & \$[/tex] 20 & \text{N/A} & \[tex]$ 14 & \text{N/A} & \$[/tex] 6 \\
\hline 2 & \[tex]$ 19 & \$[/tex] 38 & \[tex]$ 18 & \$[/tex] 24 & \[tex]$ 10 & \$[/tex] 14 \\
\hline 3 & \[tex]$ 18 & \$[/tex] 54 & \[tex]$ 16 & \$[/tex] 39 & \[tex]$ 15 & \$[/tex] 15 \\
\hline 4 & \[tex]$ 17 & \$[/tex] 68 & \[tex]$ 14 & \$[/tex] 61 & \[tex]$ 22 & \$[/tex] 7 \\
\hline 5 & \[tex]$ 16 & \$[/tex] 80 & \$ 12 & \text{N/A} & \text{N/A} & \text{N/A} \\
\hline
\end{array}
\][/tex]
Answering the Question:
From the calculations, the profit or loss is positive for all quantities except quantity 5 where the total cost information is missing. Therefore, the firm is not experiencing any losses for quantities 1 through 4.
Since there are no negative profits (losses) observed in any of the first four quantities, the business does not experience a loss at any of these output quantities.
Thus, the business firm is not experiencing a loss at quantities 2, 3, 4, or 5. Therefore, the correct answer is:
None. (The business does not experience a loss at any of the given output quantities with provided data.)
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