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Sagot :
Let's complete the given chart with the missing data and then determine at which output quantity the business firm is experiencing a loss.
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
Quantity & Price & Total Revenue & Marginal Revenue & Total Cost & Marginal Cost & \begin{tabular}{l}
Profit or Loss \\
(TR - TC)
\end{tabular} \\
\hline
1 & \[tex]$20 & \$[/tex]20 & --- & \[tex]$14 & --- & \$[/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 & \[tex]$12 & \$[/tex]95 & \[tex]$34 & -\$[/tex]15 \\
\hline
\end{tabular}
To find the Marginal Revenue (MR) and Marginal Cost (MC):
1. Marginal Revenue (MR) at a given quantity is the change in Total Revenue (TR) when output quantity increases by one unit.
[tex]\[MR_{2} = TR_{2} - TR_{1} = 38 - 20 = 18\][/tex]
[tex]\[MR_{3} = TR_{3} - TR_{2} = 54 - 38 = 16\][/tex]
[tex]\[MR_{4} = TR_{4} - TR_{3} = 68 - 54 = 14\][/tex]
[tex]\[MR_{5} = TR_{5} - TR_{4} = 80 - 68 = 12\][/tex]
2. Marginal Cost (MC) at a given quantity is the change in Total Cost (TC) when output quantity increases by one unit.
[tex]\[MC_{2} = TC_{2} - TC_{1} = 24 - 14 = 10\][/tex]
[tex]\[MC_{3} = TC_{3} - TC_{2} = 39 - 24 = 15\][/tex]
[tex]\[MC_{4} = TC_{4} - TC_{3} = 61 - 39 = 22\][/tex]
[tex]\[MC_{5} = TC_{5} - TC_{4} = 95 - 61 = 34\][/tex]
3. Profit or Loss is calculated as Total Revenue (TR) minus Total Cost (TC) at each quantity.
[tex]\[Profit\,or\,Loss_{1} = TR_{1} - TC_{1} = 20 - 14 = 6\][/tex]
[tex]\[Profit\,or\,Loss_{2} = TR_{2} - TC_{2} = 38 - 24 = 14\][/tex]
[tex]\[Profit\,or\,Loss_{3} = TR_{3} - TC_{3} = 54 - 39 = 15\][/tex]
[tex]\[Profit\,or\,Loss_{4} = TR_{4} - TC_{4} = 68 - 61 = 7\][/tex]
[tex]\[Profit\,or\,Loss_{5} = TR_{5} - TC_{5} = 80 - 95 = -15\][/tex]
From the completed chart, we observe that the business firm is experiencing a loss at Quantity 5, where the Profit or Loss is [tex]\(-\$15\)[/tex].
Therefore, the business firm is losing money at output quantity 5.
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
Quantity & Price & Total Revenue & Marginal Revenue & Total Cost & Marginal Cost & \begin{tabular}{l}
Profit or Loss \\
(TR - TC)
\end{tabular} \\
\hline
1 & \[tex]$20 & \$[/tex]20 & --- & \[tex]$14 & --- & \$[/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 & \[tex]$12 & \$[/tex]95 & \[tex]$34 & -\$[/tex]15 \\
\hline
\end{tabular}
To find the Marginal Revenue (MR) and Marginal Cost (MC):
1. Marginal Revenue (MR) at a given quantity is the change in Total Revenue (TR) when output quantity increases by one unit.
[tex]\[MR_{2} = TR_{2} - TR_{1} = 38 - 20 = 18\][/tex]
[tex]\[MR_{3} = TR_{3} - TR_{2} = 54 - 38 = 16\][/tex]
[tex]\[MR_{4} = TR_{4} - TR_{3} = 68 - 54 = 14\][/tex]
[tex]\[MR_{5} = TR_{5} - TR_{4} = 80 - 68 = 12\][/tex]
2. Marginal Cost (MC) at a given quantity is the change in Total Cost (TC) when output quantity increases by one unit.
[tex]\[MC_{2} = TC_{2} - TC_{1} = 24 - 14 = 10\][/tex]
[tex]\[MC_{3} = TC_{3} - TC_{2} = 39 - 24 = 15\][/tex]
[tex]\[MC_{4} = TC_{4} - TC_{3} = 61 - 39 = 22\][/tex]
[tex]\[MC_{5} = TC_{5} - TC_{4} = 95 - 61 = 34\][/tex]
3. Profit or Loss is calculated as Total Revenue (TR) minus Total Cost (TC) at each quantity.
[tex]\[Profit\,or\,Loss_{1} = TR_{1} - TC_{1} = 20 - 14 = 6\][/tex]
[tex]\[Profit\,or\,Loss_{2} = TR_{2} - TC_{2} = 38 - 24 = 14\][/tex]
[tex]\[Profit\,or\,Loss_{3} = TR_{3} - TC_{3} = 54 - 39 = 15\][/tex]
[tex]\[Profit\,or\,Loss_{4} = TR_{4} - TC_{4} = 68 - 61 = 7\][/tex]
[tex]\[Profit\,or\,Loss_{5} = TR_{5} - TC_{5} = 80 - 95 = -15\][/tex]
From the completed chart, we observe that the business firm is experiencing a loss at Quantity 5, where the Profit or Loss is [tex]\(-\$15\)[/tex].
Therefore, the business firm is losing money at output quantity 5.
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