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The table below shows the total cost (TC) and marginal cost (MC) for Baker Street, a perfectly competitive firm producing different quantities of apple pies. The market price of apple pies is [tex]\$ 4.00[/tex] per pie.

a. Fill in the marginal revenue (MR) and average revenue (AR) columns.

Instructions: Round your answers to two decimal places.

Baker Street's Costs and Revenues

\begin{tabular}{|c|c|c|c|c|}
\hline
\begin{tabular}{l}
Quantity \\
(apple pies)
\end{tabular} & TC (dollars) & MC (dollars) & \begin{tabular}{c}
MR \\
(dollars)
\end{tabular} & \begin{tabular}{c}
AR \\
(dollars)
\end{tabular} \\
\hline 5 & [tex]$\$[/tex] 55.00[tex]$ & $[/tex]\[tex]$ 1.00$[/tex] & [tex]$\[tex]$[/tex]$ & \\
\hline 10 & [tex]$\$[/tex] 57.50[tex]$ & $[/tex]\[tex]$ 0.50$[/tex] & [tex]$\$[/tex]$[/tex] & \\
\hline 15 & [tex]$\$[/tex] 62.50[tex]$ & $[/tex]\[tex]$ 1.00$[/tex] & [tex]$\[tex]$[/tex]$ & \\
\hline 20 & [tex]$\$[/tex] 72.50[tex]$ & $[/tex]\[tex]$ 2.00$[/tex] & [tex]$\$[/tex]$[/tex] & \\
\hline 25 & [tex]$\$[/tex] 92.50[tex]$ & $[/tex]\[tex]$ 4.00$[/tex] & [tex]$\[tex]$[/tex]$ & \\
\hline 30 & [tex]$\$[/tex] 122.50[tex]$ & $[/tex]\[tex]$ 6.00$[/tex] & [tex]$\$[/tex]$[/tex] & \\
\hline
\end{tabular}

Instructions: Enter your answers as a whole number.

b. At the market price of [tex]\[tex]$ 4.00[/tex] per apple pie, how many apple pies should Baker Street make? $[/tex]\qquad$ apple pies

c. If the market price for apple pies were to rise to [tex]\[tex]$ 6.00[/tex] per apple pie, how many apple pies should Baker Street make? $[/tex]\qquad$ apple pies

Sagot :

GinnyAnswer
Sure, let's go through each part of the question.

### Part a: Fill in the Marginal Revenue (MR) and Average Revenue (AR) columns

To get started, let's recall that in a perfectly competitive market, the market price is both the Marginal Revenue (MR) and the Average Revenue (AR). Since the market price per apple pie is \[tex]$4.00, both MR and AR should be \$[/tex]4.00 for all quantities.

So, we simply fill in the MR and AR columns with the market price:

[tex]\[ \begin{array}{|c|c|c|c|c|} \hline \text{Quantity (apple pies)} & \text{TC (dollars)} & \text{MC (dollars)} & \text{MR (dollars)} & \text{AR (dollars)} \\ \hline 5 & 55.00 & 1.00 & 4.00 & 4.00 \\ \hline 10 & 57.50 & 0.50 & 4.00 & 4.00 \\ \hline 15 & 62.50 & 1.00 & 4.00 & 4.00 \\ \hline 20 & 72.50 & 2.00 & 4.00 & 4.00 \\ \hline 25 & 92.50 & 4.00 & 4.00 & 4.00 \\ \hline 30 & 122.50 & 6.00 & 4.00 & 4.00 \\ \hline \end{array} \][/tex]

### Part b: Determine the number of apple pies to produce at a market price of \$4.00 per apple pie

In order to maximize profit, the firm should produce at the quantity where Marginal Cost (MC) equals Marginal Revenue (MR). Given MR = \[tex]$4.00, we look for the quantity where MC = \$[/tex]4.00:

From the table, we observe:
\begin{itemize}
\item At quantity 25, \( MC = \$4.00 \)
\end{itemize}
Thus, the firm should produce 25 apple pies.

### Part c: Determine the number of apple pies to produce at a market price of \$6.00 per apple pie

Similarly, if the market price rises to \[tex]$6.00 per apple pie, we need to find the quantity where MC equals this new price, which is \$[/tex]6.00:

From the table, we observe:
\begin{itemize}
\item At quantity 30, \( MC = \$6.00 \)
\end{itemize}
Thus, the firm should produce 30 apple pies.

### Summary:
a. The complete table with MR and AR filled in:
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline \text{Quantity (apple pies)} & \text{TC (dollars)} & \text{MC (dollars)} & \text{MR (dollars)} & \text{AR (dollars)} \\ \hline 5 & 55.00 & 1.00 & 4.00 & 4.00 \\ \hline 10 & 57.50 & 0.50 & 4.00 & 4.00 \\ \hline 15 & 62.50 & 1.00 & 4.00 & 4.00 \\ \hline 20 & 72.50 & 2.00 & 4.00 & 4.00 \\ \hline 25 & 92.50 & 4.00 & 4.00 & 4.00 \\ \hline 30 & 122.50 & 6.00 & 4.00 & 4.00 \\ \hline \end{array} \][/tex]

b. The firm should produce 25 apple pies at a market price of \$4.00 per apple pie.

c. If the market price rises to \$6.00 per apple pie, the firm should produce 30 apple pies.
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