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Sagot :
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.
### 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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