To determine the profit-maximizing price for a nondiscriminating monopolist facing zero production costs, we need to calculate the total revenue for each price point and then identify the price at which total revenue is highest.
The total revenue ([tex]\( TR \)[/tex]) is calculated by multiplying the price ([tex]\( P \)[/tex]) by the quantity demanded ([tex]\( Q_d \)[/tex]) at that price. Let's go through each price point given in the table and compute the corresponding total revenue:
[tex]\[
\begin{array}{|c|c|c|}
\hline
P & Q_d & TR \\
\hline
\$15 & 1 & 15 \times 1 = 15 \\
\hline
\$12 & 2 & 12 \times 2 = 24 \\
\hline
\$9 & 3 & 9 \times 3 = 27 \\
\hline
\$8 & 4 & 8 \times 4 = 32 \\
\hline
\$6 & 5 & 6 \times 5 = 30 \\
\hline
\end{array}
\][/tex]
The total revenue calculations are as follows:
- At a price of \[tex]$15, the total revenue is \$[/tex]15.
- At a price of \[tex]$12, the total revenue is \$[/tex]24.
- At a price of \[tex]$9, the total revenue is \$[/tex]27.
- At a price of \[tex]$8, the total revenue is \$[/tex]32.
- At a price of \[tex]$6, the total revenue is \$[/tex]30.
Now, we compare these total revenues to determine which is the highest. From the calculations:
- The highest total revenue of \[tex]$32 occurs when the price is set at \$[/tex]8.
Therefore, the profit-maximizing monopolist will set the price at \[tex]$8. The correct answer is:
\$[/tex]8.
