Let's walk through the problem step-by-step to determine the marginal revenue generated by the pure monopoly from selling the third unit of output.
First, we need to determine the total revenue (TR) at each level of quantity demanded. The total revenue is calculated as:
[tex]\[ \text{Total Revenue} = \text{Price} \times \text{Quantity Demanded} \][/tex]
Here's the calculation for each quantity demanded:
1. When the price is [tex]$7:
\[ \text{TR} = \$[/tex]7 \times 1 = \[tex]$7 \]
2. When the price is $[/tex]6:
[tex]\[ \text{TR} = \$6 \times 2 = \$12 \][/tex]
3. When the price is [tex]$5:
\[ \text{TR} = \$[/tex]5 \times 3 = \[tex]$15 \]
4. When the price is $[/tex]4:
[tex]\[ \text{TR} = \$4 \times 4 = \$16 \][/tex]
5. When the price is [tex]$3:
\[ \text{TR} = \$[/tex]3 \times 5 = \[tex]$15 \]
Now, we have the total revenues at each level of quantity:
\[ \text{Total Revenues} = [7, 12, 15, 16, 15] \]
Next, we calculate the marginal revenue (MR) for selling the third unit. Marginal revenue is the change in total revenue when one more unit is sold, calculated as:
\[ \text{Marginal Revenue (MR)} = \text{Total Revenue at current quantity} - \text{Total Revenue at previous quantity} \]
For the third unit (Q=3):
\[ \text{MR} = \text{Total Revenue at Q=3} - \text{Total Revenue at Q=2} \]
\[ \text{MR} = 15 - 12 \]
\[ \text{MR} = 3 \]
Therefore, the marginal revenue generated by the pure monopoly from selling the third unit of output is \$[/tex]3.
