Sure! Let's break down how to find the marginal revenue (MR) for the 10th unit step-by-step.
### Step 1: Calculate Total Revenue
Total Revenue (TR) is calculated by multiplying the price (P) by the quantity (Q) for each row in the table.
Using the given prices and quantities:
1. [tex]\( P = \$40 \)[/tex] and [tex]\( Q = 0 \)[/tex]:
[tex]\[
TR = 40 \times 0 = 0
\][/tex]
2. [tex]\( P = \$35 \)[/tex] and [tex]\( Q = 5 \)[/tex]:
[tex]\[
TR = 35 \times 5 = 175
\][/tex]
3. [tex]\( P = \$30 \)[/tex] and [tex]\( Q = 10 \)[/tex]:
[tex]\[
TR = 30 \times 10 = 300
\][/tex]
4. [tex]\( P = \$25 \)[/tex] and [tex]\( Q = 15 \)[/tex]:
[tex]\[
TR = 25 \times 15 = 375
\][/tex]
5. [tex]\( P = \$20 \)[/tex] and [tex]\( Q = 20 \)[/tex]:
[tex]\[
TR = 20 \times 20 = 400
\][/tex]
6. [tex]\( P = \$15 \)[/tex] and [tex]\( Q = 25 \)[/tex]:
[tex]\[
TR = 15 \times 25 = 375
\][/tex]
The Total Revenues are: [tex]\([0, 175, 300, 375, 400, 375]\)[/tex].
### Step 2: Calculate Marginal Revenue
Marginal Revenue (MR) is calculated as the change in Total Revenue divided by the change in Quantity.
1. For the quantity between 0 and 5 units:
[tex]\[
MR = \frac{175 - 0}{5 - 0} = \frac{175}{5} = 35
\][/tex]
2. For the quantity between 5 and 10 units:
[tex]\[
MR = \frac{300 - 175}{10 - 5} = \frac{125}{5} = 25
\][/tex]
3. For the quantity between 10 and 15 units:
[tex]\[
MR = \frac{375 - 300}{15 - 10} = \frac{75}{5} = 15
\][/tex]
4. For the quantity between 15 and 20 units:
[tex]\[
MR = \frac{400 - 375}{20 - 15} = \frac{25}{5} = 5
\][/tex]
5. For the quantity between 20 and 25 units:
[tex]\[
MR = \frac{375 - 400}{25 - 20} = \frac{-25}{5} = -5
\][/tex]
The Marginal Revenues are: [tex]\([35, 25, 15, 5, -5]\)[/tex].
### Step 3: Determine the Marginal Revenue for the 10th unit
To find the MR for the 10th unit, we look at the interval between 5 and 10 units, which gives us the second MR value:
[tex]\[
MR \text{ for the 10th unit} = 25
\][/tex]
So the marginal revenue for the 10th unit is $25.
