Example
The inverse supply for bananas is `P = 1 + 2 Q_s`.
If a banana is sold for $5, producers will produce `Q_s = \frac{5 - 1}{2} = 2`.
The Producer Surplus is `\text{PS} = \frac{\left( 5 - 1 \right) \times 2}{2} = \frac{4 \times 2}{2} = $4`.
Question
The supply for bananas is `Q_S = \frac{P - 6300}{63}`.
What is the Producer Surplus when the price is $12600?
Step 1: Quantity Supplied
At price $12600, the quantity demanded is `Q_S = \frac{P - 6300}{63} = \frac{12600 - 6300}{63} = 100`.
Step 2: Inverse Supply
$$ \begin{align*} Q_S &= \frac{P - 6300}{63} \\ 63 Q_S &= P - 6300 \\ 6300 + 63 Q_S &= P \end{align*} $$So the inverse supply curve follows the equation `P = 6300 + 63 Q_S`.
Step 3: Draw the graph
Step 4: Calculate the Producer Surplus
`\text{PS} = \frac{(12600 - 6300) \times 100}{2} = 315000.0`