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 - 2550}{51}`.
What is the Producer Surplus when the price is $38250?
Step 1: Quantity Supplied
At price $38250, the quantity demanded is `Q_S = \frac{P - 2550}{51} = \frac{38250 - 2550}{51} = 700`.
Step 2: Inverse Supply
$$ \begin{align*} Q_S &= \frac{P - 2550}{51} \\ 51 Q_S &= P - 2550 \\ 2550 + 51 Q_S &= P \end{align*} $$So the inverse supply curve follows the equation `P = 2550 + 51 Q_S`.
Step 3: Draw the graph
Step 4: Calculate the Producer Surplus
`\text{PS} = \frac{(38250 - 2550) \times 700}{2} = 12495000.0`