## 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 - 195}{65}`.

What is the Producer Surplus when the price is $13650?

### Step 1: Quantity Supplied

At price $13650, the quantity demanded is `Q_S = \frac{P - 195}{65} = \frac{13650 - 195}{65} = 207`.

### Step 2: Inverse Supply

$$ \begin{align*} Q_S &= \frac{P - 195}{65} \\ 65 Q_S &= P - 195 \\ 195 + 65 Q_S &= P \end{align*} $$So the inverse supply curve follows the equation `P = 195 + 65 Q_S`.

### Step 3: Draw the graph

### Step 4: Calculate the Producer Surplus

`\text{PS} = \frac{(13650 - 195) \times 207}{2} = 1392592.5`