Producer Surplus

The Producer Surplus sums the difference between how much producers sell a product and the minimum amount they are willing to get for producing it.

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 - 153}{17}`.

What is the Producer Surplus when the price is $6120?

Step 1: Quantity Supplied

At price $6120, the quantity demanded is `Q_S = \frac{P - 153}{17} = \frac{6120 - 153}{17} = 351`.

Step 2: Inverse Supply

$$ \begin{align*} Q_S &= \frac{P - 153}{17} \\ 17 Q_S &= P - 153 \\ 153 + 17 Q_S &= P \end{align*} $$

So the inverse supply curve follows the equation `P = 153 + 17 Q_S`.

Step 3: Draw the graph

Step 4: Calculate the Producer Surplus

`\text{PS} = \frac{(6120 - 153) \times 351}{2} = 1047208.5`