Example
The inverse demand for bananas is `P = 5 - 0.5 Q_d`.
A banana is sold \$1. Consumers will demand `Q_d = 10 - 2 \times 1 = 8` bananas.
The Consumer Surplus is `\text{CS} = \frac{\left( 5 - 1 \right) \times \left( 8 \right)}{2} = \frac{4 \times 8}{2} = 16`
Question
The demand for bananas is `Q_d = 6000 - 100 P`.
What is the Consumer Surplus when the price is $30?
Step 1: Quantity Demanded
At price $30, the quantity demanded is `Q_D = 6000 - 100 P = 6000 - 100 \times 30 = 3000`.
Step 2: Inverse demand
$$ \begin{align*} Q_d &= 6000 - 100 P \\ 100 P &= 6000 - Q_d \\ P &= \frac{6000 - Q_d}{100} \\ P &= \frac{6000}{100} - \frac{Q_d}{100} \\ P &= 60 - \frac{Q_d}{100} \end{align*} $$Step 3: Draw the graph
Step 4: Calculate the Consumer Surplus
`\text{CS} = \frac{(60 - 30) \times 3000}{2} = 45000.0`.