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 = 4950 - 55 P`.
What is the Consumer Surplus when the price is $32?
Step 1: Quantity Demanded
At price $32, the quantity demanded is `Q_D = 4950 - 55 P = 4950 - 55 \times 32 = 3190`.
Step 2: Inverse demand
$$ \begin{align*} Q_d &= 4950 - 55 P \\ 55 P &= 4950 - Q_d \\ P &= \frac{4950 - Q_d}{55} \\ P &= \frac{4950}{55} - \frac{Q_d}{55} \\ P &= 90 - \frac{Q_d}{55} \end{align*} $$Step 3: Draw the graph
Step 4: Calculate the Consumer Surplus
`\text{CS} = \frac{(90 - 32) \times 3190}{2} = 92510.0`.