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 = 168 - 56 P`.
What is the Consumer Surplus when the price is $3?
Step 1: Quantity Demanded
At price $3, the quantity demanded is `Q_D = 168 - 56 P = 168 - 56 \times 3 = 0`.
Step 2: Inverse demand
$$ \begin{align*} Q_d &= 168 - 56 P \\ 56 P &= 168 - Q_d \\ P &= \frac{168 - Q_d}{56} \\ P &= \frac{168}{56} - \frac{Q_d}{56} \\ P &= 3 - \frac{Q_d}{56} \end{align*} $$Step 3: Draw the graph
Step 4: Calculate the Consumer Surplus
`\text{CS} = \frac{(3 - 3) \times 0}{2} = 0.0`.