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 = 185 - 37 P`.
What is the Consumer Surplus when the price is $4?
Step 1: Quantity Demanded
At price $4, the quantity demanded is `Q_D = 185 - 37 P = 185 - 37 \times 4 = 37`.
Step 2: Inverse demand
$$ \begin{align*} Q_d &= 185 - 37 P \\ 37 P &= 185 - Q_d \\ P &= \frac{185 - Q_d}{37} \\ P &= \frac{185}{37} - \frac{Q_d}{37} \\ P &= 5 - \frac{Q_d}{37} \end{align*} $$Step 3: Draw the graph
Step 4: Calculate the Consumer Surplus
`\text{CS} = \frac{(5 - 4) \times 37}{2} = 18.5`.