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 = 1900 - 19 P`.
What is the Consumer Surplus when the price is $15?
Step 1: Quantity Demanded
At price $15, the quantity demanded is `Q_D = 1900 - 19 P = 1900 - 19 \times 15 = 1615`.
Step 2: Inverse demand
$$ \begin{align*} Q_d &= 1900 - 19 P \\ 19 P &= 1900 - Q_d \\ P &= \frac{1900 - Q_d}{19} \\ P &= \frac{1900}{19} - \frac{Q_d}{19} \\ P &= 100 - \frac{Q_d}{19} \end{align*} $$Step 3: Draw the graph
Step 4: Calculate the Consumer Surplus
`\text{CS} = \frac{(100 - 15) \times 1615}{2} = 68637.5`.