Consumer Surplus

Consumer Surplus sums the dollar amount consumers are willing to pay and subtracts the price they pay.

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 = 132 - 22 P`.

What is the Consumer Surplus when the price is $3?

Step 1: Quantity Demanded

At price $3, the quantity demanded is `Q_D = 132 - 22 P = 132 - 22 \times 3 = 66`.

Step 2: Inverse demand

$$ \begin{align*} Q_d &= 132 - 22 P \\ 22 P &= 132 - Q_d \\ P &= \frac{132 - Q_d}{22} \\ P &= \frac{132}{22} - \frac{Q_d}{22} \\ P &= 6 - \frac{Q_d}{22} \end{align*} $$

Step 3: Draw the graph

Step 4: Calculate the Consumer Surplus

`\text{CS} = \frac{(6 - 3) \times 66}{2} = 99.0`.