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 = 5040 - 84 P`.

What is the Consumer Surplus when the price is $51?

Step 1: Quantity Demanded

At price $51, the quantity demanded is `Q_D = 5040 - 84 P = 5040 - 84 \times 51 = 756`.

Step 2: Inverse demand

$$ \begin{align*} Q_d &= 5040 - 84 P \\ 84 P &= 5040 - Q_d \\ P &= \frac{5040 - Q_d}{84} \\ P &= \frac{5040}{84} - \frac{Q_d}{84} \\ P &= 60 - \frac{Q_d}{84} \end{align*} $$

Step 3: Draw the graph

Step 4: Calculate the Consumer Surplus

`\text{CS} = \frac{(60 - 51) \times 756}{2} = 3402.0`.