Example
The supply curve for bananas is `Q_S = 3P` and the demand for bananas is `Q_D = 10 - 2 P`.
In equilibrium,
$$ \begin{align*} Q_S &= Q_D \\ 3P &= 10 - 2P \\ 5P &= 10 \\ P &= 2 \end{align*} $$A banana is sold $2 in equilibrium. So producers will supply 3x2=6 bananas.
The inverse supply is `P = \frac{Q_S}{3}`.
The inverse demand is `P = \frac{10 - Q_D}{2} = 5 - \frac{Q_D}{2}`.
Consumer Surplus is `\text{CS} = \frac{(5 - 2) \times 6}{2} = 9`.
Producer Surplus is `\text{PS} = \frac{(2 - 0) \times 6}{2} = 6`.
Total Surplus is `\text{TS} = \text{CS} + \text{PS} = 9 + 6 = 15`.
Question
The inverse demand for cookies is `P = 729 - 63 Q_d` and the supply is `P = 33 + 53 Q_s`.
What are the equilibrium price and quantity? What is the Total Surplus?
Step 1: Find the equilibrium price and quantity
Step 2: Draw the graph
Step 3: Calculate the Consumer Surplus.
`\text{CS} = \frac{(729 - 351.0) \times 6.0}{2} = 1134.0`.
Step 4: Calculate the Producer Surplus.
`\text{PS} = \frac{(351.0 - 33) \times 6.0}{2} = 954.0`.
Step 5: Calculate the Total Surplus.
`\text{TS} = \text{CS} + \text{PS} = 1134.0 + 954.0 = 2088.0`.