Welfare

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 at $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