# Welfare

Welfare (or Total Surplus) sums the Consumer Surplus and the Producer Surplus. $$TS = CS + PS$$

## 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

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