# Price Floor

The Price Floor is the minimum price chosen by the government.

## Example

The government sets a price floor of $10. The inverse demand is P = 14 - Q_D and the inverse supply is P = 2 + Q_S. After the price floor, there are 4 millions bananas sold at$10.

Consumer surplus is CS = \frac{\left( 14 - 10 \right) \times 4}{2} = 6.

Producer surplus is PS = \left( 10 - 6 \right) \times 4 + \frac{\left( 6 - 2 \right) \times 4}{2} = 16 + 8 = 24.

Total Surplus is equal to TS = CS + PS = 6 + 24 = 30.

The Dead weight loss is equal to DWL = \frac{\left( 10 - 6 \right) \times \left( 6 - 4 \right)}{2} = 4.

### Question

The inverse demand for bananas is P = 151 - 12Q_D. The inverse supply is P = 95 + 2Q_S.

The government sets a \$139 price floor.

What is the market quantity? Calculate the Consumer Surplus, the Producer surplus, Total Surplus, and the Dead Weight Loss.

Plug P = 139 into the inverse demand function \begin{align*} P &= 151 - 12 Q \\ Q &= \frac{ 151 - P }{ 12 } \\ Q &= \frac{ 151 - 139 }{ 12 } \\ Q &= 1.0 \end{align*}

\begin{align*} CS &= \frac{ \left( 151 - 139 \right) \times 1 }{ 2 } \\ &= \frac{ 12 \times 1 }{ 2 } \\ &= \frac{ 12 }{ 2 } \\ &= 6.0 \\ \end{align*}

\begin{align*} PS &= \left( 139 - 97 \right) \times 1 + \frac{ \left( 97 - 95 \right) \times 1 }{ 2 } \\ &= 42 \times 1 + \frac{ 2 \times 1 }{ 2 } \\ &= 42 + \frac{ 2 }{ 2 } \\ &= 43.0 \\ \end{align*}

\begin{align*} TS &= CS + PS \\ &= 6.0 + 43.0 \\ &= 49.0 \\ \end{align*}

\begin{align*} DWL &= \frac{ \left( 139 - 97 \right) \times \left( 4.0 - 1 \right) }{ 2 } \\ &= \frac{ 42 \times 3.0 }{ 2 } \\ &= 63.0 \\ \end{align*}