Example
The supply for cookies follows the following equation: `Q_s = 10 + 2P`.
Solving for P:
$$ \begin{align*} Q_s &= 10 + 2P \\ 2P &= Q_s - 10 \\ P &= \frac{Q_s - 10}{2} \end{align*} $$ The inverse supply is `P = \frac{Q_s - 10}{2}`Question
The supply for bananas follows the equation `Q_s = 675 + 45 P`.
Find the inverse supply function.
Determine the price of bananas when the quantity supply is 54000.
Let's transform the supply function into the inverse supply function.
$$ \begin{align*} Q_s &= 675 + 45 P \\ 45 P &= Q_s - 675 \\ P &= \frac{675 - Q_s}{45} \end{align*} $$The inverse supply function is `P = \frac{675 - Q_s}{45}`.
If the quantity supplied is 54000, then
$$ P = \frac{675 - 54000}{45} = 1185 $$The price producers get for a banana is $1185.