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 = 459 + 51 P`.
Find the inverse supply function.
Determine the price of bananas when the quantity supply is 1836.
Let's transform the supply function into the inverse supply function.
$$ \begin{align*} Q_s &= 459 + 51 P \\ 51 P &= Q_s - 459 \\ P &= \frac{459 - Q_s}{51} \end{align*} $$The inverse supply function is `P = \frac{459 - Q_s}{51}`.
If the quantity supplied is 1836, then
$$ P = \frac{459 - 1836}{51} = 27 $$The price producers get for a banana is $27.