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 = 440 + 22 P`.
Find the inverse supply function.
Determine the price of bananas when the quantity supply is 3080.
Let's transform the supply function into the inverse supply function.
$$ \begin{align*} Q_s &= 440 + 22 P \\ 22 P &= Q_s - 440 \\ P &= \frac{440 - Q_s}{22} \end{align*} $$The inverse supply function is `P = \frac{440 - Q_s}{22}`.
If the quantity supplied is 3080, then
$$ P = \frac{440 - 3080}{22} = 120 $$The price producers get for a banana is $120.