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 = 261 + 29 P`.
Find the inverse supply function.
Determine the price of bananas when the quantity supply is 10440.
Let's transform the supply function into the inverse supply function.
$$ \begin{align*} Q_s &= 261 + 29 P \\ 29 P &= Q_s - 261 \\ P &= \frac{261 - Q_s}{29} \end{align*} $$The inverse supply function is `P = \frac{261 - Q_s}{29}`.
If the quantity supplied is 10440, then
$$ P = \frac{261 - 10440}{29} = 351 $$The price producers get for a banana is $351.