Inverse Supply

The inverse supply curve represents the price as a function of the quantity supplied.

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 = 207 + 23 P`.

Find the inverse supply function.

Determine the price of bananas when the quantity supply is 414.

Let's transform the supply function into the inverse supply function.

$$ \begin{align*} Q_s &= 207 + 23 P \\ 23 P &= Q_s - 207 \\ P &= \frac{207 - Q_s}{23} \end{align*} $$

The inverse supply function is `P = \frac{207 - Q_s}{23}`.

If the quantity supplied is 414, then

$$ P = \frac{207 - 414}{23} = 9 $$

The price producers get for a banana is $9.