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 = 456 + 57 P`.

Find the inverse supply function.

Determine the price of bananas when the quantity supply is 456.

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

$$ \begin{align*} Q_s &= 456 + 57 P \\ 57 P &= Q_s - 456 \\ P &= \frac{456 - Q_s}{57} \end{align*} $$

The inverse supply function is `P = \frac{456 - Q_s}{57}`.

If the quantity supplied is 456, then

$$ P = \frac{456 - 456}{57} = 0 $$

The price producers get for a banana is $0.