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 = 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.