## Example

The market for cookies is huge, with many consumers and many sellers.

The supply follows the equation `Q_S = 3 P`.

The demand follows the equation `Q_D = 10 - 2 P`.

In equilibrium, supply equals demand

$$ \begin{align*} Q_S &= Q_D \\ 3 P &= 10 - 2 P \\ 5 P &= 10 \\ P &= 2 \end{align*} $$In equilibrium, a banana is sold $2 and there are 6 bananas on the market.

### Question

The supply equation for bananas is `Q_S = -5098 + 89 P`.

The demand is `Q_D = 5702 - 31 P`.

What is the equilibrium price? What is the equilibrium quantity?

### Step 1: Equate supply and demand

###
##

$$
\begin{align*}
Q_S &= Q_D \\
-5098 + 89 P &= 5702 - 31 P \\
31 P + 89 P &= 5702 + 5098 \\
(31 + 89) P &= 5702 + 5098 \\
P &= \frac{5702 + 5098}{31 + 89} \\
P &= 90.0
\end{align*}
$$

$$
\begin{align*}
Q_S &= Q_D \\
-5098 + 89 P &= 5702 - 31 P \\
31 P + 89 P &= 5702 + 5098 \\
(31 + 89) P &= 5702 + 5098 \\
P &= \frac{5702 + 5098}{31 + 89} \\
P &= 90.0
\end{align*}
$$

### Step 2: Plug into the supply curve (or the demand curve)

###
##

$$
\begin{align*}
Q_S &= -5098 + 89 \times 90.0 \\
Q_S &= 2912.0
\end{align*}
$$

$$
\begin{align*}
Q_S &= -5098 + 89 \times 90.0 \\
Q_S &= 2912.0
\end{align*}
$$