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 = -136 + 45 P`.
The demand is `Q_D = 1334 - 53 P`.
What is the equilibrium price? What is the equilibrium quantity?
Step 1: Equate supply and demand
$$
\begin{align*}
Q_S &= Q_D \\
-136 + 45 P &= 1334 - 53 P \\
53 P + 45 P &= 1334 + 136 \\
(53 + 45) P &= 1334 + 136 \\
P &= \frac{1334 + 136}{53 + 45} \\
P &= 15.0
\end{align*}
$$
Step 2: Plug into the supply curve (or the demand curve)
$$
\begin{align*}
Q_S &= -136 + 45 \times 15.0 \\
Q_S &= 539.0
\end{align*}
$$
$$
\begin{align*}
Q_S &= Q_D \\
-136 + 45 P &= 1334 - 53 P \\
53 P + 45 P &= 1334 + 136 \\
(53 + 45) P &= 1334 + 136 \\
P &= \frac{1334 + 136}{53 + 45} \\
P &= 15.0
\end{align*}
$$
Step 2: Plug into the supply curve (or the demand curve)
$$
\begin{align*}
Q_S &= -136 + 45 \times 15.0 \\
Q_S &= 539.0
\end{align*}
$$
$$
\begin{align*}
Q_S &= -136 + 45 \times 15.0 \\
Q_S &= 539.0
\end{align*}
$$