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 = -147 + 41 P`.
The demand is `Q_D = 363 - 44 P`.
What is the equilibrium price? What is the equilibrium quantity?
Step 1: Equate supply and demand
$$
\begin{align*}
Q_S &= Q_D \\
-147 + 41 P &= 363 - 44 P \\
44 P + 41 P &= 363 + 147 \\
(44 + 41) P &= 363 + 147 \\
P &= \frac{363 + 147}{44 + 41} \\
P &= 6.0
\end{align*}
$$
Step 2: Plug into the supply curve (or the demand curve)
$$
\begin{align*}
Q_S &= -147 + 41 \times 6.0 \\
Q_S &= 99.0
\end{align*}
$$
$$
\begin{align*}
Q_S &= Q_D \\
-147 + 41 P &= 363 - 44 P \\
44 P + 41 P &= 363 + 147 \\
(44 + 41) P &= 363 + 147 \\
P &= \frac{363 + 147}{44 + 41} \\
P &= 6.0
\end{align*}
$$
Step 2: Plug into the supply curve (or the demand curve)
$$
\begin{align*}
Q_S &= -147 + 41 \times 6.0 \\
Q_S &= 99.0
\end{align*}
$$
$$
\begin{align*}
Q_S &= -147 + 41 \times 6.0 \\
Q_S &= 99.0
\end{align*}
$$