Consider the following demand and supply curves: $Q ^ { \mathrm { d } } = 100 - 2 \mathrm { P }$, and $\mathrm { Q } ^ { s } = 1 / 2 \mathrm { P }$, calculate the equilibrium $P$ and $Q$ for this initial situation and assuming the supply curve changes to $Q ^ { s } = 1 / 2 P$ $+ 10$. Which of the following is correct?
A) the initial equilibrium is $P = 40 , Q = 20$ and the supply curve shifts left.
B) the initial equilibrium is $P = 40 , Q = 20$ and the new equilibrium is $P = 36 , Q = 28$.
C) the initial equilibrium is $\mathrm { P } = 40 , \mathrm { Q } = 20$ and the new equilibrium remains the same.
D) the initial equilibrium is $P = 40 , Q = 20$ and the new equilibrium is $P = 38 , Q = 28$.

Question

Quizplus · Accepted Answer

To find the equilibrium, we set the quantity demanded equal to the quantity supplied:

\begin{align*}
100-2P &= \frac12 P\
200-4P &= P\
P &= 40
\end{align*}

Substituting P back into either the demand or supply equation gives us the equilibrium quantity:

\begin{align*}
Q &= 100-2(40)\
&= 20
\end{align*}

When the supply curve changes to $Q ^ { s } = 1 / 2 P + 10$, we repeat the process.

\begin{align*}
100-2P &= \frac12 P + 10\
190 &= \frac52 P\
P &= 38\
\end{align*}

Substituting back into either equation gives us the new equilibrium quantity:

\begin{align*}
Q &= 100 - 2(38)\
&= 24
\end{align*}

Therefore, the initial equilibrium is $P = 40 , Q = 20$, and the new equilibrium is $P = 38 , Q = 24$, which is closest to choice B.

Consider the Following Demand and Supply Curves Qd=100−2PQ ^ { \mathrm { d } } = 100 - 2 \mathrm { P }Qd=100−2P

Consider the Following Demand and Supply Curves $Q ^ { \mathrm { d } } = 100 - 2 \mathrm { P }$