The demand function of a good is given by $q_d(p)=\frac{22}{p^2}$, $(p> 0)$ and the supply function by $q_s(p)=p^2+9$, $(p\geq 0)$. Determine all the market equilibria.
Antwoord 1 correct
Correct
Antwoord 2 optie
$(q,p)=(5.5,2)$
Antwoord 2 correct
Fout
Antwoord 3 optie
$(q,p)=(5.5,2)$ and $(q,p)=(-11, 130)$
Antwoord 3 correct
Fout
Antwoord 4 optie
$(q,p)=(11,-\sqrt{2})$ and $(q,p)=(11,\sqrt{2})$
Antwoord 4 correct
Fout
Antwoord 1 optie
$(q,p)=(11,\sqrt{2})$
Antwoord 1 feedback
Correct:
$$\begin{align*}
q_d(p)=q_s(p)& \Leftrightarrow \frac{22}{p^2}=p^2+9\\
& \Leftrightarrow 22=p^4+9p^2\\
& \Leftrightarrow p^4+9p^2-22=0.
\end{align*}$$
Substitute $x=p^2$. Then
$$\begin{align*}
x^2+9x-22= 0 & \Leftrightarrow (x+11)(x-2)=0\\
& \Leftrightarrow x=-11 \mbox{ or } x=2.
\end{align*}$$
$p^2=-11$ gives no solutions.
$p^2=2$ gives $p=-\sqrt{2}$ or $p=\sqrt{2}$. Due to non-negativity $p=-\sqrt{2}$ is not possible.
Hence, $(q,p)=(11,\sqrt{2})$ is the market equilbrium.
Go on.
$$\begin{align*}
q_d(p)=q_s(p)& \Leftrightarrow \frac{22}{p^2}=p^2+9\\
& \Leftrightarrow 22=p^4+9p^2\\
& \Leftrightarrow p^4+9p^2-22=0.
\end{align*}$$
Substitute $x=p^2$. Then
$$\begin{align*}
x^2+9x-22= 0 & \Leftrightarrow (x+11)(x-2)=0\\
& \Leftrightarrow x=-11 \mbox{ or } x=2.
\end{align*}$$
$p^2=-11$ gives no solutions.
$p^2=2$ gives $p=-\sqrt{2}$ or $p=\sqrt{2}$. Due to non-negativity $p=-\sqrt{2}$ is not possible.
Hence, $(q,p)=(11,\sqrt{2})$ is the market equilbrium.
Go on.
Antwoord 2 feedback
Wrong: Note that $p^2=2$, not $p=2$.
See for instance Feature logarithmic functions: Example (film).
See for instance Feature logarithmic functions: Example (film).
Antwoord 3 feedback
Antwoord 4 feedback