If the market demand for shoes is given by $QD = 10000-250P$ and the supply is
$QS = 5000$, what is the equilibrium price of shoes? How many pairs of shoes will be sold?
Thanks in advance.
[Math] Economics supply and demand question
economics
Related Solutions
For context, I grabbed this picture from Wikipedia
The red area is the integral of $D(x) - 45$ from $0$ to $81$. Namely, $$ \int_0^{81} \left(\frac{405}{\sqrt{x}}-45\right)\,dx $$ To integrate, write $405/\sqrt{x}$ as $x^{-1/2}$ and use the formula $\int x^a = x^{a+1}/(a+1)$.
To check the answer, you can use Wolfram Alpha: it's $3645$.
Best Answer
As $QD = QS$ at market equilibrium:
$$10000-250P=5000,$$
$$10000-5000=250P,$$
$$\frac{5000}{250}=P.$$
Thus, $P=20$.