Economics supply and demand question

Question

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.

Answer 1

Since you know $Q_S = 5000$, this means that the quantity supplied is 5000, no matter what the price is. So if the market clears, you are correct that the number sold is 5000 (and that, from the demand equation, the market clearing price is $P=20$).

Answer 2

In this example, supply is a constant, so it really depends on what the demand is.

Equating demand and supply, 10000-250P=5000

Subtracting 5000 from both sides, then adding 250P to both sides,

5000=250P

Then P=5000/250 or 200.

Answer 3

As $QD = QS$ at market equilibrium:

$$10000-250P=5000,$$

$$10000-5000=250P,$$

$$\frac{5000}{250}=P.$$

Thus, $P=20$.