Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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.

share|cite|improve this question
The incoming money from a choice of price $P$ will be $P\cdot QD=P(10^4-250P)$, which is maximized at $P=20$ to $100000$ (I don't know your units), as can be shown with either basic calculus or algebra. For this profit-maximizing choice of price, the number of shoes sold is $10000-250P=5000$. Is this what you're asking? – anon Aug 29 '11 at 9:34
So far, I did 10000-250P = 5000 250P = 5000 P = 20. So I think that is the price. Does that mean that the number of shoes sold is 5000? Thanks – mr. chan Aug 29 '11 at 10:08

As $QD = QS$ at market equilibrium:




Thus, $P=20$.

share|cite|improve this answer

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 $P=20$).

share|cite|improve this answer

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,


Then P=5000/250 or 200.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.