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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.

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    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?2011-08-29
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    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? Thanks2011-08-29

3 Answers 3