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Suppose the market for schools in a small town is of perfect competition. The market demand for school seats, $y$, is given by $y(p)$. The long run average cost function for each school is given by $C(y)$. how do I determine the following?

(i) the long run equilibrium size of each school?
(ii) the tuition price does each school charge

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up vote 1 down vote accepted

Under perfect competition firms produce in the long run at the point in which average cost is minimum. This is a consequence of the zero profit condition needed in the long run, which in turn determines the number of firms that will operate in the market (because there can't be entry/exit of firms). In your example, this means that each firm will produce a quantity $y^*$ such that $C(y^*)\leq C(y)$ for all $y\geq 0$. Moreover, the zero profit condition also requires that the price in equilibrium to be such that $p=C(y^*)$.

EDIT: Thanks to @jack for pointing out a mistake with the average cost function.

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why is $AC(y)=\frac {C(y)}{y}$? $C(y)$ is already the average cost function. no? – Jack Nov 7 '12 at 19:41
yup. You're bad. – Cristian Nov 8 '12 at 1:20

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