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# In the United States, private schools charge tuition and compete against public schools that do not.

1.    In the United States, private schools charge tuition and compete against public schools that do not. One policy proposal to improve the quality of education involves increasing demand for private schools through school vouchers.  A school voucher is a piece of paper with a dollar amount V that is given to parents who can use the voucher to pay a portion V of their private school tuition. The private schools will then redeem the voucher for a payment of V from the government. Assume that private schools want to maximize profits and that the market for private schools is perfectly competitive.

A.  Assume the private school market is currently in long run equilibrium. For a single representative private school in this market sketch their LRAC (long run average cost curve) and their MC (marginal cost) curve.  The X axis will be labeled number of seats in the school and the Y axis is tuition in dollars.  Then, in a separate graph next to this, illustrate a hypothetical city-wide market demand curve for seats in the private school as a function of price (i.e., tuition). Finally, include in your second graph a hypothetical supply curve that intersects with the demand function at the price that causes the private school market to be in long run equilibrium.

B.   What are the LR profits for this representative private school?

C.   Illustrate what happens to the market demand curve as a result of the government making available vouchers in the amount of V to all families that live in the city.  What happens to the number of seats made available in each existing private school, and what happens to the tuition level in the short run?  Is it likely that an existing representative private school is now making positive profits? How can you tell from your graph(s)?

D.  Next, consider the long run again when additional private schools can enter the market.

Illustrate these additional schools in your graph. How does this affect the tuition price, the number of seats in each school, and the overall number of children attending private schools?

E.   One concern about vouchers that is sometimes expressed is that the implementation of vouchers will simply cause private schools to increase their tuition level and thus cause no real change in who attends private school.  Evaluate this concern from both a short-run and long-run perspective using your answers from C and D.

F.   Proponents of private school vouchers often argue that the increased availability of private schools will cause public schools to offer higher quality education.  If this claim is true and public schools are now offering a higher quality education how would that change your answers to parts C and D.

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