Public Schools and Private School Vouchers: Consider a simple model of how economic circumstances are changed when the government enters the education market.
A: Suppose a household has an after-tax income of $50,000 and consider its budget constraint with “dollars of education services” on the horizontal axis and “dollars of other consumption” on the vertical. Begin by drawing the household’s budget line (given that you can infer a price for each of the goods on the axes from the way these goods are defined) assuming that the household can buy any level of school spending on the private market.
(a) Now suppose the government uses its existing tax revenues to fund a public school at $7,500 per pupil; i.e. it funds a school that anyone can attend for free and that provides $7,500 in education services. Illustrate how this changes the choice set.
(b) Continue to assume that private school services of any quantity could be purchased but only if the child does not attend public schools. Can you think of how the availability of free public schools might cause some children to receive more educational services than before they would in the absence of public schools? Can you think of how some children might receive fewer educational services once public schools are introduced?
(c) Now suppose the government allows an option: either a parent can send her child to the public school or she can take a voucher to a private school and use it for partial payment of private school tuition. Assume that the voucher is worth $7,500 per year; i.e. it can be used to pay for up to $7,500 in private school tuition. How does this change the budget constraint? Do you still think it is possible that some children will receive less education than they would if the government did not get involved at all (i.e. no public schools and no vouchers)?
B: Letting dollars of education services be denoted by x1 and dollars of other consumption by x2, formally define the choice set with just the public school (and a private schoolmarket) as well as the choice set with private school vouchers defined above.