4. (Nechyba 2.14) Public Housing and Housing Subsidies: For a long period, the U.S. government focused its attempts to meet housing needs among the poor through public housing programs. Eligible families could get on waiting lists to apply for an apartment in a public housing development and would be offered a particular apartment as they moved to the top of the waiting list Suppose a particular family has a monthly income of $1,500 and is offered a 1,500-square-foot public housing apartment for $375 in monthly rent. Alternatively, the family could choose to rent housing in the private market for $0.50 per square foot. (a) Illustrate all the bundles in this family's choice set of square feet of housing" (on the horizontal axis) and "dollars of monthly other goods consumption" (on the vertical axis). (b) In recent years, the government has shifted away from an emphasis on public housing and toward providing poor families with a direct subsidy to allow them to rent more housing in the private market. Suppose, instead of offering the family in part (a) an apartment, the government offered to pay half of the family's rental bill. How would this change the family's bu constraint? (e) Is it possible to tell which policy the family would prefer? 5. (Nechyba 2.16) Public Schools and Private School Vouchers: Consider a simple model of how economic circumstances are changed when free public education is provided. Suppose a house- hold 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; that is, 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. (Hint: One additional point will appear in 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 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; that is, 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)