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.
A: 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 budget constraint?
(c) Is it possible to tell which policy the family would prefer?
B: Write down the mathematical expression for the choice sets you drew in 2.14A (a) and 2.14A(b), letting x1 denote square feet of monthly housing consumption and x2 denote dollars spent on non housing consumption.