The government is concerned that rent takes up so much of a low-income families’ monthly budget. In order to subsidize low income housing a policy is implemented where the government will pay ½ of the rent (which they send to the landlord). So, for example, if a family chose to rent an apartment that costs $800 a month the government would pay $400 directly to the landlord and the family would pay $400 from their budget. The Cunningham family, who lives in Milwaukee have an income of $1,000 a month and qualify for this subsidy. Knowing they have to pay only half they optimally choose an apartment to rent listed at $500 a month.

a. On a diagram, draw the budget set and indifference curves of the Cunningham family (with dollars per month of other goods consumed on the vertical axis and dollars of housing per month on the horizontal axis (use the listed rent for the horizontal axis not the amount the consumer pays). Show the consumer’s choice. Label all relevant points including the vertical and horizontal intercepts of the budget set and the chosen level of housing (the listed rent of housing) and other goods consumed.

b. Now assume a new policy has been proposed that instead of paying for half the price of the rent the government provides each low-income household with a housing voucher worth $250 a month. The voucher can be used only for housing expenditures (and is non-tradeable). Technically, if the family chose to rent the same $500 apartment, they would simply hand over the voucher and have to pay $250 to the landlord (who would then collect the $250 from the government by sending in the voucher). Draw a diagram showing the budget set under this housing voucher policy. Be sure to label all relevant points including the horizontal intercept and the vertical intercept. Use the same x-axis and y-axis as in a).

c. On the same graph include both budget sets from a) and b). Now add indifference curves to the graph to show the choice made under the housing voucher policy. Based on your drawing explain whether you think the Cunningham family would prefer the ½ off policy or the housing voucher policy. Can you draw indifference curves such that you might change your answer as to which policy they prefer?