In the US income tax code a number of expenditures are deductible. For most U.S. taxpayers the largest tax deduction is the ability to deduct the home mortgage interest. For the purpose of this question, assume that the entire yearly spending on housing is interest expense so the home mortgage interest deduction becomes a housing expense deduction. This means, for example, that if a household has a marginal tax rate of 33% then the government is subsiding one-third of their interest/housing expenses. Another way to think about the home expenses deduction in this problem is that any dollars spent on housing are tax free, and thus, the deduction is equivalent to a decrease in the price of housing relative to other goods.

A. Consider a household with an income of $200,000 that faces an income tax rate of 40% and suppose the price of a square foot of housing is $50 per year and the price of the composite good is $1. With square footage of housing on the horizontal axis and the consumption of all other goods on the vertical axis, sketch and write the budget constraints for the household with and without the tax deductibility of housing expenses. (Note: in both cases, though, the family must pay income taxes where applicable and housing expenses are the only deductible expense in this problem.)

B. Add plausible indifference curves to illustrate the family’s consumption of housing and all other goods in both scenarios.

C. Edward Glaeser, the Harvard urban economist, in his recent book titled “Triumph of the City” writes the following (slightly paraphrased):

“The biggest public home-ownership subsidy of all has ended up being the tax deductibility of mortgage interest, which began not as a housing policy but as a by-product of the general deductibility of interest expenses. Subsidizing the purchase of housing has ended up encouraging people to leave cities and buy bigger homes.” (pg. 176). Needless to say, Glaeser is in favor of eliminating that tax deduction to make cities denser and urban living more attractive.

Illustrate his point on your graph by showing that if the government offered an increase in the standard deduction (i.e., a lump sum reduction in taxes or equivalently a decrease in the tax rate) instead of the housing expense deduction, where the increase in the standard deduction provided an equivalent increase in utility as the housing expense deduction, our family would choose to consume less housing.

D. Show also that the increase in dollar value of the standard deduction needed to provide the same level of utility is less than the dollar value of the housing expense deduction. In other words, if we eliminated the housing expense deduction and replaced it with an increased standard deduction, there would be less housing consumption and more income tax revenue without negatively impacting utility.