A. Suppose we begin in a system in which mortgage interest is not deductible and then tax deductibility of mortgage interest is introduced.
(a) Using a graph (as you did in exercise 2.17) with €œsquare feet of housing€ on the horizontal axis and €œdollars of other consumption€ on the vertical, illustrate the direction of the substitution effect.
(b)What kind of good would housing have to be in order for the household to consume less housing as a result of the introduction of the tax deductibility program?
(c) On a graph that contains both the before and after deductibility budget constraints, how would you illustrate the amount of subsidy the government provides to this household?
(d) Suppose the government provided the same amount of money to this household but did so instead by simply giving it to the household as cash back on its taxes (without linking it to housing consumption). Will the household buy more or less housing?
(e) Will the household be better or worse off?
(f) Do your answer to (d) and (e) depend on whether housing is normal, reg inferior or Giffen?
(g) Under tax deductibility, will the household spend more on other consumption before or after tax deductibility is introduced? Discuss your answer in terms of income and substitution effects and assume that €œother goods€ is a normal good.
(h) If you observed that a household consumes more in €œother goods€ after the introduction of tax deductibility, could that household€™s tastes be quasilinear in housing? Homothetic?

Graph 7.13: Tax Deductibility of Mortgage Interest: Part II
B. Households typically spend about a quarter of their after-tax income I on housing. Let x1 denote square feet of housing and let x2 denote other consumption.
(a) If we represent a household€™s tastes with the Cobb-Douglas function u(x1,x2) = x1α
x2(1ˆ’α) , what should α be?
(b) Using your answer about the value of α, and letting the price per square foot of housing be denoted as p1, derive the optimal level of housing consumption (in terms of I , p1, and t ) under a tax deductibility program that implicitly subsidizes a fraction t of a household€™s housing purchase.
(c) What happens to housing consumption and other good consumption under tax deductibility as a household€™s tax bracket (i.e. their tax rate t ) increases?
(d) Determine the portion of changed housing consumption that is due to the income effect and the portion that is due to the substitution effect.
(e) Calculate the amount of money the government is spending on subsidizing this household€™s mortgage interest.
(f) Now suppose that, instead of a deductibility program, the government simply gives the amount you calculated in (e) to the household as cash. Calculate the amount of housing now consumed and compare it to your answer under tax deductibility.

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