Consider the Smith family who have the following demand for rental housing (q, m

Question

Consider the Smith family who have the following demand for rental housing (q, measured in square feet):

q = 0.5*(y/p),

where y is the Smith family income and p is the price of housing per square foot. The Smith’s income is $2000 per month and initially the price of housing is $2 per square foot.

a) If the Smiths are operating on their demand curve, how much housing are they consuming?

b) How much is the Smith family’s monthly rent? How much does the Smith family spend on other consumption?

c) Starting from the initial equilibrium, the government now grants the Smiths a proportional rent subsidy with =0.5. How much housing does the Smith family purchase given the subsidy?

d) What is the gross market rent per month paid by the Smith family? What is the net rent (after deducting the subsidy) paid by the Smith family? How much does the Smith family spend on other consumption in its new equilibrium?

e) What is total dollar outlay of the government for the Smith’s housing subsidy per month?

Explanation / Answer

q = 0.5 x (y / p)

(a) y = 2000, p = 2

q = 0.5 x 2000 / 2 = 500

(b) Monthly rent = p x q = $2 x 500 = $1000

Spending on other consumption = y - Monthly rent = $(2000 - 1000) = $1000

(c) With the rent subsidy, price decreases by 0.5, and new price = p - 0.5 = 2 - 0.5 = 1.5

New q = 0.5 x 2000 / 1.5 = 667

(d) Gross rent = 667 x $2 = $1,334

Net rent = 667 x $1.5 = $1,000

Spending on other consumption = $(1,334 - 1,000) = $334

(e) Total outlay = Unit subsidy x q = $0.5 x 667 = $333.5

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.