Consider a city where the demand for housing for the typical household is Q = 1,200...

Consider a city where the demand for housing for the typical household is Q = 1,200 – 1,000P, where Q is the square footage demanded and P is the price per square foot. (a) Draw the demand curve for housing. [Hint: you might have to manipulate the equation as it is given to you!] (b) Assume that the price of housing is $0.70 per square foot. At this price, the typical household chooses __________ square feet, and enjoys a consumer surplus of $_________. (c) Now consider a household that receives an increase in income. As a result of that increase, its new demand for housing is Q = 1,300 – 1,000P. Draw a graph below indicating the old and new demand curves, and labeling (1) the original house choice on the original demand curve (labeled i), (2) the preferred house choice on the new demand curve (labeled m), and (3) the current house choice on the new demand curve if the household cannot move (labeled s). (d) If it can move without cost, and assuming that the cost of housing remains at $0.70, this household will now demand ___________ square feet of housing, and enjoy a consumer surplus of $_________. If it cannot move, the household will consume __________ square feet of housing and now enjoy a consumer surplus of $__________.

Expert Solution

a.

b. Given P= $0.70
Q = 1200 - 0.7*1000 = 1200 - 700 = 500 square feet
Consumer surplus is given by the area of the triangle with height $ 0.5 per square feet (the difference between the maximum price and the given price) and base 500 square feet. Thus CS= 125

c. The new curve moves rightward to the original demand curve with y-axis at 1.3 and x-axis at 1300.
c1. i is the original house choice on the original demand curve (plugging P= $0.70 in the original demand curve eq)
c2. m is the preferred house choice on the new demand curve (plugging P= $0.70 in the new demand curve eq)
c3. the current house choice (500 sq ft) on the new demand curve is at price P= $0.80 labelled by point s. We find this by plugging Q=500 in the new demand curve eq

d. 600 square feet (point m in the graph) and consumer surplus = 1/2*600*(1.3-0.7) = 1/2*600*0.6 = 180
If it cannot move, the household will consume 500 square feet of housing (point s on the graph) and now enjoy CS = 1/2*500* (1.3-0.8) = 125

Rahul Sunny answered 2 years ago

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