Exercise 4.1 Suppose that landowners have the power to restrict , the distance to the edge of the city, in order to increase the land rent they earn. Suppose that, with no restriction, the urban land rent function is given by r = 100 – x, where x is distance in blocks to the CBD. Suppose that agricultural land rent rA is equal to 20.
(a) Compute in the absence of any restriction by landowners, and illustrate your result in a diagram. Now suppose that landowners can restrict to a value of 65 blocks. When they impose this restriction, the urban land-rent curve shifts up, with the new rent function given by r = 105 – x.
(b) Show the new land-rent curve in your diagram, and indicate the area corresponding to the land-rent loss resulting from the restriction, as well as the additional area showing the land-rent gain.
(c) Compute the sizes of these areas, and compute the net gain or loss in land rent from imposing the restriction. Is the restriction beneficial to the landlords? Will it be imposed? (Hint: The area corresponding to the land rent gain is a parallelogram, but instead of using the area formula for that type of shape, the area can be computed more easily by multiplying the horizontal length of the parallelogram (65 blocks) by its height.) Now suppose that the landowners can impose a further restriction, with set equal to 50 blocks. When this restriction is imposed, the urban land-rent curve shifts up more, with the new rent function given by r = 110 – x.
(d) Repeat (b) and (c). Relative to the original x restriction of 65, is this further restriction beneficial to the landlords? Will it be imposed?
(e) If your answer is different from before, explain intuitively why a difference emerges.
Brueckner, Jan K.. Lectures on Urban Economics (The MIT Press) (p. 255). The MIT Press. Kindle Edition.