Assume the following The population and lot size are fixed All households occupy the same amount of land K All households must travel to and from downtown once per day The marginal cost of travel is $t per mile; thus the marginal cost of distance to downtown is $2t.

Households are identical The number of households is P The CBD is a dimensionless point in the middle of a circular city All land is used for residential use The area of the city is PK Land rent at the edge of the city is zero.

a. Derive the bid-rent function. This is the pattern of land rents that makes all households indifferent to all locations in the city. In particular, people who live at the edge of the city are just as well off as those who live right downtown.

b. Compare aggregate land rent and travel costs in the city. (Hint: The volume of a cone is (1/3)bh, where b is the area of the base and h is the height of the cone.)

c. What is the effect on land rent of a decline in the marginal transportation cost?

d. If you answered c correctly, you found that land rents generally declined in response to a fall in transportation costs. How can this be? Are not improvements in transportation supposed to bring about increases in land rents and values?