Urban Land Economics

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Consider a Monocentric city. Export firms have two options for transporting output to city centre: a truck or a transporter. The transporter instantly moves any amount of output from the factory to the city center. It costs $12 to rent the transporter for one time period, and running the machine is costless. In contrast, the truck can transport output over any distance at a cost of $2 per unit of output per kilometer. Assume that all firms are identical, every firm produces 10 units of output that is worth $50 per unit at the city centre, and occupies 1 unit of land, that total non-land cost for a firm is $240, that all markets are competitive, and that the opportunity cost of land is 0. (Hint: this city may not have a boundary.)
a. Derive equilibrium rent function.
b. Derive equilibrium land use function.

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