We consider a monocentric city represented by a segment x [0,x_f ] where 0 stands for the CBD where everybody works and earns a uniform (exogenous) urban wage w > 0 and x_f is the city fringe. The rural wage a is normalized to zero. Agents located at a distance x from the CBD pay a rent R(x). The utility of an agent is her disposable income.

Variable commuting cost

Imagine now that the unit cost of commuting by car becomes cheaper further away from the CBD: formally, this means that unit cost verifies c'_c (x)

1. In real life, what would justify this assumption?

2. Graph the rent function with and w = 100.

3. Assume that commuters by metro still incur a fixed unit cost c_m. Let , c_m = 1 and w = 100. What is the size of the largest continuous city that can be achieved with only one metro station?

4. Graph the corresponding rent function. What are the differences with question 1.2.4?

Please answer each question clearly.

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