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I'm supposed to learn to derive the monocentric city model from these assumptions: everyone has the same preferences, same income, same work location (Central Business District, single point with infinitely small area) and same transportation per mile costs. They get utility from two goods, c (a composite good of everything but housing) and q (housing as measured by size or quality). The price of housing is a function of its distance from the CBD, x, like this p(x). In the end I'm supposed to see that p'(x) < 0, and population density and structural density both decrease as x increases.

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  • $\begingroup$ I think you need to provide/assume additional information about the utility function, such as convexity. $\endgroup$ – Giskard Dec 16 '15 at 14:10

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