Everyday Application: Cities and Land Values: Some of the models that we introduced in this chapter are employed in modeling the pattern of land and housing values in an urban area.
A: One way to think about city centers is as places that people need to come to in order to work and shop.
(a) Consider the Hotel ling line [0, 1] that we used as a product characteristics space. Suppose instead that this line represents physical distance, with a city located at 0 and another city located at 1. Think of households as locating along this line—with a household that locates at n ∈ [0, 1] having to commute to one of the two cities unless n = 0 or n = 1. What does this imply for the distribution of consumer “ideal points”?
(b) If land along the Hotel ling line were equally priced, where would everyone wish to locate? If the city at 0 is larger than the city at 1 — and if bigger cities offer greater job and shopping opportunities, how would this affect your answer?
(c) What do your answers imply for the distribution of land values along the Hotel ling line if land at each location is scarce and only one household can locate at each point on the line?
(d) Suppose instead that more than one household can potentially locate at each point on the line — but if multiple households locate at a point, each consumes less land. (For instance, 100 families might share a high rise apartment building.) Suppose this result in unoccupied farmland toward the middle of the Hotel ling line. How would you expect population density to vary along the line?
(e) In recent decades, a new phenomenon called “edge cities” has emerged—with smaller cities forming in the vicinity of larger cities— and land values adjusting accordingly. How would the distribution of land values change as edge cities appear on the Hotel ling line?
(f) What do you think will happen to the distribution of land values along the Hotel ling line if commuting costs fall? What would happen to population density along the line?
(g) Could you similarly see how land values are distributed in our “circle” model if cities are located at different points on the circle?`
B: Now consider the model of tastes for diversified product markets in Section 26B.4.
(a) Can you use the intuitions from this model to explain why larger cities on the Hotel ling line (or the circle) in part A of the exercise will have higher land values?
(b) Consider two cities in the same general area (but sufficiently far apart that consumers would rarely commute from one to the other). Suppose the model used to derive Table 26.2 in the text was the appropriate model for representing consumer tastes in this state, and suppose that city A had 100 restaurants and city B had 1,000. If the typical household in this economy has an annual income of $60,000 and a typical apartment in city a rents for $6,000 per year, what would you estimate this same apartment would rent for in city B?