Consider a city that conforms to the assumptions of the basic monocentric city urban model studied in class, with one key difference. The difference is that the urban residents experience crime, which varies in intensity across the city. The level of crime, as measured by the probability of being robbed on the street, is highest at the CBD. The probability of being robbed falls gradually as distance from the CBD increases, and it reaches zero 5 miles out from the CBD. From this location out to the city boundary (which lies 10 miles from the CBD), the neighborhoods are crime free. As usual, moving farther from the CBD raises commuting cost, regardless of whether a resident lives inside or outside of the crime area. Draw a graph to representing the probability of crime as a function of distance from the city center.

(a) Draw a graph to represent the probability of crime as a function of distance from the CBD.

(b) Under the above assumptions, analyze the spatial behavior of the price per square foot of housing in the city. For your analysis, provide explanations along with graphs showing the price per square foot of housing (p) as a function of distance to the CBD (x). Consider the following three different possible cases (draw one separate graph for each possible case):

(i) Urban residents have a very strong aversion to crime (so that the effect of aversion to crime dominates the effect of aversion to commute-distance)

(ii) Urban residents have only a moderate aversion to crime (so that the effect of aversion to commute-distance dominates the effect of aversion to crime)

(iii) Urban residents don't care at all about crime (hence, there is no effect of crime on decision making)

(c) Using your answer from (b) along with reasoning from class, analyze the spatial pattern of land rents and building heights in the city. Carry out this analysis only for case (i), where residents have a strong aversion to crime. Along with the explanation, draw two separate graphs, one showing the pattern of land rents (r) and the other showing the pattern of building heights (b), both as a function of distance to the CBD (x), again only for case (i).