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 atx= 5 miles out from the CBD. From this location out to the city boundary (which liesx= 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.

(a) Draw agraph to represent the probability of crime(y-axis) as a function of distancexfrom the CBD (x-axis). Clearly indicatex= 5 andx= 10 on the graph. (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 graphsshowing the price per square foot of housing (p) as a function of distance to the CBD (x). These graphs are not based on precise equations, they merely represent the direction (upward or downward) and slope (relative steepness or flatness) of the curve while paying special attention to changes that may/may not happen atx= 5. Consider the following three different possible cases (draw one separate graph for each possible case).

• i) Urban residents have avery 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 amoderate aversion to crime(so that the effect of aversion to commute distance dominates the effect of aversion to crime). (iii) Urban residentsdon'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). Hint: pay special attention to what happens atx= 5.