A city is being built where factor substitution is not allowed, and there are three types of businesses that are interested in bidding for land: service firms (S), manufacturers (M) and farmers (F). There is a circumferential highway that is located just 2 miles outside the city center. Monthly expected revenues are $1000 for S, $350 for M and $100 for F. Non-land related costs are $350, $50 and $70 for S, M and F, respectively. Monthly mortgage payment for the building costs are $200 for S, $50 for M and $0 for F. Transportation costs for the service sector are T(x) =18 x ^2 where x is the distance from the city center. For manufacturer firms it is $25 /mile to the highway, and for farmers it is $1 / mile to the highway.
a) Derive the willingness to pay function for each sector, and draw the corresponding bid-rent curves on the same graph, carefully locating all the intersection points, locating the city center at the origin and marking the location of the highway very carefully on your horizontal axis.
b) Draw (highlight) the equilibrium city-wide bid rent curve on your graph.
c) Indicate, on a 2 dimensional circular are map of the city, the equilibrium location of each sector in the city.