City Structure.Consider a city that consists of 3 groups that compete for land: Offices, manufactuers, and commuters. Both office and manufacturers compete in perfectly competitive markets. Office and manufacturers face freight, labor, and land costs.

The labor costs are given by:

L(xoffice) = 20 + 3xoffice

L(xmanufact) = 10 +xmanufact

Freight costs are given by:

F(xoffice) = 2 +xoffice

F(xmanufact) = 10 +xmanufact

wherexofficeandxmanufactare the distances that office and manufacturers locate away from the city center, respectively. Finally, both type of firms use one unit of land, so their land costs are given by the price of land, which you can denote asP(xoffice) andP(xmanufact) for offices and manufacturers, respectively. You can assume offices and manufactuers both use zero intermediate inputs in production (e.gI= 0).

Denote the revenues for each type of firm asT RofficeandT Rmanufact, respectively.Commuters allocate money between housing and commuting such that their bid rent curve is given by:

P(xcommuter) = 10xcommuter

Note:You can writexoandxminstead ofxofficeandxmanufact, if it helps.

(a) (2 points) Write out the profit function for office firms and manufacturers as a function of distance to the city center.

(b)(3 points) Derive the bid-rent curves for both offices and manufacturers. To get full credit, you need to show all relevant work and provide two equations.

(c)(2 points) What must be true for the y-intercept (the "P" intercept) of offices to exceed the P-intercept for manufacturers, and the P-intercept for manufacturers to exceed that of commuters? Note: there is more than one way to express the correct answer. You will get credit for whatever one you write, so long as it is correct.

(d)(8 points) Assume that the restrictions you placed on the model in part C hold. Graph all three bid-rent curves; make sure to label all important components (at minimum: axis', p-intercepts, and denote which line corresponds to which bid rent curve. You will need to label at-least one x intercept as well). Find the range of distance from the center that offices, farms, and commuters will be located. Label these ranges on your graph.