1. [40 points] Consider a developer having to choose a location for building a new hotel. There are two options, either build the hotel in the city where other hotels may also exist, or go to the rural area away from competition (isolated rural area no other hotels expected to join to the rural area). Expected annual revenues are $165K and $100K, in the city and rural area, respectively. (Independent of how many other hotefs there are) The annualized cost of building the hotel is $20K in the city and $10K in the rural area. Assume there are only two other costs the developer is facing: (i) advertising costs and (ii) labor costs (wages). Annual cost of advertising per hotel is measured as: C(n) = $60K/ 71, And the annual cost of labor per hotel is [(n) = $20K * n, where n is the total number of hotels in the area (city or rural). [K stands for thousands of dollars] A hotel's expected annual prots are equal to its total annual revenues minus the sum of its annual advertising, building and labor costs. a. How could an economist explain f defend (if at all possible) the assumption that a hotel's revenues are independent of how many other hotels there are in the area? Give example circumstances to expiot'n. b. Why do you think is the \"annual cost of advertising" a decreasing function of \"11"? Please discuss by relating to m key concepts (of your choice) of urban economics. What is the expected prot in the isolated rural area? If there are currently 2 other hotels in the city, what is the expected prot for the developer if she chooses to build in the city? What location should the developer choose for the new hotel? e. How many other hotels should currently exist in the city in order to make the \"isolated rural area\" the right choice for the developer? f. In the long-run, would you expect to see a cluster of hotels in the city? If yes, how many hotels would exist in the cluster? 53