I have also included some screenshots of a similar problem for reference.

1. [26 pts total] Assume the City of Musicians has a center with one circumferential highway (beltway) b located 3 miles away from the center, and a light rail system with only two stations, a station located in the center of downtown (S1), and another one located at 5 miles from downtown (52). i) ii) [7 pts] A music production firm is trying to pick a location to build a new office building, and has two options: i) A 3-floor office building, on 0.8 acre land, at monthly capital cost of $400, or ii) A 12- floor office building on a 0.2 acre land, at monthly capital cost of $1200. (Note that both building options yield the same amount of office space, hence identical revenues). Expected revenues are $2400/month, while non-land costs are $400/month, and monthly transportation costs are determined by T(x)=100x2, where \"x\" is the distance from the center of downtown (in miles). Derive the optimal willingness to pay function per acre and plot the bid rent curve per acre for the music production firm, carefully locating the centerlc) at origin, and the beltway (b) and light rail stations (S1 and 52) on your horizontal axis accordingly, and calculate and mark all the intersection points on your axes. Please label your axes. [7 pts] A developer is trying to find a land of 1 acre to build a 2-story concert hall. Expected revenues for the concert hall are higher the more accessible the concert hall is. Specifically, maximum expected revenues are $3400/month if the concert hall is located right next to a light rail station or right next to the highway. However, expected revenues decrease at a rate of $1500/month per mile from the closest highway or the train station. Non-land monthly costs are $160 and the monthly cost of capital for the building is $240. Derive the optimal willingness to pay function per acre and plot the bid rent curve per acre for the music hall developer, carefully locating the center(c) at origin, and the beltway (b) and light rail stations (51 and 52) on your horizontal axis accordingly, and calculate and mark all the intersection points on your axes. Please label your axes. iii) [7 pts] A residential developer is planning on bidding on 1-acre of land for building and renting apartments for residents. There is no factor substitution for the developer, and has to build a 4 story condo building, yielding total 12,000 square feet of housing space. However, the developer can perfectly divide up the total 12,000 square feet of space into either 800 or 1200 square feet apartments (residents demand such units). For the developer, monthly cost of capital per apartment is $550 for 800 square feet apartments and $900 for 1200 square feet apartments. Further, according to research, renters' willingness to pay for an \"x\"square feet apartment at \"m\" miles from the city center can be estimated by w (x,m)=x 50m. (For example, the market rent for a 1000 square feet apartment located 3 miles from downtown w(1000,3)=1000-3.50=$850.) Derive iii) [7 pts] A residential developer is planning on bidding on 1-acre of land for building and renting apartments for residents. There is no factor substitution for the developer, and has to build a 4 story condo building, yielding total 12,000 square feet of housing space. However, the developer can perfectly divide up the total 12,000 square feet of space into either 800 or 1200 square feet apartments (residents demand such units). For the developer, monthly cost of capital per apartment is $550 for 800 square feet apartments and $900 for 1200 square feet apartments. Further, according to research, renters' willingness to pay for an "x\"square feet apartment at \"m\" miles from the city center can be estimated by w (x,m)=x 50m. (For example, the market rent for a 1000 square feet apartment located 3 miles from downtown w(1000,3)=1000-3.50=$850.) Derive the optimal willingness to pay function per acre and plot the bid rent curve per acre for the residential developer, carefully locating the center(c) at origin, and the beltway (b) and light rail 1|Page stations (51 and $2) on your horizontal axis accordingly, and calculate and mark all the intersection points on your axes. Please label your axes. iv) [5 pts] Draw/mark/highlight the equilibrium (combined) bid rent curve for the entire town, taking into account the demand by the music production firm and the concert hall developer and the residential developer, carefully locating the center(c) at origin, and the beltway (b) and light rail stations (51 and 52) on your horizontal axis accordingly, and calculate and mark all the intersection points on your axes. Please label your axes. What parts of the city will be occupied by what type of buildings? 9. [34 pts total] Assume the City of Gorillaz has a center with two circumferential highways (beltways), an inner beltway, b1, (5 miles away from the center) and an outer beltway, b2, {10 miles from the center, therefore 5 miles away from b1). i) [13 pts] A counselling rm is trying to pick a location to build a 4 oor ofce building for their operations. Assu me no factor substitution is available, and they have to pick a land of size 1 acre. Expected revenues are 52500! month, while non-land costs are,$200/month, and monthly capital cost of the 4 story ofce building is $300/month. Monthly transportation costs are determined by T(x)=80x2, where "x\" is the distance from the center(in miles). Derive the willingness to pay function per acre and plot the bid rent curve per acre for the counselling rm, carefully locating the center(c) at origin, inner beltway (b1) and outer beitway (b2) on your horizontal axis accordingly, and calculate and mark all the Intersection points on your vertical axis. Please label your axes. wt? LK) : LS'oo soo Zoo #90 x1- ii) [13 pts] A beer brewing company is trying to find a land of 1 acre to build a one story brewery station. Expected revenues are $2000/month if located inside the inner beltway, and $1000/month if located outside the inner beltway (brand exposure), whereas transportation costs are independent of revenue levels, and always $100/month per mile from the closest highway. Non-land monthly costs are $400 and the monthly cost of brewery building costs are $120/month. Derive the willingness to pay function per acre and plot the bid rent curve per acre for the brewery, carefully locating the center(c) at origin, inner beltway (b1) and outer beltway (b2) on your horizontal axis accordingly, and calculate and mark all the intersection points on your vertical axis. Please label your axes. Let x be the closeon highway WTP-0 = WTP( Outside s, ) = 1000 - 400- 120- 100x = 480-100x WTP- IF WTP ( inside b, ) = 2005 - 400- 120- 102x = 1480-102x WIP WTO- Ito 1480 WTP_ I (5) = 980 WTP - 0 (0 ) = 480 WTP - D ( 2.5 ) = 230 Czo 1 2 3 4 5 1= 376 7 1 8 9 ( 52 = 15 ] Distance ( * = 5 ) from the ( x= 0) x = 25 ( x = Q) center Midway between the beltways . 4 | Pageiii) [8 pts] Draw/mark/highlight the equilibrium (combined) bid rent curve for the entire town (assuming no residential land demand), only taking into account the demand by the counselling firm and the brewery. What is the size of the CBD? (If you can't calculate the exact number, please give an interval of two consecutive integers, such as: "CBD extends [x,x+1] miles"). 2020 Equilibrium Bit cent Curve 1480. 980 480 - - 230 w Co bias 7.5 Size Of CBA 15 3 miler (radios )