1. The effect of city size on housing rents and urban land rents. (20 points) There are two cites of different size. City A has 1.6 million households. This represents a city the size of Washington DC metro area (5 million residents equals about 1.6 million households). City B has 25,000 households. This represents a city the size of Frederick, Maryland (75,000 residents equals about 25,000 households), Assume the following other factors are the same in both cities: Household income -y = $60,000 per year Agricultural rent --- $600 per year Structural rent -e = $5,000 per year Commute costs = k =$500 per year Proportion of city land in residential use = v=0.6 Lot size-q=0.25 acres Do the following calculations for each city: 1a. Find the distance from the central business district (CBD) at the city center to the city boundary. (Remember to use the area conversion of 1 square mile - 640 acres) 1b. Find the housing rent at the CBD. 1c. Report the three components of housing rent at the CBD as a percent share of household income. Explain why some components are the same both city sizes and other components vary by city size, 1d. Find the urban land rent at the CBD. le. Graph the housing rents as a function of distance from the CBD. Put the housing rent functions for each city on the same graph. If. Graph the land rents as a function of distance from the CBD. Put the land rent functions for each city on the same graph. 28,787 2. The effect of commuting costs on housing rents. (10 points) Consider the same two cities as outlined in Question #1 above. But now assume that all households telecommute two days per week and drive to the city center the remaining three days a week. Incorporating the effect of telecommuting, make the following calculations for each city: 2a. What is the new gradient (slope) of the housing rent? I 2b. Find the housing rent at the CBD. 2c. What is the change in housing rents at the CBD with telecommuting, relative to without telecommuting? 2d. Explain why the change in housing rents will be different for the large city (e.g. Washington DC metro area) as compared to a small city (e.g. Frederick). 28,787 22 8 1. The effect of city size on housing rents and urban land rents. (20 points) There are two cites of different size. City A has 1.6 million households. This represents a city the size of Washington DC metro area (5 million residents equals about 1.6 million households). City B has 25,000 households. This represents a city the size of Frederick, Maryland (75,000 residents equals about 25,000 households), Assume the following other factors are the same in both cities: Household income -y = $60,000 per year Agricultural rent --- $600 per year Structural rent -e = $5,000 per year Commute costs = k =$500 per year Proportion of city land in residential use = v=0.6 Lot size-q=0.25 acres Do the following calculations for each city: 1a. Find the distance from the central business district (CBD) at the city center to the city boundary. (Remember to use the area conversion of 1 square mile - 640 acres) 1b. Find the housing rent at the CBD. 1c. Report the three components of housing rent at the CBD as a percent share of household income. Explain why some components are the same both city sizes and other components vary by city size, 1d. Find the urban land rent at the CBD. le. Graph the housing rents as a function of distance from the CBD. Put the housing rent functions for each city on the same graph. If. Graph the land rents as a function of distance from the CBD. Put the land rent functions for each city on the same graph. 28,787 2. The effect of commuting costs on housing rents. (10 points) Consider the same two cities as outlined in Question #1 above. But now assume that all households telecommute two days per week and drive to the city center the remaining three days a week. Incorporating the effect of telecommuting, make the following calculations for each city: 2a. What is the new gradient (slope) of the housing rent? I 2b. Find the housing rent at the CBD. 2c. What is the change in housing rents at the CBD with telecommuting, relative to without telecommuting? 2d. Explain why the change in housing rents will be different for the large city (e.g. Washington DC metro area) as compared to a small city (e.g. Frederick). 28,787 22 8
