Marcelino Guerra (mguerra3)
9/22/2020
manufac<-read_xls(“manufacturing.xls”) manufac<-manufac%>%filter(DATE<=“2018-12-01”)
ggplot(data=manufac, aes(x=Year,y=Share of population living in urban areas (%)))+ geom_line(size=1.4, color=“skyblue4”)+ labs(x = “Year”, y=“Share of population living in urban areas (%) in Brazil”)+ theme_economist(base_size = 14) +scale_colour_economist()+ scale_x_continuous(breaks = seq(from = 1950, to =2016 , by =10))+ theme(axis.text=element_text(size=12), axis.title=element_text(size=12,face=“bold”)) — output: pdf_document: default html_document: default —
Question 1 - Monocentric city model [45 Points]
a) The city’s edge [5 points]
Suppose that the urban land rent function is given by \(r(x)=100-x\), where \(x\) is the distance in miles to the city’s Central Business District. The agricultural sector is willing to pay \(r_{a}=20\) for productive land. Compute the radius \(\bar{x}\) and the urban land area (the area of a circle with radius \(\bar{x}\)).
Answer: xbar can be equated by setting r(x) and ra equal. therefore, xbar is 80.
The city’s edge
b) A change in total population [10 points]
i) Now suppose there is a population increase in our hypothetical monocentric city. What happens with prices and quantity of floor rented by consumers? Document the whole process that culminates with the shift of the developer’s bid rent curve upwards. What happens with the ratio of capital/land used by builders? What is the consequence of that in terms of building-height and population density?
The price of floor rented by consumers increases, and the quantity of floor rented by consumers also increases. This is because an increase in population before developers can respond by creating more housing will make all developments inside the city more value to the consumers. Later, developers have the chance to respond to the increase in population by building taller structures. Obviously, if there is an increase in population, total housing within the city needs to increase. The taller buildings the developers create to make better use of the land will require more capital to create, because building taller requires more building reinforcement and elevators and such. The ratio of capital/land used (i/r) will go up because of the increase in capital required. Along with the increase in building height, there will be a corresponding increase in population density because of the model assumption that each unit only contains 1 person. Increase in building height directly corresponds to increased population density, because there are more housing units per land unit.
ii) Assume that developers’ new land rent curve is \(r(x)=110-x\) (red line). What is the new city’s edge?
The new edge of the city can be calculated the same way as it was in 1(a). Setting r(x) equal to ra means that the new city’s edge is 90.
The effect of population increase
c) A change in commuting costs [15 points]
i) Consider the effect of an increase in the commuting-cost parameter \(t\). Suppose that initially, the city was in equilibrium just as in a). However, the local government decided to raise the metro ticket price to cover the city’s network of radial roads’ maintenance costs - remember, we assume that consumers use the same transport mode. What happens when \(t\) increases? Write down the whole process that makes the land rent curve to rotate. What happens in downtown? What changes in the suburb?
By changing the price of commuting for the sole commuting method, and because of the assumption that everyone works in the CBD, it becomes more desirable to be closer to the citycenter. Initially people respond by bidding higher prices on locations closer to the CBD. Because developement takes time, they respond to the demand. In response, the developers will build taller buildings closer to the CBD, because the population would like to become more densely packed by the CBD. What changes in the downtown is that buildings become higher and the population becomes even more densely populated. The size of the city decreases, which changes the distance the subarbs are from the CBD also. All of the population (which remains unchanged) must fit into a smaller city radius, so everywhere until the edge of the city becomes more densely populated.
The effect of an increase in commuting costs
ii) Assume the new land rent function of developers is \(r(x)=120-2x\). What is the new city’s edge? What is the value of \(x\) (distance from the CBD) when the old and new developers’ land rent function intersect (call it \(\hat{x}\))? What is happening with the rent bids from 0 to \(\hat{x}\) and from \(\hat{x}\) to the new \(\bar{x}\), compared to the old rent curve? Finally, what is the meaning of \(\hat{x}\)?
The new city’s edge is 50, because when r(x) for the new function ofi the developers set equal to ra equals 50. The value of xhat is 20, when you set the new and old r(x) equal to each other. While in transition, xhat is important. xhat is the point where the distance from the CBD is the same price before and after the increase in t. From 0 to xhat rent will increase, and from xhat to xbar rent will decrease compared to the old rent curve.
d) Durable housing & Growing and declining cities [15 points]
i)Consider an extreme version of the durable housing we saw in class - the first 60 houses built in a city last forever. The demand curve function is given by \(P=70-\frac{2}{3}H\). The cities start in equilibrium with 60 houses. Compute the equilibrium price in this situation.
Using the function P=70-2/3H, and substituting in 60 for H, the value of P, or price, is calculated to be 30.
Now, suppose a factory closed its doors and all the employers were fired. Without a job, they decided to leave the city. Due to this negative shock the demand \(D_{2}\) decreases to \(P=50-\frac{2}{3}H\). What is the new equilibrium price?
The new equilibrium price is 10.
Declining cities
ii) Assume there is a positive shock and the new demand \(D_{3}\) is characterized by \(P=100-\frac{2}{3}H\). As you can see, cities A and B have different supply curves. For new housing, city’s A supply curve is given by \(H=2P\), and city B has a supply curve equal to \(H=\frac{2}{3}P+40\). Compute the respective equilibrium quantities and prices for both cities (round to the nearest integer). Do you have an explanation of why would the supply curves be (are) different in different cities? Which supply curve would characterize Houston, and which one can be associated with Santa Clara (Silicon Valley)?
The new equilibrium price in city A is 43, and housing quantity is 86. The new equilibrium price for city B is 51, and housing quantity is 74. There are many different explanations for why the supply curves as different. There could be different costs of transportation, different valuations for land at the same distance from the CBD, or many potential government regulations that limit or restrict different cities in different ways. City B would be analogous to Santa Clara because of all of the imposed government regulations (initially caused by the votes of residents). The city attempts to limit the number of residents, and because of how desirable the amenities in the area are, the value of houses there is very high. Conversely, a city like Houston, which could be characterized by supply curve A, has been able to expand a great deal because of the road infrastructure. They have been able to increase in size and houses because of the lack of imposed regulations.
Growing cities
Question 2 - Land-use regulation [30 Points]
a) The political economy of UGB [15 points]
One can argue that the real motive for an urban growth boundary is not related to correct a market failure, but to artificially increase land prices. Now, suppose that the landowners in our hypothetical monocentric city can restrict \(\bar{x}\) to 65 miles (black vertical bar in Figure 6).
i) Describe the process that drives the bid rent curve to shift upwards after implementing a UGB and its consequence (i.e., what is happening with prices, a quantity of floor space, building-heights, and population density in between Figure 1 and Figure 6).
If the city ends at the UGB, so do the amenities (maybe… there is still demand past the line). More people want to be within the city, and because there is a smaller quantity compared to equilibrium, housing is comparatively more scarce. In order to accommodate more people within the limited space, buildings will have to become taller and floorspace per person is likely to decrease. Density will also increase.
Urban growth boundary
ii) Suppose the new land rent curve for developers is \(r(x)=110-x\) - the old curve is the same as in a), with the associated old \(\bar{x}\). Calculate the rent loss due to the urban land restriction as well as the land-rent gain. In other words, compute the area associated with the land-rent loss (hint: the area V in the lecture notes is now a triangle), and the area related to the land-rent gain (hint: the area S is a parallelogram). Is the restriction beneficial to the landlords?
The area of rent loss (the triangle) is 262.5, and the area of rent gain is 300. Therefore, the regulation is beneficial because the gain is bigger than the loss.
b) Open space as an amenity [10 points]
Assume that people enjoy open-space benefits from farmland, but the landowner does not consider that \(b\) dollars benefit. Therefore, market failure makes the city’s size suboptimal. Suppose that the city’s edge’s optimal size is \(\bar{x}=65\), and the developers’ bid rent curve behaves just like in a). What should be the \(b\) dollars tax on the landowner’s rent for the city to achieve its optimal size?
We want the point (65,20) to exist on the r(x) curve, and if the original function is r(x)= 100-x, we should ammend it to r(x)= 100-x+b, and plug in (65,20). Therefore, b is equal to -25.
c) Zoning: non-conforming uses [5 points]
One of the rationales behind zoning laws is to curb externalizes. In this example, we will take a closer look at negative externalities generated by factories. Suppose the city is a rectangle composed of 10 lots (25x20). Factories occupy lots with shading lines, and the others represent the housing area. Without the noise and pollution generated by factories, every lot in this city would pay the same rent \(r\) to the landowner (that also includes the lots with factories). However, due to the presence of those negative externalities, residential lots adjacent to factories pays half of the rent \(r/2\). The spatial distribution of factories with and without zoning laws is displayed in Figure 2.2. How much (in %) is the negative externality reduced with the two factories located at the edge of the city, compared to the scenario without zoning laws? What is the increase in total rent received by the landowner in the presence of zoning, compared to no zoning?
If I am understanding the question correctly, The difference between the no zoning and zoning city is that the factory impacts less people when there is zoning. The externalities of the factory are reduced from effecting 4 rectangles to only effecting 2. In percentages, that is effecting 50% to effecting 25%, a reduction of 25%.
Zoning and Externalities
Question 3 - The great divergence [25 Points]
a) The decline of manufacturing jobs and the role of innovation jobs [10 points]
In this question, we want to take a closer look at the manufacturing sector in the U.S. economy. This data from FRED contains all employees in the from 1939 to 2020 (column PAYEMS), and all employees in the manufacturing sector (MANEMP) in thousands of persons. Compute the ratio of MANEMP/PAYEMS and store that as a column named share. After that, construct two line plots with the share of manufacturing jobs and the total number of manufacturing jobs from 1939 to 2018. What do you see, and what can explain this tendency? Why an increase in innovation jobs would matter in this context?
What I see with the first graph is that the share of manufacturing jobs has gradually decreased over time. With the total manufacturing jobs, it appears to vary, but overall there is no substantial trend– total manufacturing jobs are at about the same quantity. One explanation for this tendency is that population has increased with time, and therefore there are more total jobs. Although there were more total jobs, the quantity of manufacturing jobs remained steady, and that is probably because new manufacturing took place outside of the country. The importance of innovation jobs is really important because of how many jobs it creates, a ratio of 5 jobs created for every 1 innovation job, vs 1.6 jobs created by 1 manufacturing job. This is important in this context because with a growing population, more jobs are necessary.
b) Your Neighbor’s Education Affects your Salary [15 points]
Now, we want to explore the link between local human capital and salaries among U.S. metropolitan regions. Examining the data from the American Community Survey 2018 - 5 years using the package tidycensus, construct a scatter plot to show the relationship between the median earnings in the past 12 months for high school graduates in the 945 metropolitan areas and the share of the population 25 years and over that has a Bachelor degree. What are the main reasons for that relationship to hold?
Hint: load the variables from acs5/year 2018 first. Then, look for median earnings in the past 12 months, and get the name of the one that is labeled as Total!!High school graduate. After that, you need to get the total population and the entire population with a bachelor’s degree. You are searching for educational attainment for the population 25 years and over with labels !!Total, Total!!Bachelor's degree, Total!!Master's degree, Total!!Professional school degree, Total!!Doctorate degree. Also, remember that your geography is metropolitan regions.