ECON 414: Urban Economics
Homework 3: Suggested Answers
Marcelino Guerra
Land-use regulation [50 Points]
The political economy of UGB [20 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 40 miles (dashed vertical line in Figure 1.1).
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, quantity of floor space, building-heights, and population density in between the movement from the old (“Developers old”) to the new bid-rent curve (“Developers new”) ).
ii) Suppose the developers’ bid-rent curve was \(r(x)=80-x\) before the UGB, but now it is \(r(x)=100-x\) - the old curve is the same as in HW #1, 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). Does the UGB benefit the landlords?
Urban growth boundary
i)
The urban growth boundary restricts the land supply, and the city edge decreases from 60 - where the old \(r(x)\) equals 20 - to 40. People living in the area from 40 to 60 will push the demand for housing inside the new boundary, which bids up housing prices everywhere in the city. The increase in prices will increase the competition for land, driving the bid-rent curve upwards. Building heights and population density increase everywhere, and people will consume less floor space.
ii)
Rent loss:
\(\cfrac{(\underbrace{60}_\text{old $\bar{x}$}-\underbrace{40}_\text{new $\bar{x}$})*(\underbrace{40}_\text{ $x=40$ in old $r(x)$}-\underbrace{20}_\text{$r_{a}$})}{2}=200\)
Rent gain:
\(20*40=800\)
Another approach for the rent gain is to calculate the area between the rent curves:
\(\int_{0}^{40} [(\underbrace{100-x}_\text{upper function})-(\underbrace{80-x}_\text{lower function})]dx=\int_{0}^{40}20 dx=20*40=800\)
One can set up the function and use integrate() with the lower and upper bounds. Check the code below (you might need part of it in HW #4).
D<-function(x){(100-x)-(80-x)}
rent_gain<-integrate(D, lower=0,upper=40)
rent_gain## 800 with absolute error < 8.9e-12Open space as an amenity [20 points]
Assume that people living in the city enjoy farmland benefits, but the landowner does not consider those \(b\) dollars generated by the open-space amenity. Therefore, this market failure makes the city’s size suboptimal - the urban land area is too big. Suppose that the optimal city edge’s size is indeed \(\bar{x}=40\), and the developers’ bid rent curve behaves just like in 1.1. What should be the \(b\) dollars tax on developed land rent charged to the landowner for the city to achieve its optimal size (i.e., to make \(\bar{x}=40\))?
Answer
To treat open-space as an amenity, internalize the social benefit \(b\) into the agricultural rent. Then, the new agricultural rent would be \(r_{a}+b \rightarrow 20+b\). That would shrink the city’s spatial size, driving the bid-rent curve upward. Assuming the bid-rent curve has the same behavior as in 1.1), the new equilibrium would be \(r_{a}+b=100-x\). To reach the optimal size \(\bar{x}=40\), the tax on developed land would be \(r_{a}=100-\bar{x}-b \rightarrow 20=100-40-b \rightarrow b=40\).
Zoning: non-conforming uses [10 points]
One of the rationales behind zoning laws is to curb externalities. 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 1.2. 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?
Zoning and Externalities
Answer
Without zoning, four residential lots are affected by noise/pollution from the factories. With zoning, only two lots suffer from negative externality. Hence, the externality damage is reduced by 50%. The total rent without zoning is \(8r\): \(6r\) (the two factories also pay rent \(r\)) plus \(\frac{1}{2}*4r\) from the adjacent lots. The total rent with zoning is \(9r\), and that represents a \(12.5\%\) growth.
Manufacturing sector & The great divergence [50 Points]
The decline of manufacturing jobs [20 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 NONFARM sector from 1939 to 2020 (column PAYEMS), and all employees in the manufacturing sector (MANEMP) in thousands of persons.
First, compute the ratio of MANEMP/PAYEMS and store that as a column named share. After that, construct two line plots with i) the share manufacturing jobs/Total jobs in the NONFARM sector and ii) the total number of manufacturing jobs from 1939 to 2020. What do you see, and what can explain this trend?
Answer
The number of manufacturing jobs by the end of 2018 was 34% less than at its peak in 1979, and now only one in ten American workers is employed in the manufacturing sector. Globalization can explain part of this trend. Since it is easy to outsource the production of certain goods (the decrease in transportation costs plays a role here), and labor is cheap in developing nations, companies shift the manufacturing process to other countries to reduce costs.
On the other hand, manufacturing as a share of real GDP has been almost constant over time: the United States still produces many physical goods. This apparent paradox is related to technological improvements and investment in new machinery. Since factories are now more efficient, fewer workers are needed to produce the same output level. The increase in productivity raises salaries, lower prices but kill manufacturing jobs. Since each manufacturing job is attached to other 1.6 jobs in different sectors, the decline in the number of positions in this sector affects the whole economy. The good news is that the U.S. economy has gradually shifted away from traditional manufacturing toward creating knowledge: America’s comparative advantage lies in producing new ideas. Productivity is growing faster in the high-tech sector, and each new high-tech job in a metro area is linked to five additional jobs in other sectors.
library(tidyverse)
library(readxl)
library(ggthemes)
library(patchwork)
manufac<-read_xls("manufacturing.xls")
manufac$DATE<-as.Date(manufac$DATE)
manufac$share<-manufac$MANEMP/manufac$PAYEMS*100
p1<-ggplot(data=manufac, aes(x=DATE,y=MANEMP))+
geom_line(size=1.4, color="skyblue4")+
labs(x = "Month/Year", y="Total Jobs in the Manufacturing sector (in thousands)")+
theme_economist(base_size = 14)+
scale_colour_economist()+
theme(axis.text=element_text(size=12),
axis.title=element_text(size=12,
face="bold"))+
scale_x_date(date_breaks = "156 months",
date_labels = "%m/%Y")+
geom_segment(aes(x=as.Date("2001-01-01"),
xend=as.Date("2001-01-01"),
y=9000,
yend=19553))+
geom_segment(aes(x=as.Date("2009-12-01"),
xend=as.Date("2009-12-01"),
y=9000,
yend=19553))+
annotate("rect",
xmin = as.Date("2001-01-01"),
xmax = as.Date("2009-12-01"),
ymin = 9000,
ymax = 19553,
alpha = .2)
p2<-ggplot(data=manufac,
aes(x=DATE,y=share))+
geom_line(size=1.4, color="skyblue4")+
labs(x = "Month/Year", y="Share of Manufacturing Jobs (in %)")+
theme_economist(base_size = 14) +
scale_colour_economist()+
theme(axis.text=element_text(size=12),
axis.title=element_text(size=12,
face="bold"))+
scale_x_date(date_breaks = "192 months",
date_labels = "%m/%Y")
p1+p2
The uneven effects of globalization [20 points]
You just got the big picture - manufacturing jobs are declining in the US. However, recent studies have shown that trade liberalization has an uneven effect on wages and employment across US labor markets. For labor-intensive industries/low-skilled manufacturing (e.g., toys, cheap clothes, affordable electronics, etc.), it is tough to compete in prices with foreign companies in developing nations, where wages and therefore production costs are low. To illustrate the issue, the map below shows the most vulnerable US areas to Chinese products. The data is relative to the 1990-2007 period. Also, you might want to take a look at the China Trade Shock website.
In that context, answer the following questions:
i) Is this vulnerability to Chinese imports randomly distributed over the US? Explain
ii) With the increase in imports of cheap products from developing countries, what is expected to happen with low-skilled jobs in those US areas that are based on labor-intensive industries?
iii) What is expected to happen with the entire labor market, knowing the indirect effects of manufacturing jobs on other sectors of the economy?
iv) What are those uneven effects of globalization on labor markets? Think about Apple outsourcing part of the production to foreign countries. What are the gains of that for the firm, for its workers, and consumers?
i)
No! The most exposed US areas are located in the Midwest, where labor-intensive industries are concentrated.
ii)
With tough foreign competition, labor-intensive firms and, therefore, jobs will disappear.
iii)
There will be negative spillovers from the manufacturing jobs lost: for each manufacturing job, 1.6 jobs in other sectors will also vanish. In particular, company towns will have a hard time reinventing themselves.
iv)
We just saw one effect of globalization: less-skilled workers tend to lose their jobs. On the other hand, high-tech workers are favored by the same process. For instance, Apple cuts costs by outsourcing part of the production to other countries, using part of that money to hire highly skilled workers, investing in R&D, and producing more patents. We also know that gains in productivity are translated to lower prices that favor consumers.
The great divergence [10 points]
Read the interview of Enrico Moretti. What is the great divergence? Explain to me like I’m 5.
xkcd 1364: Like I’m Five