Urban Economics SP24
Problem Set #2
Due, Thursday, Feb 22, 11pm, ONLY ONLINE!
1) No late problem sets
2) You can only upload one single file. No multiple file submissions.
3) For this Problem Set, we only accept EXCEL formats (use a different worksheet
for each question).
4) Show your work for all questions!
Question (1): Location Choice of Transfer-Oriented Firms
Suppose a transport cost-oriented firm consumes four inputs (I1 to I4) in order to produce
one output, which is consumed at the output market M. Points H1 and H2 are
transportation hubs.
a) Assume M’s monetary weight equals $4. The monetary weight for I1 and I2 is $2 each;
the monetary weight for I3 and I4 and is $3 each. Where, if any, is the Nash Equilibrium?
(5 pts)
b) Now assume the stretch between H2 and I4 (both points included) were a Nash
Equilibrium Assume the same monetary values as under (a) – only the monetary value of
I4 can change. What is the value of I4 to attain the required equilibrium? (5 pts)
Answers
(a) The Nash equilibrium is at H1 (5 pts)
Note, the answer “between H1 and H2” is wrong, which is easy to see.
If one moves from H1 to the right one will move away from $8 (M+I1+I2) and closer
to only $6 (I3+I4). That is, leaving H1 to the right will cause cost to grow by $2.
Don’t move!

M
I3
H2
I4
I1
I2
H1
Moving from H2 to the left towards H1 will result in a net gain of $2 (one leaves $6
and moves closer to $8). Move!
(b) I4 = $11 (5 pts). It must the equal to the sum of all others.
Question (2): GINI Coefficients of Job Concentration
Go to Harvard’s Cluster Mapping Project’s main site (http://clustermapping.us) and click
on “Clusters.”
Scroll down until you see Full Portfolio View of Related Clusters.
Select EDUCATION and scroll to the map on top. (You must go to the map – don’t
download any data if you don’t see the map)
On the left sidebar you now have various choices; select Economic Areas. Calculate for
1998 and for 2016 the CR4, HHI and Gini Coefficients for employment and for the
annual payroll (which is the product of Employment x Annual Wage). For the Gini
Coefficient, assume that all regions are of identical size. Make sure you match each
area’s employment with its wage. Overall, you have to calculate 12 coefficients (see table
below).
NOTE: in case the wage is listed as zero, treat it as zero; don’t delete it.
Year CR4 HHI GINI
Employment
1998 (179 Econ Regions) 0.3033 0.0368 0.7328
2016 (179 Econ Regions) 0.3157 0.0384 0.7543
Annual Payroll
1998 (179 Econ Regions) 0.3495 0.0454 0.7899
2016 (179 Econ Regions) 0.3915 0.0508 0.8133
Question (3): Income GINI Coefficients
There are ten equally-sized counties in a state. The respective county incomes are
provided in the Table below.
County A B F H C D E G K I
income 125 225 180 15 20 100 20 35 20 140
Calculate the state’s Gini coefficient of income concentration (report 4 decimals)
Answer: GINI = 0.4534 (for details see Excel sheet on Birghtspace)
Question (4): GINI Coefficients for Counties
Go to the Bureau of Census at https://data.census.gov/ Into the search window, enter
“Bronx county income” – then select “S1901 | Income in the Past 12 Months.”
You will see American Community Survey’s ACS 1-Year Estimates for 2022 (see arrow
in the screenshot above).
You can easily change the year from 2022 to 2021 etc. – back to 2010.
Calculate 13 Gini coefficients for household incomes based on ACS 1-Year Estimates
(make sure you don’t use 5-Year Estimates).
In Excel, list up the coefficients and create a little graph like shown in the screenshot
below (note, the numbers in the screenshot are made up).
Answers: (for details see separate Excel file)
YEAR GINI
2010 0.4915
2011 0.5043
2012 0.5193
2013 0.5105
2014 0.5137
2015 0.5211
2016 0.5005
2017 0.5167
2018 0.5306
2019 0.5158
2020 0.5121
2021 0.5128
2022 0.5217

0.4915
0.5043
0.5193
0.5105
0.5137
0.5211
0.5005
0.5167
0.5306
0.5158
0.5121
0.5128
0.5217
0.47
0.48
0.49
0.50
0.51
0.52
0.53
0.54
2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022
GINI in The Bronx, 2010-2022
based on Household Incomes, ACS 1-Year