Urban Economics Quiz #2 SP24
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Urban Economics
Quiz #2
Open, Tue, Mar 12, 7pm
Due, Wed, Mar 13, 11pm
(note, I added a grace period of 4 more hours to this quiz, i.e., you have 28 hours)
1) No late quiz
2) You can only upload one single file. No multiple file submissions. (PDF, Word or Excel are okay)
3) You can resubmit a submission until the deadline.
4) Show your work!
(1) Econometrics
Refer to the Stata Data file (posted on Brightspace under Content).
In Excel or in Stata, run a multivariate linear regression with MURDERS (murders per 100,000 population) as dependent variable (y) and the following four independent x-variables:
TEMP_JAN (avg temperatures in January in Fahrenheit),
DENSITY (density in people per square mile),
INCOME (per capita income), and
CHRISTIANS (share of Christians)
a) Show your equation. (5 pts)
b) Assume the coefficients would apply to a fictitious city with a population of 1 million. What would the impact of a one-unit increase of each of the independent variables on
MURDERS in our city be ? (referring to 2 decimals is okay).
Carefully interpret the coefficients for TEMP_JAN, DENSITY, INCOME, and CHRISTIANS. Are all coefficients significant at the 5%-level (p<0.05)? What are the marginal effects? What is the effect for a city with a population of one million?
(10 pts, 2.5 pts. each)
(2) Optimal Cluster Size
In a cluster region, income is given by I=2,000+40N-2N2 and cost is given by C=22+2N+1.5N2, where N stands for cluster size (population in million). What is the utility maximizing cluster size (report 4 decimals)? (5 pts)
(3) Cities and Utility I
Assume the utility functions for two cities are identical and are given by
U=21 + 2.1N - 0.24*N2, where N denotes the city’s population in million.
(a) What is each city’s utility maximizing population? (report 4 decimals) ( 5pts)
(b) If each city had a population of 9 million people, how would these cities change their size? Assuming that the total population of 18 million cannot be changed, would there be a smaller and a larger city? Would there be three or more cities? Or would there be no change at all. Explain. (5 pts)
(4) Cities and Utility II
Assume two urban clusters, X and Y, exhibit the same utility function
Ux = Uy = 10 + 2.5N – 0.12N2
where N denotes population in million.
a) If both clusters have a population of Nx=Ny=20, what is their utility? ( 5 pts)
b) Now assume, cluster X is able to shift its utility curve up and now enjoys
Ux = 10 + 2.5N – 0.10N2
while Y remains on its old utility curve. Assuming no population change, what is X’s new utility (in the short run)? (5 pts)
c) As a response of the shift in Ux, people from Y will now move to X.
If one million people move – what is the resulting Ux and Uy? Are X and Y in equilibrium after the one million population change ? (5 pts)
d) How many people must move from Y to X in order to reach a spatial equilibrium?
Be precise – down to two decimals. You can solve this either mathematically by solving a
quadratic equation or with Excel tables, trying step by step. What is the resulting Ux and Uy (10 pts)
(5) Multiplier
Assume a company in a city exports goods worth $12,000 (Δx). After infinite rounds, the city’s income will grow to $26,500 (Δy). What is the city’s average marginal propensity to consume locally (m)? Report 4 decimals (5 pts)
2024-03-14