CBSA Participation in Joint Force Operations Evaluation Study
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Discussion
– Big League Cities or Big League Losers– Are Sports Facilities a Good Public
Investment? – What is the market failure?– Should tax payers pay for it?
Discussion (Cont) Table 1 Siegfried and Zimbalist (JEP, 2000)
Market Area and the Central Place
Theorem
Chapter 5
Goal of Today’s Class
• Explore the interactions between different cities in a regional economy
• Understand the urban hierarchy (why cities differ in size and scope)
• Introduce the Central Place Theorem
Cities in the United States (Source U.S. Census)
City 1990 Urbanized Area 1990
City Rank Population
Rank Population
New York, NY 1 7,323 1 16,044
Los Angeles, CA 2 3,485 2 11,403
Chicago, IL 3 2,784 3 6,792
Houston, TX 4 1,631 9 2,902
Philadelphia, PA 5 1,586 4 4,222
San Diego, CA 6 1,111 11 2,348
Detroit, MI 7 1,028 5 3,698
Dallas, TX 8 1,007 8 3,198
Phoenix, AZ 9 983 14 2,006
San Antonio, TX 10 936 31 1,129
Cities in the World (Source U.N. Population)
Basic Definitions
• Market Area: Area over which a firm can underprice its competitors.
• Net Sale Price: Sum of the price charged by the store, plus the travel costs incurred by the consumers.
Distance to Center
$
30 20 10 0 10 20 30
Equilibrium with Monopolistic Competition
• Story of the Model:•Start with one firm: Monopoly•As the firm makes extra economic profits other firms will enter the market: Monopolistic Competition
Only One Firm:Monopoly
More Than One Firm:
Monopolistic Competition
$
Q
MC
DMR
Qm
Pm
ATCPROD
$
Q
DMR
Qe
Pe
ATCPRODMC
Efficiency Tradeoffs• As firms enter into the market, the firm’s
demand curve shifts to the right, moving the quantity produced at a point different than min ATCPROD
• As firms enter into the market, the travel cost for consumers decreases$
Q
ATCPROD
Average Travel Cost
ATC
Qe Qt Qm Qpc
Equilibrium Market Areas
30 20 10 0 10 20 30
$
Distance from Center of Region
Firm’s 1 Territory
Firm’s 2 Territory
Firm’s 3 Territory
An Algebraic Model of Market Areas
• What are the factors that determine the area of a market oriented firm M?– d Per Capita Demand– e Population Density (per Square Mile)– q Output of the Typical Music Store
edq
M
Determinants of Market Areas
• Changes in Demand and Population Densities
• Changes in Scale Economies• Market Area and Traveling Costs• Market Area and Income
(income elasticity of land vs. income elasticity of demand for output)
Urban Hierarchies & the Central Place Theorem
• Shows how the location patterns of different industries are merged to form a regional system of cities
• The Central Place Theorem answers two main questions:– How many cities will develop– Why some cities are larger than
others
Central Place Theorem (A Model)
• Population Density– Distributed Uniformly at Beginning– Region’s Population X
• No Shopping Externalities• Ubiquitous Inputs• Uniform Demand• Three industries:
– Industry I: Requires a population of X– Industry II: Requires a population of X/4– Industry III: Requires a population of X/16
CPT Model (Cont)
• Industry I will locate in the center of the region, just as the Median Location Theorem predicts. Workers will want to live close to the store and City A will be born.
• There is enough people for 4 stores of Industry II, two of these stores will locate in City A and the other two stores will split the region in two creating two cities City B and City C.
• There is enough people for 16 stores of Industry III, because there are already 3 cities, some stores will go to these cities: – City A will get 4 stores of Industry III– City B and City C will get 2 stores each of Industry
III– The other 8 stores will split the region into equal
parts, creating 8 smaller City D-City L .
CPT Conclusions• 1 High Order City:
– 1 Store Industry A – 2 stores Industry B– 4 stores Industry C – Population 4*(X/16)
• 2 Medium Order City– 1 store Industry B – 2 stores Industry C– Population 2*(X/16)
• 8 Low Order City – 1 store Industry C– Population (X/16)
City D City E
City F City G
City H City I
City K City L
City B
City C
City A
Relaxing the Assumptions
Output Goods are not Perfect Substitutes:– Suppose that output in industry 2 are
not perfect substitutes– then stores will cluster to allow
consumers to take advantage of shopping externalities
– Instead of two Type B cities, all firms in industry will be in City A
– Reduces the number of cities, but not the hierarchical order
Relaxing the Assumptions
Output Goods are Complements:– Suppose that output in industry I and II
are complements– then stores will pair up to exploit this
complementarity– Instead of two Type B cities and eight
Type C cities, type III stores will cluster around all four type II stores
– Reduces the number of cities to three, but not the hierarchical order