MSA FIPS to CBSA FIPS in Class’ Website

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