Urban Economics: Understanding City Spatial Structure and Firm Clustering - Xiaofang Dong, Apuntes de Economía

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Lecture 2 Analyzing Urban Spatial Structure

Xiaofang Dong

Xiamen University xfangdong@xmu.edu.cn

October 8, 2019

Lecture 2 Analyzing Urban Spatial Structure

(^1) Review of Lecture 1

(^2) Introduction

(^3) Monocentric model Basic Assumptions Consumer Analysis Housing Production Analysis Comparative Static Analysis(Wheaton,1974) The effects of population and agriculture land rent The effects of commuting cost and income An Open city: Migration between Cities

Introduction

Urban spatial structure shows a particular dramatic fashion if you look out the airplane window or walking through the street of one city:

• (^) Building heights gradually falling as distance from the center increases
• (^) Dwelling sizes increase as distance from the center increases
• (^) Population density falls moving away from the city center,reaching a much lower level in the suburbans
• (^) Residential prices per square foot fall moving away from the city center
• (^) ......

Introduction

Economists have formulated a model of cities to capture all these characters of urban spatial structure.

• (^) this model can picture the city basic structures
• (^) can be used reliably for predictive purposes in a policy context
• (^) the model originated in Alonso(1964),Muth(1969)and Mills(1967),and systematic derivation of the model was first done by Wheaton(1974),then by Brueckner(1987)

Basic Assumptions

Simplification are chosen to capture the essential features of cities, leaving out those less important.

Assumption 1: all the city’s jobs are in a place called as ”CBD”,and collapsed to a single point at the city center, take up no space

• (^) in reality,many job sites are outside city centers;and job decentralization is a hallmark of modern cities,this model initially ignored it, and applies best to cities of the early to mid-twentieth center
• (^) can be modified to include the formation of subcenters
• (^) can be modified to CBD to have a positive land area

Basic Assumptions

Assumption 2: the city has a dense network of radial roads

• (^) a resident living some distance from the CBD can travel to work in a radial direction,straight into the center
• (^) in reality cities are criss-crossed by freeways,thus leading to non-radial auto mobile commute paths
• (^) can be added to the model without changing its essential lessons

Commuting Cost

let x denote radial distance from a consumer’s residence to the CBD, t represents the per-mile cost of commuting

• (^) ”money” cost,a ”money” out-of-pocket
• (^) time cost, captured opportunity cost, we ignored the time cost so far, but will be included in analyzing a city that contains different groups.

let the income earned per period at the CBD by each resident be denoted by y, then disposable income will be y-tx

Commuting Cost

The fact that the same commuting-cost parameter t applies to all residents reflects another implicit assumption of the model:

• (^) all residents use the same transport mode to get to work
• (^) models with competing transport modes have been developed, but they involve additional complexity

Basic Assumptions

Assumption 4: the city’s residents consume only two goods:housing and a composite good

• (^) since the model is about cities, it naturally focuses on housing
• (^) simplicity requires that all other consumption be lumped together into a single composite commodity.

Consumer Analysis

• (^) Composite good consumption, denoted by c I (^) since the price per unit is normalized to $1,c gives dollars spent on composite goods.
• (^) Housing consumption, denoted by q I (^) the physical units corresponding to q is square footage of floor space, not the construction quality, age, and amenities I (^) the price per unit of housing vary with the distance to CBD x, denoted as p(x) I (^) assumes that everyone in the city is a renter,then the rental payment is p(x)q
• (^) Budget constraint I (^) c+pq=y-tx I (^) expenditure on bread and expenditure on housing should equal to disposable cost

Property 1

Consumer locational equilibrium implies utilities can be spatially uniform only if

• (^) higher commuting cost if located far away from the city center
• (^) must exist some offset benefit to keep utility from falling
• (^) the offsetting benefit is a lower price of housing per squre foot,compensating differential

Property 1: the price per unit housing floor space falls as distance increases

Such a inverse relationship can be derived by using an indifference curve:

Property 2

Figures also contain additional information about consumer choices,shows that the suburban resident consumes more squre feet of housing and less bread than the central-city dwellings.

Property 2: Dwelling size q rises as distance from the CBD increases

The difference in bread consumption indicates an additional pattern:while occupying a small dwelling, the central-city resident consumes a lot of bread.

It doesn’t survive the generalization of the model to include multiple income groups.