LECTURE 3 URBAN ECONOMICS, Apuntes de Economía

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Lecture 3 Extension of Monocentric model

Xiaofang Dong

Xiamen University xfangdong@xmu.edu.cn

October 22, 2019

Lecture 3 Extension of Monocentric model

(^1) Review of Lecture 3

(^2) Extension of The Urban Model A City with Two Income Groups Add Time cost Cities in Developing Countries

An open city:Migration between cities

Remind: When y ,L,rA,t increase,the welfare(utility level) of urban residents if affected

An intercity migration equilibrium must make consumers equally well off regardless which city they live in.The migration between cities lead to:

• (^) a positive correlation between population and income, because the large population cancels the gains by a higher income to reach intercity migration equilibrium.
• (^) require reconsideration of these comparative ananlysis in a closed city. the higher y is automatically accompanied by a large L. I (^) large y shift,make ¯x bigger I (^) large L combined migration,then make ¯x bigger more

Extension of The Urban Model

The model presented in Lecture 3 imposed a number of simplifications so that simple conclusions could be derived.The purpose of this lecture is to introduce modifications to the model.

• (^) Model 1: A city with two income groups
• (^) Model 2: Traffic congestion
• (^) Model 3: Cities in Developing Countries
• (^) .......

Recall that the budget constraint of consumer is

c + p(x)q = y − tx

and we can drive the slope of housing price curve is

p′(x) =

−t q

One would expect qR to be larger than qP , but this only happen at the intersection point,we have −t qR

−t qP

At a point where two bid rent curves intersect, the rich rent curve must be flater than the poor one

• (^) The rich group live suburban, while the poor group live in the CBD

Economic intuition:The increase in desired dwelling size as income increasing gives a household incentive to move further from CBD

Add Time cost

The model doesn’t offer a clear prediction about the relative locations of rich and poor. Two conficting forces:

• (^) the desire to rent their large dwellings at a lower price pulls the rich toward the suburbans
• (^) the desire to limit their high time cost of commuting pulls rich toward the center
• (^) depends on the relative strengths of these forces

Add time cost

Empirical hints:

• (^) Most American cities like Chicago and New York, the rich people enclaves near the CBD
• (^) The overall positive correlation of income and distance to CBD.

Other explanations:

• (^) Glaeser, Kahn, and Rappaport(2008)
• (^) transport mode choice explanation, poor people highly rely on public transit

Cities in Developing Countries

It is interesting to consider a different type of open city: one that experience in-migration from rural areas than from other cities.This kind of migration play an important role in developing countries.

• (^) the equilibrium city size determined via rural-urban migration can be analyzed

When to move?

Suppose that rural residents earn an income yA,which is lower than the urban income y .Since the rural residents live next to where they work, the comuting cost is zero, and their disposable income is just equal to yA.

When will a rural resident want to move to the city?

• (^) the urban income y and paying for commuting and housing makes him better off than living in countryside.
• (^) need only compare his situation with the resident living at the city’s edge

The effect on the equilibrium city size

The above conditon can be used to determine the effect of related variables on L.

suppose rA is low due to lower agricultral productivity:

• (^) then cities reach a large population size
• (^) developing countries with low rural incomes should contain especially large cities

The effect on the equilibrium city size

The city’s income y and its commuting cost per mile t on equilibrium L:

• (^) less straightforward because ¯x depends on y and t
• (^) suppose a fixed population density β, and

π ¯x^2 = βL

• (^) we have y − t(βL/π)

1 (^2) = yA

• (^) cities with high incomes or low commuting costs will attract a large number of rural migrants

The end