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Questions 1 Lecture 2

The document outlines an economic model of residential location choice within a monocentric city. It asks the reader to: 1) Derive the individual's budget constraint and bid rent function given exogenous housing consumption, commuting costs, wages, and rents. 2) Determine the equilibrium conditions for a closed city with absentee landlords, and how equilibrium values like city fringe and land rent vary with parameters like population size. 3) Extend the analysis to an open city with absentee landlords and effects of wages, commuting costs, and outside utility. 4) Consider variations of the model with closed and open cities under resident rather than absentee landlords.

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59 views2 pages

Questions 1 Lecture 2

The document outlines an economic model of residential location choice within a monocentric city. It asks the reader to: 1) Derive the individual's budget constraint and bid rent function given exogenous housing consumption, commuting costs, wages, and rents. 2) Determine the equilibrium conditions for a closed city with absentee landlords, and how equilibrium values like city fringe and land rent vary with parameters like population size. 3) Extend the analysis to an open city with absentee landlords and effects of wages, commuting costs, and outside utility. 4) Consider variations of the model with closed and open cities under resident rather than absentee landlords.

Uploaded by

Nabila Sedki
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Questions on: The basic model with identical

agents
Yves Zenou
Research Institute of Industrial Economics

July 3, 2006

Exercise 1. Linear utility function with exogenous


housing consumption

We assume that the city is linear and monocentric. This means that the city
is described by a line in which all jobs and all firms (which are assumed to be
identical) are located in the Central Business District (CBD hereafter), which
is normalized to zero for simplicity, and all workers/consumers endogenously
decide their residential location between 0 and the city fringe xf . Landlords
allocate the land to the highest bids in the city. All workers/consumers are em-
ployed and are identical in all respect. There are exactly N identical workers.
There are neither mobility costs within the city nor migration costs between
outside the city and the city. However, individuals do incur commuting costs
to go to work.

Part 1. The individual location choice

All individuals consume the same amount of land, which is normalized to


1. This means that hL = 1. This assumption implies that the utility function
of each individual can be rewritten as:

Γ(zL , 1) = zL (0.1)

They have the following commuting costs

T (x) = τ x
where τ is the commuting cost per unit of distance and x is the distance to
the CBD. Each individual has a wage of wL and pay a rent R(x) at a distance
x from the CBD.
(1a) Write the budget constraint.

(1b) Determine the bid rent function.

(1c) Show how the bid rent vary with x, wL , τ and the utility WL . Give
the intuition.

(1d) Determine the Alonso-Muth condition

Part 2: The urban land use equilibrium

Assume now that there are N identical individuals in the city.

(2a) Write the equilibrium conditions

(2b) Consider a closed city with absentee landlords. Determine the equilib-
rium values of the city-fringe x∗f , the utility WL∗ and the equilibrium land rent
R∗ (x). How x∗f vary with N? How WL∗ vary with wL , τ , N and RA ? Explain.
Also, how R∗ (x) vary with N? Explain.

(2c) Consider now an open city with absentee landlords. Determine the
equilibrium values of the city-fringe x∗f , the population size N ∗ and the equi-
librium land rent R∗ (x). How x∗f and N ∗ vary with wL , τ , WL and RA ?
Explain. Also, how R∗ (x) vary with wL , τ , WL and RA ? Explain.

(2d) Consider now a closed city with resident landlords. Determine the
equilibrium values of the city-fringe x∗f , the utility WL∗ and the equilibrium
land rent R∗ (x).

(2e) Consider now an open city with resident landlords. Determine the
equilibrium values of the city-fringe x∗f , the population size N ∗ and the equi-
librium land rent R∗ (x).

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