ECN741: Urban Economics. The Basic Urban Model 2: Solutions . The Basic Urban Model. Motivation for Urban Models Urban models are built on the following simple sentence: People care about where they live because they must commute to work. This sentence contains elements of 6 markets:
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ECN741: Urban Economics
The Basic Urban Model 2: Solutions
Motivation for Urban Models
Motivation for Urban Models, 2
Housing Demand
Housing Demand, 2
Housing Demand, 2
and
so
Housing Demand, 2
Housing Demand, 3
Deriving a Bid Function
The Indirect Utility Function Approach
where
Indirect Utility Function Approach, 2
or
The Locational Equilibrium Condition
The Differential Equation Approach
Differential Equation Approach, 2
Differential Equation Approach, 3
or
Housing Supply
where the “S” subscript indicates aggregate supply at location u, K is capital and L is land.
Input Demand
Note on Land Prices
Solving for R{u}
Solving for R{u}, 2
or
where
Solving for R{u}, 3
Anchoring R{u}
Determining the Outer Edge of the Urban Area
R(u)
_
R

Anchoring R{u}, 2
Anchoring P{u}
where the “opportunity cost of housing” is
A Complete Urban Model
Housing
where N{u} is the number of households living at location u.
Land
The Capital Market
The Transportation Market
Labor and Goods Markets
Labor and Goods Markets, 2
Locational Equilibrium
The Complete Model
The Complete Model, 2
Open and Closed Models
Open and Closed Models, 2
Solving a Closed Model
Solving a Closed Model, 2
Solving a Closed Model, 3
Solving a Closed Model, 4
The Integral
where c1 = Y, c2 = t, and n = [(1/aα)1].
The Integral, 2
where b = 1/aα and the right side must be evaluated at 0
and .
The Integral, 3
The Problem with Closed Models
Solving an Open Model
Solving an Open Model, 2
The Problem with Open Models
Density Functions
Building Height
where