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PPA786: Urban Policy. Class 3: Housing Concepts, Household Bids. Urban Policy: Housing Concepts Household Bids. Outline of Class Land concepts Housing concepts Housing bids and locational equilibrium. Urban Policy: Housing Concepts Household Bids. Land Concepts

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ppa786 urban policy

PPA786: Urban Policy

Class 3:

Housing Concepts, Household Bids

urban policy housing concepts household bids
Urban Policy: Housing Concepts Household Bids
  • Outline of Class
    • Land concepts
    • Housing concepts
    • Housing bids and locational equilibrium
urban policy housing concepts household bids1
Urban Policy: Housing Concepts Household Bids
  • Land Concepts
    • Land rent is the price for using one unit of land, say an acre, for one unit of time, say a year.
    • Land value is the price of buying one unit of land, again say an acre.
urban policy housing concepts household bids3
Urban Policy: Housing Concepts Household Bids
  • The Determination of Land Rent
    • Land is an input; the price of land (= annual rent) is a derived demand—derived from its role in producing an output, say Q.
    • In equilibrium, the price of an input equals the value of its marginal product:
urban policy housing concepts household bids4
Urban Policy: Housing Concepts Household Bids
  • Land Rent, Continued
    • Now suppose that
      • Qmust be shipped to a market
      • The distance to the market, designated u, varies across firms.
      • It costs $s to ship a unit of Q one mile.
      • The marginal product of land equals a.
    • Then land rent is determined by:
urban policy housing concepts household bids5
Urban Policy: Housing Concepts Household Bids

Land Rent and Distance from the Market

without with

substitution substitution

< Figure 1 >

R(u) A R(u) B

Marketu Market u

urban policy housing concepts household bids6
Urban Policy: Housing Concepts Household Bids
  • Housing Concepts
  • Housing is measured in units of housing services = H
    • H= quality-adjusted square feet.
    • Depends on housing characteristics (X1, X2, …)
  • P = the price per unit of H per year.
  • R = rent for a housing unit = PH.
    • If the unit is an apartment, R = contract rent.
    • If the unit is owner-occupied, R is not observed.
urban policy housing concepts household bids7
Urban Policy: Housing Concepts Household Bids
  • Housing Concepts, Continued
  • V = the value of a housing unit = the present value of the rental flow (not observed for renters).
  • So:
urban policy housing concepts household bids8
Urban Policy: Housing Concepts Household Bids
  • How Does a CBD Worker Decide Where To Live?
    • She compares the marginal benefit (MB) and the marginal cost (MC) of moving one mile farther from the CBD.
urban policy housing concepts household bids9
Urban Policy: Housing Concepts Household Bids
  • How Does a CBD Worker Decide Where To Live? (Continued)
    • She then keeps moving out until she comes to the location (u*) at which MB equals MC:
urban policy housing concepts household bids10
Urban Policy: Housing Concepts Household Bids

Tradeoff Between Housing and Commuting Costs

urban policy housing concepts household bids11
Urban Policy: Housing Concepts Household Bids
  • The Twist: How Housing Prices Are Determined
    • Now suppose that all households are alike (an assumption to be relaxed!). Then they all pick the same u*!
    • This is impossible, so P{u} adjusts until people are equally satisfied no matter where they live.
      • This is called locational equilibrium.
urban policy housing concepts household bids12
Urban Policy: Housing Concepts Household Bids
  • The Twist: How Housing Prices Are Determined (Continued)
    • Thus, P{u} adjusts until, at all locations,
    • that is, until the slope of the P{u} function equals –t/H.
urban policy housing concepts household bids13
Urban Policy: Housing Concepts Household Bids
  • The Twist: How Housing Prices Are Determined (Continued)
    • Because the slope is negative, P{u} is higher closer to the CBD than it is in the suburbs.
    • When P{u} is high, people substitute away from housing so that H is low.
    • When H is low, the slope of P{u}, namely, -t/H, is high in absolute value.
    • It follows that P{u}is steep near the city center but flattens as one moves out toward the suburbs.
urban policy housing concepts household bids14
Urban Policy: Housing Concepts Household Bids

The Bid Function for Housing

(Price per Unit of Housing Services)

Slope = ΔP/Δu

= -t/H

< Figure 3 >

P(u)

  • CBD u

ΔP

Δu

urban policy housing concepts household bids15
Urban Policy: Housing Concepts Household Bids

Finding the Edge of the City

  • Urban activities must compete with rural activities for access to land.
  • Suppose P* is the opportunity cost of pulling land out of agriculture and into housing.
  • Then urban activities will take place out to the point, say, u*, at which the price of housing exceeds P*.
urban policy housing concepts household bids16
Urban Policy: Housing Concepts Household Bids

Determining the Outer Edge of the Urban Area

< Figure 3A >

P(u)

P*

  • CBD u* u
urban policy housing concepts household bids17
Urban Policy: Housing Concepts Household Bids

Policy Questions and Bid Functions

  • Some policies affect a single urban area.
    • If they make the area more attractive, people move in; otherwise, people move out to other areas.
    • These policies are analyzed with an “open” model.
  • Other policies affect all urban areas.
    • These policies do not give anyone an incentive to move out of an area.
    • These policies are analyzed with a “closed” model.
urban policy housing concepts household bids18
Urban Policy: Housing Concepts Household Bids

The Height of the Bid Function

and the Size of the Area

  • To understand the distinction between open and closed models, recall that we derived a formula for the slope of P{u}, not for its height.
  • As the height of P{u}, goes up,
    • The level of satisfaction in an urban area goes down,
    • And the population goes up.
urban policy housing concepts household bids19
Urban Policy: Housing Concepts Household Bids

The Height of the Bid Function

and the Size of the Urban Area

< Figure 3B >

P(u)

  • CBD u
urban policy housing concepts household bids20
Urban Policy: Housing Concepts Household Bids

Open versus Closed Models

  • In an open model, one selects the height of P{u}that yields the same level of satisfaction as a household can obtain in another urban area.
    • At any other height, people would move in or out.
  • In a closed model, one selects the height of P{u} that makes the area large enough to fit all its population.
urban policy housing concepts household bids21
Urban Policy: Housing Concepts Household Bids

Open versus Closed Examples

  • Suppose one city in a regions cleans up its air and no other city does.
    • The impacts are given by an open model.
    • People move in and housing prices go up until the higher cost of living offsets the utility gain from cleaner air!
  • Suppose all cities in the region clean their air.
    • The impacts are given by a closed model.
    • Nobody has an incentive to move out and utility goes up due to cleaner air.
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