Land Use in Monocentric City

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Land Use in Monocentric City

• Chapter 8
• OSullivan

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What does the city look like?

• We have lots of activity downtown.
• Less activity as we go further away.
• Why is that?

Distance
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Answers

• Transportation technologies lead to nodes from
  which we ship items.
• Scale economies imply that we are likely to see
  clustering around activities that are subject to
  economies of scale.
• There are informational and shopping
  externalities.

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Who locates where?

• The fundamental story is one that weve seen
  before.
• Firms maximize profits. The profits come from a
  function that looks like this
• ? Rev - Costs - transportation costs - rent
• If there is perfect competition, ? 0.
• So

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Who locates where?

• 0 Rev - Costs - transportation costs - rent
• rent Rev. - Costs - tXu
• where X is what is shipped, t is the cost per
  unit to ship it, and u is the distance shipped.
• So
• Rent is inversely related to distance.

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What will we see?

• Tall buildings downtown.
• Higher density downtown
• People commuting to the downtown, or

Distance
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Is this efficient?

• What is efficient?
• Answer -- Since production is usually taken as
  fixed, the efficient allocation minimizes
  transportation costs. Those with the highest
  transportation costs are locating the closest, so
  the allocation is efficient.

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What about households?

• Households dont maximize profits, so lets look,
  first, at their budgets, but then look at their
  utility.
• Households, in this model, eat chicken, rent
  housing, and commute to work. So
• Income Chick. Exp. House Exp. trav.
• y 1 c p h tu

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Household expenditures

• y 1 c p h tu
• where c pounds of chicken at 1/pound
• h housing, at price p
• u distance commuting at price t/mile
• As the household moves further away from
  downtown, what MUST change?
• Agt Commuting cost ?.
• Then what?

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Household expenditures

• Then what?
• Does the price of chicken change?
• OK, transportation costs go up by t. So, the
  price of housing must fall in order to make up
  for the transportation costs.
• If tu increases, ph must decrease, or else income
  rises.

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Household expenditures

• So if we move 1 mile further, transportation cost
  increases by t. Thus
• t - h ? p, or
• ? p -t / h.
• Lets look at a spreadsheet (EXCEL).

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What does this say about the rents?

• ? p -t / h.
• This is a straight line, just like we saw before.
• What kinds of substitutions might we see?
• A picture!

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Indifference curves

• Suppose Clyde takes home 2,000 per month. Clyde
  lives on chicken and housing, and commutes to
  work.
• Chicken costs 1/pound.
• Housing costs 0.50/sq. ft.
• Commuting costs 100.
• All are per month.

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Income net of commuting
1900
Chicken
1400
3800
1000
Housing
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Income net of commuting
Income net of commuting (20 ?)
1900
1880
Housing price MUST fall
Chicken
1400
3800
3760
1000
Housing
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Housing price falls

• People must stay on same indifference curve!
• As price of housing falls, people substitute away
  from chicken. Utility rises.
• To keep utility the same, price of housing is bid
  up a little more than the transportation costs
  would indicate. This makes it convex.

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Rich and poor

• Lets compare the rich and the poor.
• Look at the equation
• ? p -t / h.
• What changes between the rich and the poor?
• Agt The rich buy more h than the poor. So, the
  denominator of the equation is bigger. The price
  of housing must fall LESS per square foot per
  mile for the rich than for the poor.

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Who locates where?

• Transp. is relatively important for poor ? steep
• Transp. is relatively less important for rich ?
  shallow

/sq.ft.
Poor
Rich
Distance
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Who locates where?

• Poor in central city, rich further out. Why?
• Look at EXCEL spreadsheet and discuss.
• Next time
• Density
• Segregation