Lecture 4- Transportation and the Structure of Cities Flashcards by Seth Collinson

Give 1 way how economists generally explain the existence of cities?

Scale economies, production of goods and services become more efficient with larger scale (average cost decreases with quantity)
Therefore production establishments employ a large number of people, who want to live close to their job.

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Explain agglomeration economies

-Firms benefit from locating closer to eachother

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Give 2 reasons why firms benefit from being closer to eachother.

Cheaper inputs (pecuniary economies)
More productive inputs (technological economies)

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Give an example of pecuniary economies in action

The concentration of workers results in a larger labour market, making it easier to find a qualified worker at a reasonable cost.

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Give an example of technological economies in action

Knowledge spillovers, as contact between workers of different firms facilitate the spread of ideas and innovation; this is easier if firms are closer to each other (ie Silicon Valley)

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So why are households attracted to cities?

They provide better employment opportunities

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What about consumption-related agglomeration economies?

A concentration of shops implies more competition, therefore lower search costs for customers

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So what is the role of transport costs?

Firms want to locate close to their customers, save on transportation costs
Consumers prefer to live close to other consumers and, thus, producers/sellers to save on travel costs and access larger markets

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List 4 very common features of cities:

The concentration of tall buildings in city centres
Density of dwellings at its maximum in city centres
Size of dwellings increase as you move away from city centres
Price of land declines as you move away from city centres

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Who originally founded the “monocentric city” model?

Alonso, Muth and Mills (in the 1960s)

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Who re-elaborated the idea of the monocentric city model?

Wheaton, Brueckner

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What is the rough concept of the monocentric city model?

City structured around a Central Business District (CBD), where all jobs are located
Households live outside CBD, work and commute there regularly

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List the assumptions for the monocentric city model

All jobs within the CBD
CBD point-sized
City has a network of radial roads: everyone can travel from their home to the CBD on a straight line
Commuting is costly (money)
Cost of commuting increases proportionally to distance from CBD, denoted x
Identical travel mode for everyone (e.g. car). Same cost per mile, denoted t
Households are identical (same income and preferences)
Fixed total population

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What is the travel cost of commuting then?

tx, ie the cost per mile*number of miles

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What is the big trade-off?

Live in a small house and not commute, or big house and commute

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In the monocentric city model, what do households care for?

Housing space- ie they’re always happier with a larger house
Generic, composite consumption of all other goods (food?)

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What is the household budget in the monocentric city model?

y-tx = pq+c

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In the budget y-tx = pq+c, what do the letters signify?

y = income (exogenous)
t = commuting cost per mile
x = distance of residence from CBD
p = rental price of dwelling space (land), per sqm
q = units (sqm) of dwelling space
c = consumption of composite good (price normalized to one)

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Of the budget y-tx = pq+c, what do households care for?

Households care for dwelling space (q) and consumption (c)

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Is the utility function U(q,c) increasing or decreasing, and is it concave or convex?

Utility: U(q,c) increasing and concave

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Do we consider the quality of dwellings to matter to households?

No, we only assume the size od dwellings to matter to households

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Do we include construction costs in the costs of producing dwellings?

No we do not, we only consider the cost of land.

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What is the spcial equilibrium condition? Explain it initially technically, and then simply.

Households get the same utility level
at any location (identified by distance x from CBD) such that a positive quantity of households lives at that location i.e households are indifferent as to the distance from CBD, x, they live at.

What is the logic behind the spacial equilibrium condition?

If households got a higher utility from Location A to Location B, there cannot be an equilibrium.

What is the implication of the spacial equilibrium condition?

The welfare of hosueholds must not change with a change in x. However, those closer to the CBD get a higher net income due to a reduction in commuting costs.

What compensates households for living further away?

q increases with x

So if households living further away have a smaller net income, but can afford larger dwellings, how can this be true?

If a square metre of housing gets cheaper as we move away from the centre, ie p decreases with x

What is an explanation for higher real estate prices (p) as a closer distance to the CBD?

Locations closer to the CBD are more coveted due to lower commuting costs. Higher demand for space, therefore, results in higher real estate prices per square meter.

What happens to price of dwellings per square meter when distance from CBD increases?

𝑝 ↓ 𝑤ℎ𝑒𝑛 𝑥 ↑

What happens to the size of dwellings per square meter when distance from CBD increases?

𝑞 ↑ 𝑤ℎ𝑒𝑛 𝑥 ↑

What happens to population density when distance from the CBD increases?

Population density ↓ 𝑤ℎ𝑒𝑛 𝑥 ↑

What happens to building heights when distance from the CBD increases?

Building heights ↓ 𝑤ℎ𝑒𝑛 𝑥 ↑

On the graph portraying the relationship btween rent price and distance, what is significant about xbar?

This is the city boundary, where the price people individuals are willing to pay is lower than the price of agricultural land.

What is the slope of the function representing the relationship between rent price and distance?

The slope of this function is − 𝑡/𝑞(𝑥): it gets smaller (in absolute value) as we move away from the CBD, because 𝑞(𝑥) gets bigger.

What would happen to a city in equilibrium with an increase in t?

Suburban households would like to move closer to the CBD to reduce commuting costs, as now housing prices cannot adequately compensate households that live far from the CBD.

What would happen to the graphical relationship between p and x city in equilibrium with an increase in t? Why?

Land near the CBD is in greater demand, and is increasing in value, whereas further away rom the CBD, it is decreasing.

What are the implications of an increase in t for dwelling sizes, city sizes and population densities?

* Dwellings become smaller close to the CBD, larger in suburbs * Population density increases close to CBD, decreases in suburbs * Land area occupied by the city shrinks

What is notable about the sizes of European cities compared to US ones?

They are generally smaller in size than US cities, which fits with the model, as petrol is much cheaper in the USA than in Europe.

In Europe, do rich people live predominantly in centre or suburbs? How about USA?

Europe's rich generally live in the centres, USA's rich generally live in suburbs.

What is the budget constraint when comparing 2 separate incomes?

𝑦𝑖 − 𝑡𝑖𝑥 = 𝑝𝑞 + 𝑐

What was is max available utility?

max𝑞𝑈(𝑦𝑖 − 𝑡𝑖𝑥 − 𝑝𝑞, 𝑞)

Why is the cost of commuting greater for a high income individual than a low income individual?

Because high income individual's have a higher value of time

What doe the equilibrium consumption qi(x) satisfy?

𝜕𝑈𝑖/𝜕𝑞 − 𝑝(𝑥) 𝜕𝑈𝑖/𝜕𝑐 = 0, 𝑖 = 𝐻, L

At a given distance from the CBD, which income group consumes a greater level of housing. How is this known?

High income groups consume greater housing. This is known as where 𝑈𝑖 = 𝑈(𝑦𝑖 − 𝑡𝑖𝑥 − 𝑝𝑞, 𝑞), i=H,L, it can be shown that as long as 𝑦𝐻 − 𝑡𝐻𝑥 > 𝑦𝐿 − 𝑡𝐿𝑥, for any x, then 𝑞𝐻(𝑥) > 𝑞𝐿 (𝑥) holds

What does the equilibrium consumption equation 𝜕𝑈𝑖/𝜕𝑞 − 𝑝(𝑥) 𝜕𝑈𝑖/𝜕𝑐 = 0, mean in simple terms?

You choose a quantity of space such that the marginal utility of space equals price times marginal utility of consumption

What is the "bid-rent" function?

The relation between the price the individual is willing to pay for the land and the distance of the plot of land from the CBD.

What is the goal of the two-income levels model?

We want the model to give us an indication of which individuals are likely to occupy the plots of land closest to the CBD, or farthest from it.

What must be true about the individuals who occupy land in equilibrium?

That those individuals must have the highest willingness to pay for it.

What do we call the point of intersection between 2 big rent functions?

X̂

If at X̂ pH(x) is steeper than pL(x), what must be true?

High income types outbid the low income ones at all locations x closer to the CBD than X̂. ie the high income types live closer to the centre.

If at X̂ pH(x) is less steep than pL(x), what must be true?

Low income types outbid the high income ones at all locations x closer to the CBD than X̂. ie the low income types live closer to the centre.

What is the slope of a bid rent function?

−𝑡𝑖/𝑞𝑖(𝑥), 𝑖 = 𝐻, 𝐿

So when do high incomes have a steeper bid-rent function?

−𝑡H/𝑞H(𝑥) < −𝑡L/𝑞L(𝑥) ⇒ 𝑡𝐻/𝑡𝐿 >𝑞𝐻(𝑥)/𝑞𝐿(𝑥)

Does steeper bid rent imply rich in centre or rich in suburb?

Rich in centre

What else could explain why the rich live more in European centres than American centres?

European centres have historical monuments which the rich may value more. America doesn't have this.