Lecture 4- Transportation and the Structure of Cities

Question 1

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

Answer 1

• 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.

Question 2

Explain agglomeration economies

Answer 2

-Firms benefit from locating closer to eachother

Question 3

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

Answer 3

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

Question 4

Give an example of pecuniary economies in action

Answer 4

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

Question 5

Give an example of technological economies in action

Answer 5

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)

Question 6

So why are households attracted to cities?

Answer 6

They provide better employment opportunities

Question 7

What about consumption-related agglomeration economies?

Answer 7

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

Question 8

So what is the role of transport costs?

Answer 8

• 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

Question 9

List 4 very common features of cities:

Answer 9

• 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

Question 10

Who originally founded the “monocentric city” model?

Answer 10

Alonso, Muth and Mills (in the 1960s)

Question 11

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

Answer 11

Wheaton, Brueckner

Question 12

What is the rough concept of the monocentric city model?

Answer 12

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

Question 13

List the assumptions for the monocentric city model

Answer 13

• 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

Question 14

What is the travel cost of commuting then?

Answer 14

tx, ie the cost per mile*number of miles

Question 15

What is the big trade-off?

Answer 15

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

Question 16

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

Answer 16

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

Question 17

What is the household budget in the monocentric city model?

Answer 17

y-tx = pq+c

Question 18

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

Answer 18

• 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)

Question 19

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

Answer 19

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

Question 20

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

Answer 20

• Utility: U(q,c) increasing and concave

Question 21

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

Answer 21

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

Question 22

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

Answer 22

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

Question 23

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

Answer 23

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.

Question 24

What is the logic behind the spacial equilibrium condition?

Answer 24

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

Question 25

What is the implication of the spacial equilibrium condition?

Answer 25

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.

Question 26

What compensates households for living further away?

Answer 26

q increases with x

Question 27

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

Answer 27

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

Question 28

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

Answer 28

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.

Question 29

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

Answer 29

𝑝 ↓ 𝑤ℎ𝑒𝑛 𝑥 ↑

Question 30

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

Answer 30

𝑞 ↑ 𝑤ℎ𝑒𝑛 𝑥 ↑

Question 31

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

Answer 31

Population density ↓ 𝑤ℎ𝑒𝑛 𝑥 ↑

Question 32

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

Answer 32

Building heights ↓ 𝑤ℎ𝑒𝑛 𝑥 ↑

Question 33

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

Answer 33

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

Question 34

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

Answer 34

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.

Question 35

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

Answer 35

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.

Question 36

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

Answer 36

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

Question 37

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

Answer 37

• 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

Question 38

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

Answer 38

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.

Question 39

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

Answer 39

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

Question 40

What is the budget constraint when comparing 2 separate incomes?

Answer 40

𝑦𝑖 − 𝑡𝑖𝑥 = 𝑝𝑞 + 𝑐

Question 41

What was is max available utility?

Answer 41

max𝑞𝑈(𝑦𝑖 − 𝑡𝑖𝑥 − 𝑝𝑞, 𝑞)

Question 42

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

Answer 42

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

Question 43

What doe the equilibrium consumption qi(x) satisfy?

Answer 43

𝜕𝑈𝑖/𝜕𝑞 − 𝑝(𝑥) 𝜕𝑈𝑖/𝜕𝑐 = 0,
𝑖 = 𝐻, L

Question 44

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

Answer 44

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

Question 45

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

Answer 45

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

Question 46

What is the “bid-rent” function?

Answer 46

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.

Question 47

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

Answer 47

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.

Question 48

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

Answer 48

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

Question 49

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

Answer 49

X̂

Question 50

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

Answer 50

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.

Question 51

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

Answer 51

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.

Question 52

What is the slope of a bid rent function?

Answer 52

−𝑡𝑖/𝑞𝑖(𝑥), 𝑖 = 𝐻, 𝐿

Question 53

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

Answer 53

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

Question 54

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

Answer 54

Rich in centre

Question 55

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

Answer 55

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