Which model of urban structure describes growth in wedge-shaped sectors that extend outward from the centre along radial transport routes?

Sector model, in which similar uses extend outward in wedges along radial routes, organised by rent level

Concentric zone model (Burgess), in which successive rings form around the CBD through invasion and succession as the city grows

Sector model, in which similar uses extend outward in wedges along radial routes, organised by rent level

Multiple nuclei model, in which several specialised centres grow independently and eventually merge

Bid-rent model, in which one price surface allocates uses to rings by their willingness to pay

A city opens a new radial expressway. A few years later congestion on it is as bad as before it opened. Which explanation is the most complete?

The accessibility gain drew new development and extra trips, so demand rose to fill the capacity: the land use–transport feedback loop

The road surface deteriorated quickly, so the expressway's capacity fell back to the level of the old road within a few years

Land values fell near the expressway, so activities left and the remaining traffic was only redistributed over the other roads of the network

Population growth alone explains it, because the expressway had no influence on where people travel or where activities locate

The accessibility gain drew new development and extra trips, so demand rose to fill the capacity: the land use–transport feedback loop

Which statement about the economic rent of urban land is correct?

It is a surplus fixed by demand, since land at a location cannot be produced; it is not a cost of keeping the land available

It is set by the cost of producing and servicing the land, so it falls whenever construction costs fall anywhere in the city

It is identical to land value, since both are measured in rupees per plot and always move together in the same proportion

It is highest on the marginal land, because that land is used most intensively to cover its production cost

A hedonic regression of flat prices, including area, age and other attributes, gives a coefficient of −1.5 (₹ lakh per km) on distance to the nearest metro station. Which reading is correct?

Other attributes held constant, a flat 1 km nearer a station goes with a price about ₹1.5 lakh higher

Opening a station causes the price of every flat in the city to rise by ₹1.5 lakh for each kilometre of distance removed

Distance to the station explains 1.5 per cent of the variation in flat prices in the sample

Other attributes held constant, a flat 1 km nearer a station goes with a price about ₹1.5 lakh higher

Prices fall by 1.5 per cent for each kilometre from the station, irrespective of the size of the flat

Which of the following statements about classical models of urban structure are correct?

In Burgess's model, rings form around the CBD and the city grows outward by invasion and succession

In Hoyt's model, a high-rent residential sector tends to extend outward along a transport route

In Harris and Ullman's model, specialisation, agglomeration economies and incompatible uses produce separate nuclei

In Burgess's model, rings form around the CBD and the city grows outward by invasion and succession

In Hoyt's model, a high-rent residential sector tends to extend outward along a transport route

In Harris and Ullman's model, every land use radiates from a single CBD in uniform rings

In Harris and Ullman's model, specialisation, agglomeration economies and incompatible uses produce separate nuclei

In planning practice, transfer of development rights (TDR) is best described as

compensation in kind: the owner of land reserved for public use surrenders it and receives building rights to use or sell elsewhere

a one-time charge on owners whose land has gained value because of a nearby public work, collected as a share of that gain

borrowing against the extra property tax that an improved area is expected to generate and repaying the whole loan from it

pooling of private plots by the authority, which lays out infrastructure and returns smaller serviced plots to owners

Which of the following are land value capture instruments in principle?

A betterment levy on plots whose value rises because of a new road

Tax increment financing around a new station, repaid from the extra property tax of the area

Sale of additional FSI beyond the base FSI along a transit corridor

A betterment levy on plots whose value rises because of a new road

A uniform city-wide tax on fuel sales, unrelated to where public works are built

Tax increment financing around a new station, repaid from the extra property tax of the area

Sale of additional FSI beyond the base FSI along a transit corridor

Which feature most clearly separates true Transit Oriented Development from merely transit-adjacent development?

A connected pedestrian street network, mixed uses and limits on parking that put density within an easy walk of the station

A large park-and-ride facility beside the station to draw drivers from the whole region towards the metro line

The tallest buildings of the district placed on the plots nearest the station, whatever the street layout or parking around them

A single-use office cluster designed to guarantee heavy boardings at the station during the morning and evening peak hours

A connected pedestrian street network, mixed uses and limits on parking that put density within an easy walk of the station

Which of the following are typical challenges of brownfield redevelopment?

Possible soil or groundwater contamination that must be assessed and remediated to a standard fit for the intended use

Fragmented ownership, legal disputes and the need to rehabilitate former workers or tenants

Possible soil or groundwater contamination that must be assessed and remediated to a standard fit for the intended use

Fragmented ownership, legal disputes and the need to rehabilitate former workers or tenants

Absence of any road, water or sewer infrastructure nearby, because such land is always remote

A rule that every trace of contamination must be removed whatever the intended use of the site

Household P (income surplus ₹24,000 a month, lot 100 m²) and household R (surplus ₹48,000, lot 400 m²) both face a commuting cost of ₹800 per km per month. Using the fixed-lot bid rent Ψ = (surplus − t·d)/lot, which pattern results?

P occupies the land nearer the centre and R the land beyond about 20 km, because P's bid-rent line is steeper

R occupies the land nearer the centre, because its larger surplus gives a higher bid at every distance

P occupies the land nearer the centre and R the land beyond about 20 km, because P's bid-rent line is steeper

P occupies the land beyond about 20 km, because small lots are cheaper for the authority to serve with infrastructure

They cannot be separated by location, because both pay the same commuting cost per kilometre

In a multinomial logit model a car and a single bus have equal utility, so each takes half the trips. A second bus, identical to the first in every attribute except paint colour, is introduced. What does the model predict, and what does it show?

Car, bus and new bus 33.3% each; two identical alternatives should split one share, so the car's drop exposes IIA

Car 50% and each bus 25%; the prediction is acceptable and shows that logit handles similar alternatives well in practice

Car 25% and each bus 37.5%, because the new bus draws demand from the car more than from the old bus

Car, bus and new bus 33.3% each; two identical alternatives should split one share, so the car's drop exposes IIA

Car 50% and each bus 50%, because logit probabilities are independent of each other and need not sum to one

Which of the following statements about trip generation methods are correct?

In cross-classification, the trips of a zone are the sum over cells of households in the cell times that cell's trip rate

Fitting a regression at household level uses variation among households within zones, so it can work with a smaller survey sample than a zonal fit

Attractions are forecast mainly from household income and car ownership at the origin zone

In cross-classification, the trips of a zone are the sum over cells of households in the cell times that cell's trip rate

Fitting a regression at household level uses variation among households within zones, so it can work with a smaller survey sample than a zonal fit

A high R² on zonal data shows that each predictor in the regression causes trips

Land Use, Land Economics and Travel Demand: From Bid-Rent to the Four-Step Model

This chapter answers the first half of the Architecture and Planning (AR) paper’s Part B2, Section B2.4, “Urban Land Use and Transportation”: “Land Use-Transport-Urban form interaction; Urban structures and land use pattern; Economics concepts of land, rent, land use and land values; Land value capture; Transit Oriented Development, Urban regeneration and brown field redevelopment; Real estate pricing; Accessibility measures; Residence and employment location choice; Aggregate and disaggregate transport demand models and forecasting”. It teaches the land use–transport feedback loop and the classical models of urban structure; Ricardo, von Thünen and Alonso on rent and land value; land value capture (betterment levy, TDR, TIF, pooling) and hedonic pricing; TOD, regeneration and brownfields; accessibility measures and location choice; and the four-step model with its regression, cross-classification, gravity, growth-factor and logit steps. The numericals are von Thünen and bid-rent arithmetic, land value and levy, walkshed area, accessibility indices, gravity and Fratar trip interchange, trip generation and logit probabilities.

1. Land use, transport and urban form: one system

Land use, transport and urban form are one system, not three topics. Land use (which activity sits where, and how intensely) generates trips. The transport system (roads, transit, walking networks) decides how easily those trips can be made, which is accessibility. Accessibility in turn decides where households and firms locate, and that changes land use. This loop is the land use–transport feedback cycle. A new metro or highway raises accessibility along its line, land value and permitted density rise, development follows, trips grow and congestion returns. Building roads alone to remove congestion therefore often fails: the accessibility gain draws in more development and traffic (induced demand).

Two ends of urban form
Feature	Compact, mixed-use, connected	Dispersed, single-use, low density
Typical trip length	short; many destinations within walking distance	long; most destinations need a vehicle
Walking, cycling and transit share	high; transit becomes viable	low; car dependence
Infrastructure cost per household	lower; shorter pipes, roads and cables	higher; long networks serve few users
Energy use per person for travel	lower	higher

The classical models of urban structure explain where uses settle. Each is a simplification and a favourite exam item, so learn the driver of each.

Models of urban structure
Model	Pattern	Driver
Concentric zone (Burgess, 1925)	rings around the CBD: transition zone, workers' homes, better residences, commuter zone; growth by invasion and succession	distance from the centre: rent and commuting cost
Sector (Hoyt, 1939)	wedges radiating outward along transport routes; a high-rent residential sector extends along its route	radial routes and rent levels
Multiple nuclei (Harris and Ullman, 1945)	several specialised nuclei (CBD, wholesale, industry, suburbs) that grow and merge	specialisation, agglomeration economies and incompatible uses

⚠️ Rings, wedges, nuclei

Remember them by what organises the city: distance (Burgess), direction along routes (Hoyt), many centres (Harris and Ullman). Modern cities are mostly polycentric, and Indian cities typically combine a dense, mixed-use, walkable old core, radial arterials with ribbon development along them, and sprawl at the edge.

2. Land economics: Ricardo, von Thünen and Alonso

Land differs from other goods: its total supply is fixed, it cannot be moved, no two plots are alike (location is the difference) and it lasts. Its payment, economic rent, is a surplus above what is needed to bring it into use; because supply is fixed, demand alone sets it. Land value is capitalised rent: for a perpetual net rent R and capitalisation rate i, V = R/i. A net rent of ₹1.2 lakh a year at 8% gives V = ₹15 lakh.

Ricardo (differential rent). Cultivation spreads to ever poorer land until the marginal land, which earns no rent, is reached; a better plot earns rent equal to its extra output over the marginal plot at the same cost. If three plots give 50, 40 and 30 quintals for the same outlay, rents are 20, 10 and 0. In a city the 'fertility' is location: a central plot earns a rent equal to the transport cost it saves over the marginal plot.

Von Thünen (1826). Around a single market, location rent per unit area is R(d) = Y(p − c) − Y·f·d, where Y is yield per unit area, p the market price, c the production cost per unit, f the freight rate per unit per km and d the distance. Rent falls linearly with distance and vanishes at the margin d = (p − c)/f. Each crop has its own line; at every distance the crop with the highest rent wins, which gives concentric rings, with perishable and bulky, high-freight, high-rent crops nearest the market. Example: Y = 20, p = 100, c = 60, f = 2 gives R = 800 − 40d, so R(10) = 400 and the margin is at 20 km.

Alonso bid-rent (1964). The urban form of the idea: a household's bid rent is the most it can pay per unit land at distance d and still reach the same satisfaction. For a fixed lot q, income Y, spending Z on other goods and commuting cost t per km, Ψ(d) = (Y − Z − t·d)/q, a line of slope −t/q. Take Y − Z = ₹24,000 a month, t = ₹800 and q = 100 m²: Ψ = 240 − 8d per m² per month. Offices bid 400 − 40d. The land goes to the highest bidder, so offices occupy the centre until 400 − 40d = 240 − 8d, i.e. d = 5 km (rent ₹200), and households beyond. A steeper bid-rent line means a user who values centrality more, and so wins the centre.

🎯 Why the poor can sit near the centre

The slope t/q is steep for a user who consumes little land, so a small-lot, low-income household can outbid a large-lot, high-income one near the centre. Clark's density function, D(d) = D₀·e^(−b·d), describes the same trade-off: density falls roughly exponentially with distance from the centre, and land value peaks at the point of greatest accessibility.

3. Land value capture and real-estate pricing

Public investment (a metro station, a road) and planning decisions (rezoning, extra FSI) raise private land values, an unearned increment created by the public. Land value capture (LVC) recovers part of it to pay for the infrastructure that created it. The principle is that the beneficiary pays, and the test of an instrument is that it takes only the increment caused by public action, is legally secure and can be valued.

Value-capture instruments in principle
Instrument	How it works
Betterment levy or charge	a one-time charge on owners whose land gains from a public work, as a share of the increment
Premium or additional FSI	extra floor space beyond the base FSI is sold, usually along transit corridors
Transfer of development rights (TDR)	owner of land reserved for a road or park surrenders it and receives rights to build elsewhere, or to sell: compensation in kind
Land pooling or readjustment (town planning scheme)	owners pool plots, the authority lays out infrastructure and returns smaller, serviced plots, keeping part for roads and sale
Tax increment financing (TIF)	borrow against the future extra property tax of the improved area and repay from it
Joint development, air-rights lease	the transit agency develops or leases its station land and air space

Worked example: land at ₹20,000 per m² rises to ₹32,000 per m² after a metro line opens. For a 500 m² plot the increment is 12,000 × 500 = ₹60 lakh, and a levy of 50% of it yields ₹30 lakh. TDR is not cash capture: it pays for land in development rights, so its value depends on the receiving zones being able to absorb the extra floor space; too many rights and too few receiving areas depress the market.

Real-estate pricing. Valuation uses three approaches: sales comparison (prices of similar recent sales), income capitalisation (V = net operating income/capitalisation rate) and cost (replacement cost less depreciation, plus land). For development land the residual method subtracts costs and profit from the gross development value. Hedonic pricing treats a property as a bundle of attributes and regresses price on them: P = β₀ + β₁·area + β₂·age + β₃·distance to station. Each coefficient is the implicit (marginal) price of its attribute, holding the rest constant; in a log-price model, 100 × coefficient is roughly the percentage change per unit. If P (₹ lakh) = 12 + 0.5A − 1.5d, a 60 m² flat 2 km from a station costs 12 + 30 − 3 = ₹39 lakh, and every kilometre nearer adds ₹1.5 lakh. Associations are not causes: omitted attributes and spatial correlation bias the coefficients.

4. Transit Oriented Development, urban regeneration and brownfield redevelopment

Transit Oriented Development (TOD) is compact, mixed-use, walkable development concentrated around a high-capacity transit station, so that many residents and jobs can reach the station on foot or by cycle. It works by raising demand for transit, shortening trips and cutting car use, and it is the land-use half of a transit investment. The usual design variables are the 'Ds': density, diversity of uses, pedestrian-friendly design, destination accessibility and short distance to transit, plus restraint on parking. India's National TOD Policy (2017) promotes higher intensity and mixed use around mass transit stations.

The planning unit is the walkshed. At about 80 m per minute, 400 m is a 5-minute and 800 m a 10-minute walk. The ideal catchment is a circle (A = πr²): for r = 800 m it is π × 0.8² = 2.01 km², or about 201 ha, and for r = 400 m about 50.3 ha. Real streets give less, measured by the pedestrian catchment ratio, PCR = walkable area actually within the radius ÷ circle area; a PCR of 0.6 on the 800 m circle leaves 120.6 ha. Density should be highest at the station and taper outward.

⚠️ Transit-adjacent is not TOD

Towers beside a station with a large car park, blank walls and no through pedestrian streets are transit-adjacent development. TOD needs the pedestrian network, the mix of uses and limits on parking that make the density actually walk to the station.

Urban regeneration is the umbrella for improving built-up areas, along a ladder of intensity: conservation (protect heritage), rehabilitation (repair and upgrade), retrofitting (area-wide improvement of an existing area) and redevelopment (clearance and rebuilding). The Smart Cities Mission's area-based development used retrofitting, redevelopment and greenfield. Cross-subsidy is common: the sale component of a redevelopment, helped by extra FSI, pays for rehousing existing residents in place.

A brownfield is previously developed land, vacant or under-used, with real or suspected contamination: old mill land, railway yards, port and industrial sites. A greenfield is undeveloped land, and a greyfield an obsolete commercial site such as a worn-out shopping centre and its car park. The process is site assessment, remediation to a standard fit for the intended use (risk-based, not 'clean everything'), then financing and construction. The gains are existing infrastructure, central locations and less sprawl; the obstacles are contamination liability and cost, fragmented ownership and disputes, and rehabilitation of workers and tenants. Brownfields beside rail and metro lines are prime TOD sites.

5. Accessibility measures and residence and employment location choice

Accessibility is the ease of reaching opportunities (jobs, schools, health care, shops) from a place by a given mode. It is not mobility, the ability to move fast or far: a city can have fast roads and poor accessibility if destinations are far apart, and a compact city can have high accessibility with slow trips. Accessibility can be raised by transport (faster, cheaper links) or by land use (bringing destinations closer).

Accessibility measures
Measure	Form	Strength and weakness
Cumulative opportunities	Aᵢ = Σ Oⱼ for all j with tᵢⱼ ≤ T (jobs within T minutes)	simple and easy to explain; ignores distance within the cut-off and everything beyond it
Gravity-based (Hansen)	Aᵢ = Σ Oⱼ·f(cᵢⱼ), with f = c^(−α) or e^(−βc)	near opportunities count more, no hard cut-off; needs a calibrated decay
Utility-based (logsum)	Aᵢ = ln Σ exp(Vᵢⱼ) from a choice model	rests on behaviour and values choice itself; needs a calibrated model

Worked example. From zone i, 12,000 jobs lie 10 minutes away, 18,000 lie 15 minutes away and 40,000 lie 20 minutes away. Cumulative opportunities within 15 minutes = 12,000 + 18,000 = 30,000. The gravity index with f = 1/t = 12,000/10 + 18,000/15 + 40,000/20 = 1,200 + 1,200 + 2,000 = 4,400. Halving every travel time doubles the gravity index smoothly to 8,800, whereas the cumulative count jumps from 30,000 to 70,000 only because the 20-minute centre crosses the 15-minute cut-off: cut-off measures change in steps.

Residence location choice. A household trades housing cost and space against commuting cost and time, and also weighs neighbourhood quality, schools, tenure, social ties and the constraint of its income and of the housing actually available. Alonso's model captures the first trade-off; modern disaggregate models treat the choice as a multinomial logit over zones with attributes such as rent, commute time and amenities. Low-income households often live close to work or in informal settlements because commuting is unaffordable, while a mismatch between where cheap housing is and where jobs are (spatial mismatch) lengthens commutes.

Employment location choice. Firms choose by access to labour, customers and suppliers, agglomeration economies, rent and regulation. Offices that depend on face-to-face contact pay for the CBD, retail clusters at points of greatest accessibility to customers, and industry and logistics seek cheap land with highway, rail or port access. The Lowry model links the two sides: basic employment fixes the population that lives near it, population generates service employment (retail, schools), which generates more population, iterated until it settles.

6. Transport demand models: aggregate and disaggregate, trip generation and distribution

Travel is a derived demand: people travel to take part in activities elsewhere. Aggregate models work on zonal totals and averages (trips between zones, zonal shares) and are the classical four-step family. Disaggregate models work on individuals or households and explain each choice by a random-utility (discrete-choice) model. Activity-based models go further and link a person's trips into a daily schedule. Disaggregate models use the variation between individuals, so they need smaller samples, are more behavioural and transfer better between places; their price is the need to forecast the distribution of attributes (aggregation) and richer survey data.

The four-step model answers four questions in sequence: how many trips start and end in each zone (generation), where do they go (distribution), by which mode (modal split) and along which route (assignment). It is calibrated on a base-year survey, validated against counts, then run with forecast population, employment and networks. Its weaknesses: it is aggregate and static, treats trips as independent and is usually run in one pass; feedback loops from assignment back to distribution, or activity-based models, repair some of this.

Trip generation gives productions P (at the home end of home-based trips) and attractions A (jobs, floor space, school places). Two standard methods: multiple linear regression, T = a + b₁X₁ + b₂X₂ + …, fitted at zone or household level (watch multicollinearity and non-linearity; household-level fitting uses within-zone variation); and cross-classification (category analysis), in which households are grouped by income, vehicle ownership and size and each cell has a trip rate, so zone trips = Σ (households in cell × rate). Example: 500 households × 3.0 + 200 × 4.5 + 100 × 4.0 + 300 × 6.0 = 1,500 + 900 + 400 + 1,800 = 4,600 trips. Before distribution ΣP must equal ΣA, and attractions are scaled to productions, which are the better forecast.

Trip distribution by the gravity model: Tᵢⱼ = Pᵢ · Aⱼ·Fᵢⱼ / Σⱼ (Aⱼ·Fᵢⱼ), where F is a friction (deterrence) function such as 1/t, 1/t² or e^(−βt). This is the production-constrained form; a doubly constrained form adds balancing factors on both ends and is solved by iteration. Example: Pᵢ = 1,000, attractions 200, 400, 400 at 5, 10, 20 minutes, F = 1/t: A·F = 40, 40, 20 (sum 100), so trips are 400, 400 and 200.

Growth-factor methods need only a base-year matrix tᵢⱼ and growth factors Gᵢ by zone. Uniform: Tᵢⱼ = tᵢⱼ × (future total ÷ base total). Average factor: Tᵢⱼ = tᵢⱼ(Gᵢ + Gⱼ)/2. Fratar: Tᵢⱼ = tᵢⱼ·Gᵢ·Gⱼ·(Lᵢ + Lⱼ)/2, with the location factor Lᵢ = Σⱼ tᵢⱼ ÷ Σⱼ tᵢⱼGⱼ. Furness scales rows and columns alternately until both totals match. Example: t₁₂ = t₂₁ = 100, t₁₃ = t₃₁ = 200, t₂₃ = t₃₂ = 100, with G₁ = 1, G₂ = 2, G₃ = 1: L₁ = 300/(100×2 + 200×1) = 0.75, L₂ = 200/(100×1 + 100×1) = 1, so T₁₂ = 100 × 1 × 2 × (0.75 + 1)/2 = 175. One Fratar pass does not exactly balance the totals, so it is repeated. These methods keep today's pattern, ignore travel cost and cannot handle new zones, so they suit short-term forecasts only.

7. Modal split, assignment and forecasting

Modal split divides trips among modes. It depends on the traveller (income, vehicle ownership), the trip (purpose, length) and the mode (time, cost, comfort, reliability). It can be applied at the trip end (before distribution) or, most often, to the trip interchange (after distribution), so that mode-specific times and costs of each zone pair are used. The workhorse is the multinomial logit from random-utility theory: each mode has utility U = V + ε, with V = Σ βₖxₖ (and a mode constant), and the share is Pₘ = exp(Vₘ) / Σₖ exp(Vₖ). Shares sum to 1 and depend only on differences in V.

Worked example. V = −0.05·(time in min) − 0.01·(cost in ₹). Car: 20 min, ₹60 gives V = −1.0 − 0.6 = −1.6. Bus: 40 min, ₹20 gives V = −2.0 − 0.2 = −2.2. The difference is 0.6, so P(car) = 1/(1 + e^(−0.6)) = 1/1.5488 = 0.646, and P(bus) = 0.354. The ratio of the two coefficients is the value of time: 0.05/0.01 = ₹5 per minute, or ₹300 per hour.

⚠️ Independence of irrelevant alternatives

In multinomial logit the ratio of two modes' probabilities does not depend on any other mode. With car and one bus at equal utility, shares are 1/2 each; add a second bus identical except for colour and the model gives 1/3 each, so the car share falls to a third although nothing about it changed. Two near-identical alternatives should compete with each other, not with the car. The remedy is a nested logit, which groups similar modes in a nest.

Assignment loads the O–D flows onto the network. All-or-nothing puts every trip on the shortest path and ignores congestion. Capacity-restraint methods make link time depend on flow, usually through the BPR function t = t₀[1 + 0.15(v/c)⁴]; with t₀ = 10 min and v/c = 2 the time is 10 × (1 + 0.15 × 16) = 34 min. User equilibrium (Wardrop's first principle): every used route between a pair has the same, minimal travel time, so no traveller gains by switching. System optimum (Wardrop's second principle): flows are arranged to minimise total travel time, which in general differs from user equilibrium.

Forecasting needs base-year calibration and validation against independent counts, projections of population, employment, income and vehicle ownership, and the future network. The forecast is only as good as those inputs, and the main uncertainty is the inputs, not the model. Test several scenarios, and check that a model's behaviour (value of time, elasticities) is plausible before using it for policy.

Key takeaways

Land use generates trips, transport sets accessibility, and accessibility reshapes land use: a feedback loop, which is why new road capacity alone attracts new traffic. Burgess is rings, Hoyt is wedges along routes, Harris and Ullman is multiple nuclei.
Rent is a surplus set by demand. Von Thünen: R = Y(p − c) − Y·f·d, falling linearly to zero at d = (p − c)/f. Alonso: bid rent Ψ = (Y − Z − t·d)/q with slope −t/q; the steepest line wins the centre, and land value = R/i.
Value capture recovers the increment public action creates: betterment levy, premium FSI, TIF, pooling. TDR is compensation in development rights, not cash. Hedonic coefficients are implicit marginal prices, associations rather than causes.
TOD means walkable density, mixed use and limited parking around a station; check the walkshed (area = πr², scaled by the pedestrian catchment ratio). Brownfield redevelopment needs fit-for-use remediation, not total clean-up.
Accessibility is not mobility. Cumulative opportunities count jobs within a cut-off; the gravity (Hansen) index Σ Oⱼ·f(c) weights near ones more. Residence and employment choices trade rent and space against access.
Four steps: generation (regression, cross-classification), distribution (gravity; Fratar and other growth factors), modal split (logit, mind IIA), assignment (all-or-nothing, user equilibrium). Disaggregate models use individual variation and need smaller samples.

Practice questions (20)

Attempt each one before opening the answer. Every explanation names the tempting wrong option as well as the right one, because that is where marks are lost.

Which model of urban structure describes growth in wedge-shaped sectors that extend outward from the centre along radial transport routes?
1. Concentric zone model (Burgess), in which successive rings form around the CBD through invasion and succession as the city grows
2. Sector model, in which similar uses extend outward in wedges along radial routes, organised by rent level
3. Multiple nuclei model, in which several specialised centres grow independently and eventually merge
4. Bid-rent model, in which one price surface allocates uses to rings by their willingness to pay
Show answer
Answer: B — Sector model, in which similar uses extend outward in wedges along radial routes, organised by rent level
This is Hoyt's sector model: uses, and especially high-rent residential areas, extend outward as wedges along radial routes. The tempting alternative, the concentric zone model, is organised by distance from the centre rather than by direction along routes.
A city opens a new radial expressway. A few years later congestion on it is as bad as before it opened. Which explanation is the most complete?
1. The road surface deteriorated quickly, so the expressway's capacity fell back to the level of the old road within a few years
2. Land values fell near the expressway, so activities left and the remaining traffic was only redistributed over the other roads of the network
3. Population growth alone explains it, because the expressway had no influence on where people travel or where activities locate
4. The accessibility gain drew new development and extra trips, so demand rose to fill the capacity: the land use–transport feedback loop
Show answer
Answer: D — The accessibility gain drew new development and extra trips, so demand rose to fill the capacity: the land use–transport feedback loop
Higher accessibility raises land value and permitted density, attracts development, longer trips and a shift to the car, and so refills the new capacity. Blaming deterioration or population growth alone ignores the feedback: the road itself changes where and how people travel.
Around a single market, location rent per hectare is R(d) = Y(p − c) − Y·f·d. A crop has yield Y = 20 units per hectare, market price p = 100 per unit, production cost c = 60 per unit and freight f = 2 per unit per km. The location rent per hectare at d = 10 km is ____.
Numerical answer — type the value.
Show answer
Answer: 400
R(10) = 20 × (100 − 60) − 20 × 2 × 10 = 800 − 400 = 400. Check: the margin is at d = (p − c)/f = 40/2 = 20 km, and R = Y·f·(20 − 10) = 40 × 10 = 400.
A household has a monthly income surplus (income less non-housing spending) of ₹24,000, commuting cost of ₹800 per km per month and a fixed lot of 100 m², so its bid rent is (24,000 − 800d)/100 per m² per month at distance d km. Offices bid 400 − 40d per m² per month. Land goes to the highest bidder. The distance in km at which land passes from offices to households is ____.
Numerical answer — type the value.
Show answer
Answer: 5
Household bid = 240 − 8d. Set 400 − 40d = 240 − 8d, so 160 = 32d and d = 5 km, where both bid ₹200. Check at 2 km: offices 320 against households 224, offices win. At 8 km: offices 80 against households 176, households win.
Which statement about the economic rent of urban land is correct?
1. It is a surplus fixed by demand, since land at a location cannot be produced; it is not a cost of keeping the land available
2. It is set by the cost of producing and servicing the land, so it falls whenever construction costs fall anywhere in the city
3. It is identical to land value, since both are measured in rupees per plot and always move together in the same proportion
4. It is highest on the marginal land, because that land is used most intensively to cover its production cost
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Answer: A — It is a surplus fixed by demand, since land at a location cannot be produced; it is not a cost of keeping the land available
Land at a place cannot be produced, so its rent is a surplus fixed by what users will bid, not a cost of production. Land value is capitalised rent (V = R/i), a stock rather than a flow, and marginal land earns zero rent, not the highest.
A hedonic regression of flat prices, including area, age and other attributes, gives a coefficient of −1.5 (₹ lakh per km) on distance to the nearest metro station. Which reading is correct?
1. Opening a station causes the price of every flat in the city to rise by ₹1.5 lakh for each kilometre of distance removed
2. Distance to the station explains 1.5 per cent of the variation in flat prices in the sample
3. Other attributes held constant, a flat 1 km nearer a station goes with a price about ₹1.5 lakh higher
4. Prices fall by 1.5 per cent for each kilometre from the station, irrespective of the size of the flat
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Answer: C — Other attributes held constant, a flat 1 km nearer a station goes with a price about ₹1.5 lakh higher
A hedonic coefficient is the implicit marginal price of an attribute with the others held constant, here in ₹ lakh per km. It is an association; it does not prove the station caused the difference, and it is not a percentage unless the model is in log price.
Which of the following statements about classical models of urban structure are correct?
1. In Burgess's model, rings form around the CBD and the city grows outward by invasion and succession
2. In Hoyt's model, a high-rent residential sector tends to extend outward along a transport route
3. In Harris and Ullman's model, every land use radiates from a single CBD in uniform rings
4. In Harris and Ullman's model, specialisation, agglomeration economies and incompatible uses produce separate nuclei
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Answer: A — In Burgess's model, rings form around the CBD and the city grows outward by invasion and succession; B — In Hoyt's model, a high-rent residential sector tends to extend outward along a transport route; D — In Harris and Ullman's model, specialisation, agglomeration economies and incompatible uses produce separate nuclei
Burgess is the ring-and-succession model, Hoyt the sector model along routes, and Harris and Ullman the multiple-nuclei model. The statement that every use radiates from one CBD in rings contradicts the whole point of multiple nuclei, so it is wrong.
A plot yields a perpetual net rent of ₹3.6 lakh a year, valued at a 9% capitalisation rate. After a transit line opens its net rent rises to ₹4.5 lakh and the rate is unchanged. A betterment levy of 40% of the increase in land value is imposed. The levy is
1. ₹0.36 lakh
2. ₹4.0 lakh
3. ₹16.0 lakh
4. ₹20.0 lakh
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Answer: B — ₹4.0 lakh
Value before = 3.6/0.09 = ₹40 lakh; after = 4.5/0.09 = ₹50 lakh; increase = ₹10 lakh; levy = 0.40 × 10 = ₹4.0 lakh. Taking 40% of the rent increase gives ₹0.36 lakh, and taking 40% of the old or new value (₹16 or ₹20 lakh) taxes the whole value rather than the increment.
In planning practice, transfer of development rights (TDR) is best described as
1. compensation in kind: the owner of land reserved for public use surrenders it and receives building rights to use or sell elsewhere
2. a one-time charge on owners whose land has gained value because of a nearby public work, collected as a share of that gain
3. borrowing against the extra property tax that an improved area is expected to generate and repaying the whole loan from it
4. pooling of private plots by the authority, which lays out infrastructure and returns smaller serviced plots to owners
Show answer
Answer: A — compensation in kind: the owner of land reserved for public use surrenders it and receives building rights to use or sell elsewhere
TDR pays the owner of reserved land in development rights rather than cash. A betterment charge taxes the increment, tax increment financing borrows against future revenue, and plot pooling describes a town planning scheme.
Which of the following are land value capture instruments in principle?
1. A betterment levy on plots whose value rises because of a new road
2. A uniform city-wide tax on fuel sales, unrelated to where public works are built
3. Tax increment financing around a new station, repaid from the extra property tax of the area
4. Sale of additional FSI beyond the base FSI along a transit corridor
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Answer: A — A betterment levy on plots whose value rises because of a new road; C — Tax increment financing around a new station, repaid from the extra property tax of the area; D — Sale of additional FSI beyond the base FSI along a transit corridor
The levy, TIF and premium FSI each recover part of the value that public investment or planning permission creates on specific land. A fuel tax raises revenue but is not linked to land value created by a public work.
Which feature most clearly separates true Transit Oriented Development from merely transit-adjacent development?
1. A large park-and-ride facility beside the station to draw drivers from the whole region towards the metro line
2. The tallest buildings of the district placed on the plots nearest the station, whatever the street layout or parking around them
3. A single-use office cluster designed to guarantee heavy boardings at the station during the morning and evening peak hours
4. A connected pedestrian street network, mixed uses and limits on parking that put density within an easy walk of the station
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Answer: D — A connected pedestrian street network, mixed uses and limits on parking that put density within an easy walk of the station
TOD is defined by walkable access: a connected pedestrian network, a mix of uses and restraint on parking. Height beside a station, a big car park or a single-use office cluster can all exist without anyone walking to the station.
A metro station has an 800 m walking catchment (a circle). Its pedestrian catchment ratio is 0.6, meaning the area actually walkable within the radius is 0.6 of the full circle. The walkable area, in hectares, correct to one decimal place, is ____.
Numerical answer — type the value.
Show answer
Answer: 120.6
Circle area = π × 800² = 2,010,619 m² = 201.06 ha (1 ha = 10,000 m²). Walkable area = 0.6 × 201.06 = 120.64, i.e. 120.6 ha.
Which of the following are typical challenges of brownfield redevelopment?
1. Possible soil or groundwater contamination that must be assessed and remediated to a standard fit for the intended use
2. Fragmented ownership, legal disputes and the need to rehabilitate former workers or tenants
3. Absence of any road, water or sewer infrastructure nearby, because such land is always remote
4. A rule that every trace of contamination must be removed whatever the intended use of the site
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Answer: A — Possible soil or groundwater contamination that must be assessed and remediated to a standard fit for the intended use; B — Fragmented ownership, legal disputes and the need to rehabilitate former workers or tenants
Contamination, fragmented ownership and rehabilitation of workers and tenants are the usual obstacles. Brownfields are usually well served by infrastructure, which is one of their attractions, and clean-up is normally risk-based and fit for the intended use, not a total removal rule.
From zone i, 12,000 jobs lie 10 minutes away, 18,000 lie 15 minutes away and 40,000 lie 20 minutes away. The gravity accessibility index Aᵢ = Σ Oⱼ/tᵢⱼ is
1. 1,556
2. 30,000
3. 4,400
4. 70,000
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Answer: C — 4,400
A = 12,000/10 + 18,000/15 + 40,000/20 = 1,200 + 1,200 + 2,000 = 4,400. The figure 30,000 is the cumulative count within 15 minutes, 70,000 is simply the total number of jobs, and 1,556 divides total jobs by total time, which is not the formula.
Household P (income surplus ₹24,000 a month, lot 100 m²) and household R (surplus ₹48,000, lot 400 m²) both face a commuting cost of ₹800 per km per month. Using the fixed-lot bid rent Ψ = (surplus − t·d)/lot, which pattern results?
1. R occupies the land nearer the centre, because its larger surplus gives a higher bid at every distance
2. P occupies the land nearer the centre and R the land beyond about 20 km, because P's bid-rent line is steeper
3. P occupies the land beyond about 20 km, because small lots are cheaper for the authority to serve with infrastructure
4. They cannot be separated by location, because both pay the same commuting cost per kilometre
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Answer: B — P occupies the land nearer the centre and R the land beyond about 20 km, because P's bid-rent line is steeper
P bids (24,000 − 800d)/100 = 240 − 8d and R bids (48,000 − 800d)/400 = 120 − 2d. They are equal where 240 − 8d = 120 − 2d, i.e. d = 20 km. P's slope t/q = 8 is steeper than R's 2, so P wins nearer the centre and R beyond 20 km. The tempting answer that R wins everywhere confuses a higher surplus with a higher bid per unit of land.
Zone X produces 1,000 trips. Three destinations have attractions 200, 400 and 400 and lie 5, 10 and 20 minutes away. With a friction factor F = 1/t in a production-constrained gravity model, the trips to the 20-minute destination are
1. 200
2. 250
3. 333
4. 400
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Answer: A — 200
A·F = 200/5, 400/10, 400/20 = 40, 40, 20, with sum 100. The 20-minute destination takes 1,000 × 20/100 = 200 trips. The answer 333 would be an equal split that ignores distance, and 400 is the share of the nearer, equally attractive destination.
Base-year trips are t₁₂ = t₂₁ = 100, t₁₃ = t₃₁ = 200 and t₂₃ = t₃₂ = 100, and the growth factors are G₁ = 1, G₂ = 2, G₃ = 1. Using one pass of Fratar's method, Tᵢⱼ = tᵢⱼ·Gᵢ·Gⱼ·(Lᵢ + Lⱼ)/2 with Lᵢ = Σⱼ tᵢⱼ ÷ Σⱼ tᵢⱼGⱼ, the forecast T₁₂ is ____.
Numerical answer — type the value.
Show answer
Answer: 175
L₁ = (100 + 200)/(100×2 + 200×1) = 300/400 = 0.75. L₂ = (100 + 100)/(100×1 + 100×1) = 200/200 = 1. T₁₂ = 100 × 1 × 2 × (0.75 + 1)/2 = 200 × 0.875 = 175.
A binary logit model has V = −0.05t − 0.01c, with t in minutes and c in ₹. Car: 20 minutes and ₹60. Bus: 40 minutes and ₹20. The probability of choosing the car, correct to two decimal places, is ____.
Numerical answer — type the value.
Show answer
Answer: 0.65
V_car = −0.05×20 − 0.01×60 = −1.0 − 0.6 = −1.6. V_bus = −0.05×40 − 0.01×20 = −2.0 − 0.2 = −2.2. The difference is 0.6. P(car) = 1/(1 + e^(−0.6)) = 1/(1 + 0.5488) = 0.6457, i.e. 0.65.
In a multinomial logit model a car and a single bus have equal utility, so each takes half the trips. A second bus, identical to the first in every attribute except paint colour, is introduced. What does the model predict, and what does it show?
1. Car 50% and each bus 25%; the prediction is acceptable and shows that logit handles similar alternatives well in practice
2. Car 25% and each bus 37.5%, because the new bus draws demand from the car more than from the old bus
3. Car, bus and new bus 33.3% each; two identical alternatives should split one share, so the car's drop exposes IIA
4. Car 50% and each bus 50%, because logit probabilities are independent of each other and need not sum to one
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Answer: C — Car, bus and new bus 33.3% each; two identical alternatives should split one share, so the car's drop exposes IIA
With equal utilities every alternative gets exp(V)/Σexp(V) = 1/3. Because the ratio of two alternatives' probabilities is unaffected by others (IIA), the car loses share to a bus that is a clone of another bus, which is unrealistic. A nested logit that groups the buses fixes this. Logit probabilities always sum to one.
Which of the following statements about trip generation methods are correct?
1. Attractions are forecast mainly from household income and car ownership at the origin zone
2. In cross-classification, the trips of a zone are the sum over cells of households in the cell times that cell's trip rate
3. Fitting a regression at household level uses variation among households within zones, so it can work with a smaller survey sample than a zonal fit
4. A high R² on zonal data shows that each predictor in the regression causes trips
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Answer: B — In cross-classification, the trips of a zone are the sum over cells of households in the cell times that cell's trip rate; C — Fitting a regression at household level uses variation among households within zones, so it can work with a smaller survey sample than a zonal fit
Cross-classification multiplies cell counts by cell trip rates, and household-level regression makes use of within-zone variation. Attractions come from employment, floor space or school places, not from origin-zone household income, and a high R² shows fit, not causation.