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Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics
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Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Dec 31, 2015

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Page 1: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Transportation Economics and Project Evaluation

Evaluation process safety in evaluation process and intro to micro economics

Page 2: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Objectives of project evaluation An objective and consistent method for the

making of investment decisions Which alternative design for a project should we

select? Which competing alternative approach should

we invest in? Which project or projects should we invest in? What category of projects would it be most

productive to invest in? E.G., streets or water distribution

Page 3: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Exception Methodology Manage by exception

Invest what you have always invested unless an exception arises

Example City capital improvement budget – invest

at the same level for every city service with a small increase for inflation.

Budget for contingencies where system exhibits a chronic problem (e.g. excessive congestion)

Page 4: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Pros and Cons of Exception Method

Pros Easily understood by decision makers Requires minimal amount of decisions

support systems Cons

No basis for making efficient decisions No basis for making trade-offs between

categories Perpetuates past misallocation of

resources

Page 5: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Traditional approach (popular) Performance measurement

Manage the performance of existing system Pavement roughness Delay encountered while traveling in system Travel speed Travel times Etc.

Establish minimum levels of performance Invest in projects which provide the maximum

improvement in performance for dollars spent.

Page 6: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Pros and Cons of Traditional Approach

Pros Manages to measurable criteria Builds on good management practice Supportable to public and decision makers

Cons Supports past legacies decisions Difficult to make comparisons between

investment categories Supports past misallocations of resources

Page 7: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Economic Evaluation (big idea) Levels of decisions

Operating and maintenance budget decisions What level of performance

Project design level decisions Design decisions regarding a project User benefits of competing designs are assumed equal

Project selection decision Give a number of alternatives for a project which one should be

selected. Mutually exclusive options

Network decisions Given a number of projects, which one should be invested in and

when Non-mutually exclusive options

Program allocation decisions Which category of investment should we invest in? Safety improvements or congestion reduction?

Page 8: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Operating budgeting decisions

Operating allocation – Budget to Meet performance identified in selection decision

Project selection process assumes operating costs allocation when the selection is made

Page 9: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Example project selectionPerf

orm

ance

level

Time

Maintenance Treatment

Reconstruction

Project 1

Perf

orm

ance

level

Project 2

Each assumes its ongoing cost of maintenance

Page 10: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Project Design Selection Criteria

Select project designs which Minimizes Life Cycle Costs

Assumes that all design alternatives provides similar user benefits

Meets budget requirements Able to achieve minimum design

standards

Page 11: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Project Selection Decision Selects project from feasible alternatives Projects are mutually exclusive

Example – Two different alignments Benefit and costs streams of project

alternative vary Comparison methodologies

Benefit to cost ratio Minimum present worth Maximum internal rate of return

Comparison of incremental benefits and costs

Page 12: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Network Decision Making Planning level decision making

Should we invest in reconstructing the freeway in Council Bluffs, Davenport, four-laning U.S. 30, etc.

Non-mutually exclusive decisions Compare the benefits and costs of one

project to another Decision making criteria

Select project with greatest benefit to costs ratio Continue to select project until budget is

exhausted or there are not more cost beneficial projects.

Page 13: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Program Allocation Decisions There will always be projects where

the benefits exceed the costs so which category of activity should we invest? Example – should we be investing more

in education and less in transportation services?

Example – should we be investing more in winter maintenance and less in bridge maintenance?

Page 14: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Program allocation decision

Trade-offs between categories are very difficult

Rarely done based on economic information

Political and equity concerns conflict with pure economic rational (deep thought)

Page 15: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Benefit – Cost analysis Since transportation benefits are reduced

cost, costs and benefits often get confused. Costs are associated with the facility

Capital costs Construction costs Right-of-way costs Vehicle cost (if they are owned by the operator)

Maintenance costs Facility operation

Page 16: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Benefit-Costs analysis Reduced costs that are associated with benefits are

related to the users Travel time costs

Total hours and cost of system travel Travel time reliability

Vehicle operating costs Fuel Oil Insurance Maintenance Depreciation (vehicle ownership costs) Tires

Crash costs

Page 17: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Estimates of User Cost Savings Travel time reductions

Demand models Travel time reliability – user benefits are

difficult to measure Vehicle costs

Measure through historical data Value of reduced deaths and injuries

Technical costs are easy to measure Human loss is difficult to measure

Page 18: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

What is a human life worth Industry must make trade-offs between

safer cars and profits Government must make trade-off between

safer roads and expenditures on highways Users make trade-offs between the

likelihood of dying and travel convenience How many of you would like to drive at 5 mph?

Page 19: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Example 1 of Calculation Ford Pinto Gas Tank Guard caseFord calculations

Ford costsGuard costs $11 per guardProject run of pinto – 12.5 millionTotal retrofit cost $135,000,000

User cost44 excess fatalities530 excess injuries7,500 excess PDOs

Page 20: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Example 1 continued

Societal cost of excess fatalities and injuriesFatal $200,000 (NHTSA and Safety

Council average)Injury accident $67,000 (very high)PDO $700

Total societal costs = $49,500,000B/C = 2.8 in favor of not doing the retrofit

Page 21: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Example 1

Was Ford right or wrong?Why?

Page 22: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Example 2 Right Turn on Red

Estimated national savingsUser savings – 1.4 gallons/veh/year

- 10 seconds/driver/dayUser costs - 22 excess fatalities

- 900 excess injuries- 10,300 PDO

B/C = 7.3 in favor of right on red

Page 23: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Comparison of two examples

Are you in favor of right on red?Is right-on-red worth the extra fatalities?

Why is it that we feel better about the decision to adopt right-on-red and not about Ford’s decision?

How much should we be willing to spend to save a human life?

Page 24: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Example 3The 9 Pennsylvania Miners that were

trapped were rescued after 77 hours of drilling

The initial cost estimate of performing the rescue was $10,000,000 with a low probability of success (assume 25% probability of success)

Assume value of human life is $2.5 million

2.5*0.25*9 = $5.625 million $5.625/$10 = B/C = 0.6

Page 25: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Why are we inconsistent in our perspective on human lifeAnonymity

“Identifiable Victim Effect”Jessica McClure, 9 Pennsylvania Miners

Assumed riskWhen the individual has accepted a higher level of risk

AstronautSky diver

Page 26: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

How Should We Settle the Costs The nine miners rescued

Actual cost – approximately $6 million The mining company cannot afford to

cover these costs. U.S. Rep. John Murtha, of Johnstown,

obtained a $2 million federal grant State of Pennsylvania shelled out about

$2 million Remaining balance owed private

contractors is about $2 million How should we cover the unpaid

cost? Disney is paying each miner

$150,000 for their story – should this money be used to cover the costs?

Page 27: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

So on what basis should we make decisions?

We need to recognize that people are willing to buy some benefits with human lifeOtherwise the speed limit would be 10mph.

Page 28: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

How do we determine the value of Human Life

Societal value of life is the value to save one life.Not a specific lifeNot what you value your own lifeIt is a statistical life

Page 29: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Methods for valuing lifeWillingness to pay – what are we willing to pay

to reduce total deaths by one fatalitySince this is not a situation that is present in reality, we establish analogous situations.Suppose that 5 million people were willing to buy a car

with $100 safety improvement that would reduce their risk of dieing in car crash by one in 5,000. Thus we would be willing to pay $500 million to save 1,000 lives. Therefore, at a minimum society is willing to pay $500,000 for a life saved.

Included in the willingness to pay is the willingness to pay to avoid the pain and suffering to avoid injury or death.

Page 30: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Pain and Suffering

Accounting for the quality lifeQuality-adjusted life years lost (QALY)Value assigned to a perfect health year = 1Value assigned to a year of death = 0 Injuries fit on the continuum between 1 and 0

Page 31: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Methods for valuing human life cont.Direct-costs avoided

The amount of costs directly avoided by reducing by a single death.Medical costsEmergency servicesInsurance administrationEtc.

Human capital approachThe amount of economic value lost by a single death or injury.

Page 32: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

NHTSA values for injuries and fatalities

Item Individual Cost Percent of TotalMedical $22,095 0.66%

Emergency Service $833 0.02%

Market Productivity $595,358 17.69%

HH Productivity $191,541 5.69%

Insurance Administration $37,120 1.10%

Workplace Costs $8,702 0.26%

Legal Costs $102,138 3.03%

Travel Delay $9,148 0.27%

Property Damage $10,237 0.30%

Quality of Life $2,389,179 70.97%

2000 value of human life $3,366,351 100.00%

Page 33: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

What are states doing (1993 Survey)Forty-five states assign a dollar value to fatality

Five states do not assign a dollar value but use priorities

Three clustersEighteen states clustered around $500,000Fourteen states clustered around $1.5 million

Eight states between $2 and $3 millionMean value $1,209,704

Page 34: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Factors Causing Crashes

Driver Vehicle Roadway Environment

Page 35: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Economic Cost of Crashes

Cost to society: $230.6 billion/ year medical, rehabilitation and long term

care cost ( $ 32.6 billion) Work place lost productivity $59 billion lost tax revenue (adding $200 from each

household) property damage $59.8 billion Travel Delay $25.6 billion

Source NHTSA

Page 36: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

National Crash Frequency

Fatal Crashes – 37,795 Injury Crashes – 2,003,000 Property Damage Crashes –

4,282,000 Total killed 42,116 (5,500 were peds

and cyclists)

Page 37: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

National Crash Frequency Fatal

1.51 Per HMVM 14.79 per 100,000 people 19.04 per 100,000 vehicles 22.02 per 100,000 licensed drivers

Injury 109 per hmvm 1,065 per 100,000 people 1,371 per 100,000 vehicles 1,585 per licensed driver

Source - FHWA

Page 38: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Fatal Crash Trends

Source – FHWA Crash Facts Book

Page 39: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Crash Rate Trend

Source – FHWA Crash Facts Book

Page 40: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Age Distribution of People Killed

Source – FHWA Crash Facts Book

Page 41: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Fatality Rate by Age

Page 42: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Iowa Crashes (2000)

445 fatalities 100 had BAC > 0.1 63,371 crashes 35,974 injuries

Page 43: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Iowa Fatal Crash Trends

Page 44: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Crash Rate Calculation

Accounts for volume May account for vehicle miles traveled (VMT)Crash rate =

where:n = analysis time period in years (5 years for the Iowa DOT) DEVnode = actual daily entering vehicles for nodes and

average daily traffic for road segments (for road segments up to 0.6 miles long and spot locations)

DEVlink = Absolute value of [(Link length/0.3)x(Actual DEV)]

(for road segments 0.6 miles and longer)

days/year) (365years) ( (DEV)

)(10 crashes) of(Number 6

n

Page 45: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Crash Rate Example

350 crashes over 5 years10,000 vehicles enter the intersection daily

Crash rate =

days/year) (365years) ( (DEV)

)(10 crashes) of(Number 6

n

= _____(350 x 106)_____ = 19.2 crashes per million vehicles

(10,000) x 5 x 365

Page 46: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Severity

Measures seriousness of accidents Iowa DOT (2001 values)

Fatality: $1,000,000 Major Injury: $150,000 Minor Injury: $10,000 Possible Injury: $2,500 Property damage: actual value or $2,000

if unknown

Page 47: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Crash Trend

Mn/DOT Traffic Safety Fundamentals Handbook

Page 48: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Fatality Rates in Upper Midwest

Mn/DOT Traffic Safety Fundamentals Handbook

Page 49: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Location of Crashes

Mn/DOT Traffic Safety Fundamentals Handbook

Page 50: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Crash Rates by Functional Class

Mn/DOT Traffic Safety Fundamentals Handbook

Page 51: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Crash Rates by Design Standard

Mn/DOT Traffic Safety Fundamentals Handbook

Page 52: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Crash Frequency on Mn Expressways

Traffic Safety Performance Function

Crash Density = 2x10-6(ADT)1.4632

0

5

10

15

20

25

0 10,000 20,000 30,000 40,000 50,000

Segment ADT

Cra

sh F

req

uen

cyC

rash

es p

er M

ile p

er Y

ear

Page 53: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Crash Frequency on Iowa Expressways

Traffic Safety Performance Function

Crash Density = 2x10-5(ADT)1.2896

0

2

4

6

8

10

12

0 5000 10000 15000 20000 25000

Segment ADT

Cra

sh F

req

uen

cyC

rash

es p

er m

ile

per

ye

ar

Page 54: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Crash Type Distribution

Mn/DOT Traffic Safety Fundamentals Handbook

Page 55: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Crash Rate per Accesses

Mn/DOT Traffic Safety Fundamentals Handbook

Page 56: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Crash Rates by Intersection Control

Mn/DOT Traffic Safety Fundamentals Handbook

Page 57: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Crash Type by Intersection

Mn/DOT Traffic Safety Fundamentals Handbook

Page 58: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Improving Safety 3 aspects

Driver Driver training Blood alcohol limits Speed limits Driver license restrictions

Road Design Maintenance operational

Vehicle Vehicle design has improved Air bags Better tires

Page 59: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Introduction to Economics Economics is the study of scarce resources.

Micro Economics is concerned with individual consumers and producers and groups of producers and consumers known as markets

Macro Economics is concerned with economic aggregates or the economy as a wholeMicro Economics Macro EconomicsPricing UnemploymentDemand InflationSupply Monetary policy

Page 60: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Elements of Economic Systems

Scarcity – all goods and services have relative degrees of scarcity

Activities Consumption of goods or services Production, conversion of inputs to

outputs Exchange – trading objects for other

objects

Page 61: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Markets – Demand-Supply Relationships

Demand Curves – The relationship between price and quantity consumed.

Price

Quantity

Page 62: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Characteristics of Demand Demand refers to a relationship

Quantity demanded refers to a point in the relationship

Demand is a reflection of wants and not needs

Demand curve defines what people would do when faced with certain conditions

Quantity demand is a function of time Demand curves slope downward to the

right

Page 63: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Market demand

Individual 1 Individual 2 Market Demand

Q1 Q2 Q3 Q4

P1

P2

Q1+Q3 Q2+Q4

2. Market Demand consists of two or more demanders of a good

Page 64: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Characteristics of Demand Market demand always has a slope that is

greater or equal to individual demand curves Price elasticities of demand is a

measurement of the relative relationship between price and quantity demand. Slope is no good because it is dependent on scale

DD

QQ

1

10

0

10

d

PPP

QQQ

Page 65: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Arc Elasticity

$6.00

$4.00

12 18

5.133.0

5.0

646

121812

Q

P

P

Q

P

P

Q

QPoint Elasticity

Page 66: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Properties of Elasticities Dimensionless Demand elasticities are always negative Demand elasticities are discussed in terms

of absolute valueLess then 1 = inelasticEqual to 1 = unitary elasticGreater than 1 = elastic

The elasticity of demand curves change across the entire range of the curve

Page 67: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Elasticity of Demand Curves

2/

)(

Function Demand

pq

Price

Quantity

1

Region Elastic

p

1

Region Inelastic

p

Unit Elasticity

Page 68: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Constant elasticity

0

0.5

1

1.5

2

2.5

3

3.5

0 5 10 15 20 25

5.13 PQ

5.3 PQ

Page 69: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Elasticity

Q

P

P

Q

P

P

QElasticityPo

Qint

5.13

*5.4

5.4

3

5.1

5.2

5.2

5.1

P

PP

PP

Q

PQ

p

Page 70: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Elasticity

DP*

- EP

Infinitely Elastic Demand

Page 71: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Elasticities

Would you expect transportation to be elastic or inelastic?

How would elasticities vary in the short and long runs?

Page 72: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Gasoline demand in the short run and the long run

DSR

DLR

People tend to drive smaller and more fuel efficient

cars in the long-run

Gasoline

Page 73: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Supply Curves The relationship between price and the

quantity produced Characteristics of Supply

Supply is a relationship but quantity supplied refers to a specific point along a supply curve

Supply defines what a producer would actually do, not what he or she would like to do.

Quantity supplied is always measured in time units.

Supply curve for normal goods slope upward and to the right

Page 74: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Supply – Demand analysis The study of supply – demand relationships

with respect to change

Problem – How do you know if you identified two points on a supply or a demand curve

Analysis of supply and demand can be done with either time series or cross sectional data

D

D

SS’

S’

D’

D’

D

DS

S

Page 75: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Time series Examining a phenomena's change through

time Changes in prices related to a good’s

demand. For example, price of gasoline is related to

demand for new cars (demand shift) Changes in prices of related to a goods

supply. For example, better opening a parralle route

would reduce congestion and, hence, change shift supply (supply shift)

Changes in income levels (demand Shift)

Page 76: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Cross-Section Analysis Changes in the real price of a good.

For example, changes in the real price of service as locations from different distances are examined (supply shift)

Changes in the real prices of alternative good. For example, the quantity of auto travel demand

relative the available of transit (demand shift) Change in income levels of cross sections

(demand shift)

Page 77: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Equilibrium Markets

q1

p1

q2

p2

q3

p3

Page 78: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Network Equilibrium

The paths through the network represent an equilibration between supply and demand

Page 79: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Wardrop’s principles Wardrop's first principle states: The journey times in

all routes actually used are equal and less than those which would be experienced by a single vehicle on any unused route. Each user non-cooperatively seeks to minimize his cost of transportation. The traffic flows that satisfy this principle are usually referred to as "user equilibrium" (UE) flows, since each user chooses the route that is the best. Specifically, a user-optimized equilibrium is reached when no user may lower his transportation cost through unilateral action.

Page 80: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Wardrop’s principles Wardrop's second principle states:

At equilibrium the average journey time is minimum. This implies that each user behaves cooperatively in choosing his own route to ensure the most efficient use of the whole system. Traffic flows satisfying Wardrop's second principle are generally deemed "system optimal" (SO).

Page 81: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

Marginal Quantities

1

1

10

10 Q

P

TR Revenue Marginal

icePrQuantity

Revenue Total Revenue Average

Quantity x Price Revenue Total

Q P TR AR MR

0 10 0 0 0

1 9 9 9 9

2 8 16 8 7

3 7 21 7 5

4 6 24 6 3

5 5 25 5 1

6 4 24 4 -1

7 3 21 3 -3

8 2 16 2 -5

9 1 9 1 -7

10 0 0 0 -9

Page 82: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

25

0

0 5 10

Total Revenue

Page 83: Transportation Economics and Project Evaluation Evaluation process safety in evaluation process and intro to micro economics.

p

q

10

10 5

AR

MR

66.06

41)6,4(

5.14

61)4,6(

15

51- 1

10

)5,5(

Demand ofty Elasticiti

d

QP

QP

P

Q

QP

Q

P

P

QQP

d

d

Average quantity is falling the marginal quantity is below the average.Average quantity is rising the marginal quantity is above the average Quantity.