Introduction to Transportation Economics Continued

Utility

Good x

Good y

UtilityA

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B

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A good is a commodity where more is preferred to less

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Quantity Consumed

UtilityU

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Quantity Consumed

Marginal Utility

Decreasing marginal utility of consumption

Utility is the variable whose relative magnitude indicates the strengths of preferences. In finding the most preferred position, the individual maximizes utility.

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Indifference Curves

Speed Q1

Comfort Q2

Increasing Utility Points of equal

Utility – IndifferenceCurves

Utility1. Marginal rate of substitution is the rate at which one good can

traded for another and remain on the same indifference curve

Q1

Q2

u

MRSMU

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QU

QU

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Utility Maximization Criterion2. Utility maximization

Q1

Q2

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MRSp

p

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Substitution

Q1

Q2

u

3. Substitution effect is the substitution of one good for another to maintain the same utility when price change

Income Effect

Q1

Q2

Income Expansion Path (IEP)

Type of Good

Q1

Q2

Income Expansion Path

Inferior good

Superior Good

Any good that decreases in consumption with increasing income is an inferior good. All other goods are superior goods.

Income effects on demand

p

Q

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Superior good

Inferior good

Price Expansion Path

Q1

Q2

Price expansion path

If we can derive price and quantity from the price expansion path, what important relationship does this provide?

Demand Equation

Cross elasticity example

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Gasoline of Price PG FareTransit TF

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Cross Elasticities

Complementary Goods: Those goods which the access to one impacts the utility of the other:

Right Shoes and Left Shoes Autos and Gasoline

Substitutes: Those pairs of goods which perform similar functions

Butter and Margarine Transit Trips and Auto Trips

Cross Elasticities

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demand of elasticity-Cross The

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CostCost functions are derived from production functions

Mach

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Labor

Increasing Production

Asphalt Layer per hour

Contours of equal production are Isoquants

Production function

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P

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P

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C1Production function

The production function represents the technically optimal level of resources at each level of output

Production function

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Types of costs

Fixed – Variable costs Long-run and Short-run Marginal, average, and total costs Joint and traceable costs Past and future costs Opportunity and outlay costs Capital costs

Fixed-cost

Fixed-costs are paid regardless of the output level or level of use of a resource. Examples

Rents Property taxes Salaries to contracted employees Insurance

Variable costs Variable costs are costs that change with levels of

output and inputs and when throughput is zero, variable costs are zero.

Examples: Fuel Costs Wages to non-contract employees Expenses

TC=F+V(X1, …., Xn)TC = Total CostF = Fixed costsV = Variable costs functionsXi = inputs, outputs or throughputs

Importance of fixed and variable costs

Which transportation industries feature high fixed costs as compared to variable and which ones are the reverse?

Why is scale important to high fixed cost transportation carriers?

Long-run and Short-run

Short-run costs are the costs incurred over a fixed capacity system. “Operating Cost Function”

Long-run costs are costs incurred over capacity adjustments or technology changes. “Planning costs functions”

Long-run and Short-run costs

$

Q

Long-runaverage cost

Short-run average cost

Marginal, average, and total costs

Average cost is the average cost per unit of output

Marginal cost is the costs of the jth output

ACQuantity

costs Total

Q

TCMC

TCTC jj

11

Kinds of Costs Functions

Increasing average cost

1

1 1 Where

KZMC

KZZ

FAC

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Cost functions

MC

AC

Variable cost

Economies to Scale

Diseconomies toScale

Engineering Efficient Operating Point

Quantity

$

Cost functionDecreasing average costs function 1

TC

AC

MC

Q

F

$

Marginal costs

Marginal costs are the key to optimality, as are all marginal values.

MC = The cost of the last unit produced

When P> MC & AC<MC Then producers will produce more When P< MC & AC< MC Then Producers will produce less

When P=MC optimal conditions for the market

Suppose a producer can decide to select any level of output that they desire to produce (monopoly)

What level would a monopolist chose to produce?

Pick q Such that Max = R(Q) – C(Q)

R(Q) = revenue function C(Q) = Cost function

Assuming a linear demand function

Elastic Inelastic

MR

MC

Total Cost

Total Revenue

Max

$

QProfits are maximized when MC = MR

A monopolist will restrict capacity to a lower level than will a competitive market

Calculus of profit maximization

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Opportunity, Shadow prices and Outlay Costs

Opportunity Costs are the value forgone by having the resources used in a particular project.

Shadow price is the impact on the result of one less unit of input.

Outlay costs are the costs themselves

Cost of Capital

Capital cost is the time value of money

What should be the cost of capital for a public project?

How do we determine the time social discount rate

The social discount rate should be established so that society is compensated (accrues benefits) at a rate equal to or higher than what they would earn on their own.

Discount rates

Private sector analogy: Capital can be used for two purposes

1. Consumption

2. Investment Thus to attract money for investment, it must

offer the individual a greater return than consumption

Public Sector Social discount rate is the value were society is

indifferent between personal consumption and investment.

Theoretically how you would calculate the social discount rate

Opportunity costs of consumption > ig Opportunity costs of investment > ig/(1-t)

Where:

ig = Interest on risk free government bonds t = tax rate on investment

If A is the portion of all income that goes towards consumption (0< A <1)

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Discount Social

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Theoretical calculation of social discount rate continued

If t = 0.5

Social discount rate is about (2-A)ig

How it is actually done in the U.S.

Federal AverageGovernment= Opportunity – Risk - InflationDiscount Cost of Rate Private

InvestmentAssumption – the federal government invests in so many projects that the probability of failing (in total) is nearly zero. Therefore, the federal government should not have to pay a risk premium

Implication of Inflation

Joint and traceable costs

Traceable costs are those that can be attributed to one use (ie. The cost of HOV lanes is a cost that is directly traceable to commuter traffic)

Joint costs are those that can not be attributed to one use (ie., is the cost of highway attributable to freight or passenger cars)

Past (sunk) and future costs

Sunk costs are not recoverable and therefore, should be brought into decision making.

Future cost are the only costs important to decision making. Past costs should be used to project future costs.

Benefits of Transportation (engineers perspective)

Demand

H

CBPb

Pa A D

Consumer Surplus for price Pb

Suppose that through a traffic management system, travel times are reduced making the trip price Pa, The benefits are increase by the area ABCD.

Benefits of Transportation (economist perspective)

Net Benefits

Benefits of Transportation (economist perspective)

Total Cost

Benefits of Transportation (economist perspective)

Net Benefits = Total Benefits –Total Cost = Consumer Surplus

Benefits of Transportation (economist perspective)

Supplier Surplus

Intermodal changes in real price of service

Suppose a new light rail service is opened between West Des Moines and Des Moines

S’

S

Transit Demand

Benefits

Demand on I-235

D’

D

D’D

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Pricing criteriaIn a non-competitive market, a producer will attempt to produce so that marginal cost = marginal revenue = price

However, in a competitive market a producer can not with holds supply, new suppliers will enter until price = marginal costs.

Methods to adjust Q

In markets where there is no competition or markets are not appropriately clearing, q can be adjusted by through pricing – tolls, taxes, tariffs, or through supply restrictions – price ceilings, metering, restricting permits, rationing

Optimal Toll = Short Run Marginal Costs –Short Run Average Cost

TollShort Run Marginal Cost

Short Run Average Cost

D

D

Toll

Different supply-demand relationships

Low demand facility

Short Run Marginal Cost

Short Run Average Cost

D

D

Subsidy

Questions to ask about low demand markets

Is demand likely to increase in long-run

Should a subsidy be used to make-up the differences?

Should price discrimination be permitted?

D

D

D’

D’

SRMC

SRAC

LRAC

Increased demandPushes for increased capacity

In the long-run, the market will cause expansion along the longrun curve

Question for high demand locations regarding marginal pricing Improper pricing may have lead to

improper locational decisions. Do public agencies have the responsibility to price to prevent misallocations?

Marginal cost pricing tends to price-out low-income classes?

What is done with the profits if transportation facilities can not be expanded?

Those that are tolled are likely to be worse-off than the initially were in the short-run. What about their losses?

Example of marginal costing in high fixed cost industries

Charging developers for improvements to off-set the impacts on traffic facilities

Airlines

Telephone

Price ceilingsImmediatesupply

Perceived short fall

D

D’

DD’

Short-run supply

Long-run supply

Q

Pi

Pc

Windfall profit =(Pi – Pc)QCeiling prices stop consumers from losing wind fall profits but stop the forces which cause the development of supply

Price ceilingA price ceiling distributes supply with respect to price Pc but does not allow those that are willing to pay Pi to receive what they are willing to pay for. Thus, some consumers may benefit at the expense of other.

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Short-run supply

Long-run supply

Q

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Tax

Tax advantages Shortage is eliminate; supply and demand

are in balance There is no windfall benefit to suppliers.

Buyers will lose consumer surplus, but the windfall amount goes to the government.

The limited supply avaialbel impmediately is allocated only to those willing to pay at least Pi

There are not tendencies for supply over expanding

Tax plus Price Ceiling

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Qo Q’Pt = Gross PriceP- = Net price Windfall profit = P- -Po (Q0) (P- - Po)(Q’-Qo)

2

More on Costs Generally there are economies to scale in

transportation in long-run

Ship Size (thousand of dwt) 15 25 41 61 120 200Index of Size 100 167 267 423 793 1318Capital Cost Index 100 140 197 291 457 641Operating Cost Index (excluding fuel) 100 121 134 155 201 275Fuel Consumption Index 100 155 230 353 578 843Crew Size 31 38 38 38 38 38

Bulk Containers Ships

From Gross and Jones

Counter veiling forces

Almost uniquely, users of transportation services pay with their own time or resources Private transportation – user time and

safety costs Freight shipments – costs of inventory,

storage facilities, terminals

Examples of relative costs

Crew 10.91% Fuel 16.50%Fuel 24.28% Spares 4.40%Maintenance 9.13% Tires 3.80%Depreciation 6.68% Other Materials 0.70%Landing Fees 6.01% Maintenance 8.90%Ground services 16.26% Drivers and technician 33.30%Passenger services 6.90% Registration and insurance 6.20%Ticketing and promotion 15.81% Depreciation and interest 10.20%Other 4.01% Buildings 7.70%

Other Staff Wages 8.30%

Air Carrier Trucking

Higher fixed cost services enjoy economies of density

Air fare (Oct. 10, 2006 on Orbitz)Next week on a week day airfare Los Angles to New York 298$ Los Angles to Washington D.C. 322$ Los Angles to Buffalo 306$ Los Angles to Harrisburg 607$ Los Angles to Cleveland 330$ Los Angles to St. Louis 218$ Los Angles to Des Moines 410$ Los Angles to Madison 430$ Los Angles to Topeka 491$

Cost of transportation We generally deal with generalized cost of

transportation These are the sum of the costs component of a trip

Parking Travel time Access costs Parking cost Terminal costs Etc. Holding cost of freight in transit

Not included are costs associated with opportunity costs (what else would you be doing with your time) and cost of interrupting synchornus activities

Reason for misrepresentation of costs

Money and time cost is so small that it is not worth taking into account

Certain variable costs are wrongly assumed fix costs Depreciation of vehicle due to travel

When selecting life style and habits users are not aware of the full cost implecations.

Externalities Costs that are not directly borne by those

generating them What are some externalities? Are auto pollution and auto congestions

externalities? Why might they be viewed differently?

Benefits that are not directly borne by those generating them Wide roadways make good fire breaks Improving waterways for barge traffic reduces

the mosquito population

Optimal level of externalities

$

Environmental improvement

Marginal Benefits

Marginal Cost

e.g. feweremissions

e.g. few cancerdeaths

Optimal levelOf improvement

Entire fleet of vehicle Operating on Hydrogen

How do we value externalities

Stated preferences tests Very difficult to evaluate behavior

through hypothetical situations Revealed preferences tests

The problem is decisions regarding externalities and aversion to externalities represent a trade-off of a variety of incomparable trade-offs.

Model evaluating airport noise

Utility before airport

Utility after airport

Compensation need to maintain utility level

Wealth

Utility

Typical air pollutant

Sources of pollutant UK sources of CO2 emissions

House hold 25% Power stations 52% Refineries 5% Other Industries 37% Transport 31% (growing) Other 9%

Typical transportation pollutant Gasoline engines (in parts per million while

cursing) (From Button, 2003) Carbon monoxide (27,000) Hydrocarbons (1,000) Nitrogen oxides (20) Aldehydes (10)

Diesel engines Carbon monoxide (trace) Hydrocarbons (300) Nitrogen oxides (240) Aldehydes (10)

Value of Travel Time Why is it so tough to determine a value for

travel time Not all segments of time have the same value

How valuable is a minute less of having root channel?

How valuable is a minute less of sitting in first class sipping Champaign

Time is non-linear with amount of time How valuable is it to save 30 seconds ten times How valuable is it to save 5 minutes one time

The value of time varies with alternative uses for time

If you are commercial driver, your value of time is your wage

If you are drive to the grocery store on a Saturday, what is the alternative use of your time and what is its value?

How do we come up with one value of time when individual make different wage rates?

Earliest and most commonly used theory

An individual has the opportunity to assign his/her time to working or consumption. At the margin, these activities should

offer the same utility Thus time should be valued at users true

wage rate Wage minus taxes, insurance, etc.

Discrete travel choice models

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Example discrete travel time value modelBeesleygraph (Professor Beesley, 1978)

C

T

Option 1 more expensiveslower

Option 1 less expensiveslower

Option 1 more expensiveFaster

Option 1 less expensive faster

Beesley, M.E., “Value of time, modal split and forecasting,” in Behavior Travel Modeling, London:Croom Helm, Chapter 21, Part 7

C

T

Red dots select option 2Green dots select option 1

Slope is equal to the value of time

Select a line which minimizes the miss allocations. This case has six mis-classification score

Common discrete modeling methods

Revealed preference (RP) Actual decisions Problems with correlation between

Travel costs Travel time Travel Time reliability

State preference (SP) Hypothetical situations Problems with SP

Hypothetical choices

SR 91

SR 91

SR 91 evaluation, Small, Winston, and Yan

Example toll West bound $1.65 (at 4 – 5 am M-Thr) West bound $3.30 (at 7 – 8 am M-Thr) HOV (3 or more) pay half.

Reveal preference Median value of time $20.20/hour or 87

percent of wage rate Median value of reliability $19.56/hour

Small, K.A., Winston, C., and Yan, J., “Uncovering the Distribution of Mororists’s Preferences for Travel Time and reliability: Implications for Road Pricing, August, 2002.

Selected discrete choice model variables

Median household income Median travel time Unreliability of travel time Female driver Age Flexible arrival-times

Value of freight travel time Depends of perishability of good

transportation Average about $40 per hour (European studies) Average about $75 per hour opportunity cost to

carrier More important is travel time reliability

Depending synchronous activities Ranging from $40 per hour to $1,200 per hour