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Introduction to Transportation Economics Continued
Utility
Good x
Good y
UtilityA
C
B
D
A good is a commodity where more is preferred to less
Uti
lity
Quantity Consumed
UtilityU
tili t
y p
er
l as t
un
i t
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.
ii
i
n
Q
uMU
Q
QQFU
i alterntive of attributeAn : Where
),....,(FunctionUtility
1
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
MU
QU
QU
2
1
2
1
Utility Maximization Criterion2. Utility maximization
Q1
Q2
u
1p
C
2p
C
MRSp
p
2
1
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
D
D
D’
D’
D’’
D’’
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
? ,, of signs theareWhat
Gasoline of Price PG FareTransit TF
Income I Trips Auto
:)()()(
321
3210
BBB
Dwhere
PGBTFBIBBD
a
a
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
fare transit repect to with tripsautofor
demand of elasticity-Cross The
aD
TFx
TF
D
CostCost functions are derived from production functions
Mach
ines
Labor
Increasing Production
Asphalt Layer per hour
Contours of equal production are Isoquants
Production function
W
C1
W
C2
W
C3
P
C3
P
C2
P
C1Production function
The production function represents the technically optimal level of resources at each level of output
Production function
i
i
i
X
PMP
Xf
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i
i
X
P
iinput in increasean ofresult a as production Marginal)(P function Production
functioncost a develop tousedcan function prodution TheW
P
MP
MPMRS
i
j
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
KZFTC
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
Q
C
Q
C
Q
R
Q
QCQR
Q
R when occursMax Thus
0
)()(
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)
)1(
)1(
Rate
Discount Social
t
iAAi g
g
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
S
S
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.
D
D’
DD’
Short-run supply
Long-run supply
Q
Pi
Pc
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
D’
D’
PI
Pt
P-
Po
Tax
IS
LS
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
21
321
210
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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