Transcript Pricing - Civil and Environmental Engineering

Civil Systems Planning
Benefit/Cost Analysis
Scott Matthews
12-706 / 19-702
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Announcements
(Group) Project 1 Feedback so Far
HW 3 Out
Read Facility Case for Wednesday
Case Study Writeup Due (NO late accepted)
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Profit Maximization under Perfect
Competition
P
P
S = MC
S
D
p
p = MR
D
q
Q
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Q
3
Allocative Efficiency
Allocative efficiency occurs when MC = MB (or S = D)
Equilibrium is max social surplus - prove by considering Q1,Q2
Price
S = MC
b
P*
D = MB
a
Q1
Q*
Q2
Is the market equilibrium Pareto efficient?
Yes - if increase CS, decrease PS and vice versa.
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Quantity
4
Deadweight Loss
Price
A
CS1
P2
B
P*
0
1
2
Q*
Q1
Quantity
Yellow paid to gov’t as tax
Green is pure cost (no offsetting benefit)
Called deadweight loss
Consumers buy less than they would w/o tax
(exceeds some people’s WTP!) - loss of CS
There will always12-706
be and
DWL
when tax imposed
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Monopoly - the real game
One producer of good w/o substitute
Not example of perfect comp!
Deviation that results in DWL
There tend to be barriers to entry
Monopolist is a price setter not taker
Monopolist is only firm in market
Thus it can set prices based on output
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Monopoly - the real game (2)
Could have shown that in perf. comp.
Profit maximized where p=MR=MC (why?)
Same is true for a monopolist -> she can
make the most money where additional
revenue = added cost
But unlike perf comp, p not equal to MR
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Monopoly Analysis
MC
In perfect competition,
Equilibrium was at
(Pc,Qc) - where S=D.
Demand – horizontal line
But a monopolist has a
Function of MR that
Does not equal Demand
Pc
So where do they supply?
MR
Qc
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D
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Monopoly Analysis (cont.)
MC
Pm
Monopolist supplies
where MR=MC for
quantity to max.
profits (at Qm)
But at Qm, consumers
are willing to pay Pm!
Pc
What is social surplus,
Is it maximized?
Qm
MR
Qc
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D
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Monopoly Analysis (cont.)
MC
What is social surplus?
Orange = CS
Yellow = PS (bigger!)
Pm
Grey = DWL (from not
Producing at Pc,Qc) thus
Soc. Surplus is not
maximized
Pc
Qm
MR
Qc
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Breaking monopoly
D Would transfer DWL to
Social Surplus
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Natural Monopoly
Fixed costs very large relative to variable costs
Ex: public utilities (gas, power, water)
Average costs high at low output
AC usually higher than MC
One firm can provide good or service cheaper
than 2+ firms
In this case, government allows monopoly but usually
regulates it
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Natural Monopoly
Faced with these curves
Normal monop would
Produce at Qm and
Charge Pm.
a
Pm
We would have same
Social surplus.
d
P*
b
Qm
MR
e
AC
c
MC
Q*
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But natural monopolies
Are regulated.
D What are options?
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Natural Monopoly
Forcing the price P*
Means that the social
surplus is increased.
DWL decreases from
abc to dec
a
Pm
d
P*
b
Qm
MR
e
Society gains adeb
AC
MC
c
D
Q*
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Other options?
Q0
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Monopoly – Other Options
Other options - set P = MC
But then the firm loses money
Subsidies needed Phone
to keep
in business
service
Give away good for free (e.g. road)
Free rider problems
Also new deadweight loss from cost
exceeding WTP
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Making Cost Functions
Fundamental to analysis and policies
Three stages:
 Technical knowledge of alternatives
 Apply input (material) prices to options
 Relate price to cost
Obvious need for engineering/economics
Main point: consider cost of all parties
Included: labor, materials, hazard costs
Pricing Strategies
Highway pricing
If price set equal to AC (which is assumed to be TC/q
then at q, total costs covered
p ~ AVC: manages usage of highway
p = f(fares, fees, travel times, discomfort)
Price increase=> less users (BCA)
P=MC: maximizes economic efficiency (why?)
more users, higher price
Might want to set p=MSC
PA Turnpike Commission
Revenues and Costs
Also Post-Gazette, “Turnpike tolls to rise”, 9/14/03
2005 Data: Toll Revenue $545 million
Distribution: 57% commercial, 43% cars
537 miles in length
5.62 billion vehicle miles travelled
Annual maintenance $43 million
60 fare collection facilities
Annual fare collection costs $60million
Overall tolls $545 M/ 5760 M miles
Average toll: X cents per mile
Looks like $500M revenue, $100 M cost

Newer data http://www.paturnpike.com/geninfo/2006_Annual_Report_PTC.pdf
Where is the rest of cost?
“Construction” or major renovations are not paid
for out of operating revenues
They are paid for by selling bonds
Then the yearly interest is paid as cost
What must current debt load be, assuming the rest of
the ‘cost’ is debt expense?
If ‘rest of cost’ is $300M, then at 10% bond rate
it would be about $3 billion
In reality, there are other costs, and rate is not 10%,
and current outstanding debt is about $2.1 billion
“New” exit numbers
are mile markers
How is turnpike
doing pricing?
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Toll Road Pricing
How can we represent costs in this
domain? Average? Marginal?
At proposed rates, how are they
charging?
What costs would you charge?
Average cost? What and how?
Marginal cost? What and how?
What would be good/bad aspects of
each?
Marginal Cost Pricing
If srmc pricing is used in natural monopolies,
total costs will not be covered and subsidies will
be needed to keep the service at breakeven
Idea is to charge the incremental cost to all
users (marginal social cost) to the newest user
Highways: show marginal cost of travel delay,
congestion, pollution from additional car on road
Note this is very different from simply charging the
marginal private cost of the highway (which is likely
near $0)
Also note that operator, not users, get revenues
Other Markets - Pricing?
Railroads
SRMC pricing - “cost of running another train”
(generally excludes infrastructure upgrades)
Amtrak - if pricing at srmc, need big subsidies
Ramsey pricing- different prices can be charged
to recover cost
Originally a way of minimizing distortion from taxes
Highest taxes on goods with inelastic demand, lowest
on goods with elastic demand (inverse elasticity rule)
Transit - Higher prices for those least responsive to
price (e)
Another Option - 2 part tariffs
Charge separately for fixed, variable cost
Fixed charge is entry fee
Variable set to srmc
Where do we see this?
Notes - Pricing Chapter
(Hendrickson/Wohl)
Sufficient revenue must often be raised
from tolls to cover operation and debt
repayment funds
Inverse elasticity: higher fares during
times of day when demand inelastic
Differential pricing may be problematic
Cost Function Example
Avg var cost expresses average user cost in time,
effort, money (without toll)
Is “private cost of transportation”- i.e. what people pay
If sravc1(q)=t1 + v/(V1-d1q)
Then srmc1(q)= sravc1(q)+ vd1q/(V1-d1q)2
Appropriate ‘marg. cost toll’ is srmc1- sravc1
Cost of disutility of time to the q-1 drivers when q
enters the road
Otherwise the qth driver only considers her own costs
Use sravc =6.2 + 350/ (28-0.008q) (cents/v-mi)
From Our Example
Marginal change in time is very small (1 second) for adding 1
trip after 1999 trips already taken. q is flow rate (trips/hr)
q
1999
2000
2399
2400
sravc1
(cents)
176.74
176.83
229.68
229.86
srmc1 (cents)
370.82
371.28
662.60
663.75
diff
194.09
194.44
432.92
433.88
avg time
(sec)
1499.00
1500.00
2043.60
2045.45
Who is Better Off?
Society gains the toll revenues
Society gains environmental benefits.
 The benefits to society should exceed (in
theory) the losses to the drivers.
Can some form of compensation be used
to make everyone better off?
Hard to do.
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Another Approach
If demand linear (for 5 mile trips):
Demand ~ Marginal Benefit (MB)
q=3060 - 2.857p <=> p = MB= 1071 - 0.35q
For MC pricing, find where p = MB = srmc
Now p=371(cents) and q=2000
Sravc=177, toll = 194 cents, time=25 mins