Download Mark-up Rules - FEB

Task 1.4: Mark-up Rules
Saskia van der Loo
K.U.Leuven
Funding meeting, Leuven, 8-9 dec 2005
Mark-up rules for funding
investments
• Internal mark-ups (users pay more)
• External financing from rest of transport sector
Efficiency
cost of
external
financing
Internal
Efficiency cost of
higher user prices
(internal mark-up)
External
Deficit with msc pricing
Mark-up rules | Internal mark-ups | One & Two mode approach | External mark-ups
Internal mark-ups
•
Research question:
what is feasibility and economic efficiency cost of
decreasing the financial deficit of the project?
•
a)
Methodology:
One mode approach: consider only the project and
assuming other modes are priced correctly
b)
Two mode approach: consider spillover effects on other
mode that is incorrectly priced
Mark-up rules | Internal mark-ups | One & Two mode approach | External mark-ups
One mode approach
1. What is the cost recovery with marginal
cost pricing?
2. What is the efficiency cost of mark-ups?
Mark-up rules | Internal mark-ups | One & Two mode approach | External mark-ups
The cost recovery question
• Cost-recovery results:
(Revenue Chapter 2, A. de Palma & R Lindsey)
Theorem:
Assume the user cost function is homogeneous of degree
0, and capacity is perfectly divisble. Then with marginal-cost
pricing the cost-recovery ratio is
toll revenues


Capacity cost

= elasticity of capacity cost function
Mark-up rules | Internal mark-ups | One & Two mode approach | External mark-ups
Illustration
Euro/trip
D
User cost
Welfare loss
Deficit
Deficit decrease
Marginal
Capacity cost
Toll revenues = capacity cost
toll*
Capacity
Pass trips/day
Mark-up rules | Internal mark-ups | One & Two mode approach | External mark-ups
Functional Forms
• Model:
N
C N, K   d  
K
User cost
Capacity cost:
F  K   kK 
Demand:
p  N   p0 N  
Mark-up is set at a
fraction f of the 1st best
optimal toll conditional on
usage
s
  f  *  f  cN N
Mark-up rules | Internal mark-ups | One & Two mode approach | External mark-ups
Functional Forms
Welfare:

n 0
p N   c N, K  

0
K
N
P  n  dn C  N , K  N  F  K 


p0
N  K   

1

fs
d
 

1
 s
 ds   fs 
K N  

k



s


K
s
 s
N, K
1
s 
N
s 1
s 
 & 
Mark-up rules | Internal mark-ups | One & Two mode approach | External mark-ups
Cost recovery ratio
• Cost-recovery for non-optimal pricing and second best capacity :

s 
f 1 


 

 
 s 
1 f 

  
s = elasticity of users costs with respect to
the volume/capacity ratio,
β = price elasticity of demand,
ε = elast capacity cost
f = toll / first-best toll
• Limits :


s



Mark-up rules | Internal mark-ups | One & Two mode approach | External mark-ups
Cost recovery ratio
• Maximum cost-recovery ratio for given elasticities:
s = elasticity of users costs with respect to the volume/capacity ratio,
β = price elasticity of demand,
ε = elast capacity cost
f = toll / first-best toll


f 
 s


 s 
• Example:
β=2, s=4 then 

f 
1.5
typically ε = 0.3 → maximum cost-recovery: ρ=0.45
Mark-up rules | Internal mark-ups | One & Two mode approach | External mark-ups
Numerical Example
s
β
ε
4
0.9
0.3
toll
s = elasticity of users costs with respect to the
volume/capacity ratio,
β = price elasticity of demand,
ε =elast capacity cost
0,044
0,050
0,055
0,061
0,066
0,072
0,078
0,083
0,089
quantity
100
94
87,7
81,7
76
70,8
66
61,7
57,8
capacity
100
99,6
98,7
97,3
95,6
93,9
92
90,2
88,4
0,300
0,317
0,330
0,340
0,347
0,352
0,355
0,358
0,360
###
-0,162
-0,329
-0,491
-0,646
-0,789
-0,925
-1,048
-1,163
cost recovery
ΔΩ/z
z = decrease in deficit
1.163 euro loss for 1 euro less deficit
Mark-up rules | Internal mark-ups | One & Two mode approach | External mark-ups
Two mode approach
• Spillover effects on another mode:
Assume:
second mode is underpriced
• Mark-up on mode 1 → Users will shift to
underpriced mode → extra welfare loss
Mark-up rules | Internal mark-ups | One & Two mode approach | External mark-ups
Spillover effects on
underpriced mode
P
MSC2
P’
C2
msc2-p2
MRC2
ΔN2
 2  N2  msc2  p2 
Mark-up rules | Internal mark-ups | One & Two mode approach | External mark-ups
Numerical Example
p2ms
c2
s
β
ε
ε12
4
0.9
0.3
0.07
p2  msc2
 1.3
user cost1
ε12 cross-price elasticity
z = decrease in deficit
-0.015
0,044
0,050
0,055
0,061
0,066
0,072
0,078
0,083
0,089
quantity (1)
100
94
87,7
81,7
76
70,8
66
61,7
57,8
capacity (1)
100
99,6
98,6
97,3
95,6
93,9
92
90,2
88,4
0,300
0,317
0,330
0,340
0,347
0,352
0,355
0,358
0,360
Δq1/Δq2
###
3
2,8
2,6
2,4
2,3
2,1
2
1,9
ΔΩ1/z
###
-0,162
-0,329
-0,491
-0,646
-0,789
-0,925
-1,048
-1,163
ΔΩ2/z
###
-0,114
-0,135
-0,157
-0,179
-0,202
-0,226
-0,249
-0,273
ΔΩ1/z + ΔΩ2/z
###
-0,276
-0,464
-0,647
-0,825
-0,992
-1,151
-1,297
-1,436
toll (1)
cost recovery
Mark-up rules | Internal mark-ups | One & Two mode approach | External mark-ups
Non-linear pricing
• Previous approach was based on one price for all trips
and only one type of user
• In practice one can
– discriminate between users and increase the cost coverage
– Charge a non linear tariff (degressive, two part tariffs etc.) and
transfer more consumer surplus into revenues
• In the limit one can of course extract all consumer
surplus but we are still looking for realistic estimates on
cost coverage increase and associated efficiency loss
→ Still looking for information
Mark-up rules | Internal mark-ups | One & Two mode approach | External mark-ups
External mark-ups
• External mark ups = extra taxes on other transport
sectors that can via transport funds be used to finance
TEN’s
• Two types of charges:
– Extra gasoline and diesel tax
– Road tolls
– Air traffic charges…
• Efficiency costs will depend on the difference between
user prices and marginal social costs or between current
taxes and marginal external costs
Mark-up rules | Internal mark-ups | One & Two mode approach | External mark-ups
Gasoline and Diesel taxes
• Advantages:
– Easy to handle
– Net additional revenues possible if increases in a balanced way
for both products
• Although long term price elasticity may be approaching -1
• Disadvantages
– Efficiency is poor because gasoline and diesel taxes are a very
poor proxy for external costs
• Not related to congestion (may even generate negative rebound
effect in the sense that more fuel efficient cars may be used more
rather than less)
• Directly related to CO2 emissions but these are already overtaxed
• Not well related to other air pollutants and to accident risks
Mark-up rules | Internal mark-ups | One & Two mode approach | External mark-ups
Tolls
• Feasibility:
– Short term: only Germany and France
– Longer term (2010 or so ?)
• Advantages
– Can be better targeted to congestion
• Disadvantages
– Still hypothetical
Mark-up rules | Internal mark-ups | One & Two mode approach | External mark-ups