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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