Topics Today (5/2/13)  Congestion game  Congestion taxes  Hwk 9 posted, due next Tues, May 7 1Congestion Game I  You need to go back and forth to work for a week  There are two routes: the short way and the long way  The long way has no traffic congestion and always takes 30 minutes  The short way can be faster, but it involves crossing a narrow bridge and so the commute time (in minutes) depends on the traffic according to: T=10 +N/2  The cost of travel is in terms of time, and is $1/minute  Record your time on each commute, and your total commute time during the week.  Reward: two students at random, split $10 according proportional to their total commute times (the student with the shorter time gets the greatest share of the $10 2Congestion Game I: Explanation slide I  With number of commuters on the horizontal axis, the aggregate marginal private cost of commuting the long route is 30. the aggregate total cost of commuting the long route is 30*NL.  For the long route, MPC=MSC because there is no externality  Demand (=MB=MWTP) for commuting is sufficiently high that everyone goes to work (no one decides not to work because of commuting costs).  Because demand for commuting is sufficiently high that everyone goes to work, the focus is on cost effectiveness; we are interested in the question, What is the lowest aggregate cost of commuting? 3commutersMSCL=30D=MB$3Congestion Game I: Explanation, slide 2  The aggregate marginal private cost of commuting the short route is 10+ N/2  What is the number of commuters using the bridge given rational behavior? Is this what we actually see in the game? 4 commuters MSCL =30 40 $ MPCS =10+ N/2Congestion Game I: Explanation, slide 3  What is the externality imposed by each additional commuter?  And so the expression of the marginal social cost of the short way is… 5 commuters MSCL =30 40 $ MPCS =10+ N/2 20 MSCS = MPCS +MEC =(10+ N/2) +N/2 =10+N6 commuters MSCL =30 20 40 $ MPCS =10+ N/2 MSCS = MPCS +MEC =(10+ N/2) +N/2 =10+N Congestion Game I: Explanation, slide 4 B A C D E F O What is the SNB (value) of the short route at the optimal level of use? A=ABFE B=BFD C=AEB D=BCD E=EBF7 commuters MSCL =30 20 40 $ MPCS =10+ N/2 MSCS = MPCS +MEC =(10+ N/2) +N/2 =10+N Congestion Game I: Explanation, slide 5 B A C D E F O What is the welfare loss associated with the privately rational outcome? A=ABFE B=BFD C=AEB D=BCD E=EBF8 commuters MSCL =30 20 40 $ MPCS =10+ N/2 MSCS = MPCS +MEC =(10+ N/2) +N/2 =10+N Congestion Game I: Explanation, slide 6 B A C D E F O The welfare loss associated with going from the efficient number of commuters to the privately rational outcome (40 commuters) is just equal to the value of the bridge at the efficient outcome; the bridge has no value under the privately rational outcome! Note the conceptual parallel to open access fishing!Congestion Game I: summary 9 commuters MSCL =30 D=MB 20 40 $ MPCS =10+ N/2 MSCS = MPCS +MEC =(10+ N/2) +N/2 =10+NCongestion Game II  Now suppose the city widens the bridge.  The commute time on the long route is still always 30 minutes.  The commute time on the short route is now 10+N/4  The cost of travel is in terms of time, and is still $1/minute  Record your time on each commute, and your total commute time during the week.  Reward: two students at random, split $10 according proportional to their total commute times (the student with the shorter time gets the greatest share of the $10 10Congestion Game II: Explanation, slide 1  The aggregate marginal private cost of commuting the short route is 10+ N/4  What is the number of commuters using the bridge given rational behavior? Is this what we actually see in the game? 11 commuters MSCL =30 80 $ MPCS =10+ N/4Congestion Game II: Explanation, slide 2  What is the externality imposed by each additional commuter?  And so the expression of the marginal social cost of the short way is… 12 commuters MSCL =30 80 $ MPCS =10+ N/4 40 MSCS = MPCS +MEC =(10+ N/4) +N/4 =10+N/213 commuters MSCL =30 40 80 $ MPCS =10+ N/4 MSCS = MPCS +MEC =(10+ N/4) +N/4 =10+N/2 Congestion Game II: Explanation, slide 3 B 30 C D 10 F What is the congestion tax generating the efficient number of commuters? A=30 B=20 C=10 D=514 commuters MSCL =30 40 80 $ MPCS =10+ N/4 MSCS = MPCS +MEC =(10+ N/4) +N/4 =10+N/2 Congestion Game II: Explanation, slide 4 B C D F O What is the value of the bridge this time? 30 10Discussion of Congestion Game II  The Pigou-Knight-Downs paradox  There is latent demand for the short route  The latent demand is NOT just a “Field of Dreams” residential build-out phenomenon. It can happen immediately. (And note that it is not just about having an alternative route; could have demand-shifting back to peak hours). Arnott and Small, American Scientist 1994 15 Another paradox: Downs-Thomson Paradox  Two commuting routes again, only this time one of them is a train line (instead of a fixed-time “long route”), the other is still a short route with a congestino bottleneck.  The greater the number of people using the train, the more frequently trains run, and so commuting by train provides a positive externality.  Suppose that once again the commuting equilibrium is 30 minutes by both routes  What happens when government attempts to relieve traffic congestion on the bridge by widening it? Discussion of Congestion Game II 16Congestion fees in NYC The Komonoff Balanced Transportation Analyzer http://www.komanoff.net/cars_II/ http://blogs.reuters.com/felix-salmon/2009/07/03/how-driving-a-car-into-manhattan-costs-160/ 17The Komonoff Balanced Transportation Analyzer  Traffic Plans tab: options for analysis  Bloomberg Plan: $8 to enter city between 6AM-7PM weekdays  Assumptions tab: Basic model in the flowchart  Results tab:  Travel time savings to drivers coming to/in/thru CBD  Travel time savings to other drivers  Travel time savings to commuters (consistent with Downs-Thomson result)  Change in vehicle speeds in CBD 18The Komonoff Balanced Transportation Analyzer  Cost-benefit tab:  Saved time (drivers)  Saved time (transit)  Environmental 19The Komonoff Balanced Transportation Analyzer  Cost-benefit tab:  Saved time (drivers)  Saved time (transit)  Environmental  Delay costs tab:  Marginal externality associated with one additional round to the