Topics Today (5/2/13)  Congestion game  Congestion tax  Hwk #9 posted, Due next Tuesday 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 $10 2Congestion Game 1 --results 3 CommuteCost((time)(on(the(long(routeCost((time)(on(the(short(routeNMon(AM 30 34 48Mon(PM 30 39.5 59Tues(AM 30 27.5 35Tues(PM 30 22 24Wed(AM 30 45 70Wed(PM 30 39 58Thurs(AM 30 33.5 47Thurs(PM 30 31 42Fri(AM 30 33 46Fri(PM 30 25 3001020304050Commuting)cost)($)Cost((time)(on(the(long(routeCost((time)(on(the(short(routeThe number of commuters on the short route predicted by theory is 40. As noted in slide 6, the efficient number of commuters on the short route is only 20. Excluding Monday, during which commuters are getting their bearings, the game generated an average of 44 commuters. Their average cost of commuting across these four days was $32Congestion 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$4Congestion 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? 5 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 LV« 6 commuters MSCL =30 40 $ MPCS =10+ N/2 20 MSCS = MPCS +MEC =(10+ N/2) +N/2 =10+N7 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=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 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=EBF9 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 10 commuters MSCL =30 D=MB 20 40 $ MPCS =10+ N/2 MSCS = MPCS +MEC =(10+ N/2) +N/2 =10+N Welfare loss from the congestion externality =$200 50 30 10 Social net benefit (value) of the bridge under economcally efficient commuting =$200 In the absence of government intervention, the value of the short route is zero; commuters gain nothing by the existence of the short route!Congestion 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 $10 11Congestion Game II results 12 CommuteCost((time)(on(the(long(routeCost((time)(on(the(short(routeNMon(AM 30 24.75 59Mon(PM 30 24.25 57Tues(AM 30 32.25 89Tues(PM 30 30.75 83Wed(AM 30 29.25 77Wed(PM 30 27.5 70Thurs(AM 30 29.75 79Thurs(PM 30 26.75 67Fri(AM 30 32.5 90Fri(PM 30 29.25 7705101520253035Commuting)cost)($)Cost((time)(on(the(long(routeCost((time)(on(the(short(routeThe number of commuters on the short route predicted by theory is 80. As noted in slide 14, the efficient number of commuters on the short route is only 40. Excluding Monday, during which commuters are getting their bearings, the game generated an average of 79 commuters. Their average cost of commuting across these four days was $29.75.Congestion 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? 13 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 LV« 14 commuters MSCL =30 80 $ MPCS =10+ N/4 40 MSCS = MPCS +MEC =(10+ N/4) +N/4 =10+N/215 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=516 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 What is the value of the bridge this time? Increasing the bridge capacity generates 0 commuting benefit! 30 10 50 Welfare loss from the congestion externality =$400 Social net benefit (value) of the bridge under economcally efficient commuting =$400 20Discussion of Congestion Game II  The Pigou-Knight-Downs paradox  There is latent demand for the short