ECO 100 Problem Set 9

ECO 100 Problem Set 9 - ECO 100 Problem Set 9 Rik Sengupta...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
ECO 100 Problem Set 9 Rik Sengupta Friday 12:30 Congestion Externalities a. Each commuter will compare his/her own travel time for each road. More people  will choose the Pike, until the Pike time equals or starts to exceed the other route  times. This occurs when 80 = 60 + x/50, i.e. x = 1000 cars (i.e. during rush hour). Total commuting time = (1000 + 200) * 80 = 96000 minutes = 1600 hours, which is the  same  as the scenario without the Pike. b. We wish to minimize the total commuting time: X(60 + X/50) + (1200 – X)*80 = 1/50 X 2  – 20X + 96000. We look for the vertex of a parabola of the form y = ax 2  + bx + c, which occurs at x =  -b/2a = 20*(1/50) -1  = 500 cars. The Coase theorem suggests that if the commuters were to make deals with one another  in a free-market-like environment, social optimality (minimized total travel time) would  be reached. However, commuters cannot make deals regarding toll for the road, and the sheer number  of potential negotiators makes this communication unfeasible. c. Our goal is to set a toll so that only 500 commuters will use the Pike. Since each commuter values time at $0.25 per minute, a toll T can be treated as an added  T/0.25 = 4T minutes instead. The Pike transit time is then 60 + x/50 + 4T. We want a T to equate this to 80 when x = 
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 05/03/2010 for the course ECO 100 taught by Professor R.willig during the Spring '08 term at Princeton.

Page1 / 4

ECO 100 Problem Set 9 - ECO 100 Problem Set 9 Rik Sengupta...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online