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(civl362)[2008](f)quiz2~PPSpider^_10081.pdf
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CIVL 362 Transportation System Operations
Tutorial Quiz 2 (Suggested Solution)
Name: Student ID: Week 3, 24 Sep 2008
A roadway has a cost function (total cost or total travel time of all users) T = 5q + 10q2, and the demand function is given by D = 20 - 0.2t, where t is the individual travel time in minutes. Value of time is $2 per minute.
a)
Determine and sketch the average, marginal cost functions and demand function.
b)
Determine the optimum flow
c)
Determine the toll that should be charged to limit the flow to the optimal flow.
d)
Indicate on the plot the toll revenue collected by the government.
a)
b), c) Solve for Point M
(q,t) = (3.8,81)
Thus, optimum flow = 3.8
When q = 3.8, AC = 43
Optimum toll = (81 C 43) x 2 = $76
d) Toll collected by government = shaded area
(3.8,81)
MC
AC
Demand
t = 100 C 5q