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CIVL 362 Transportation System Operations
Tutorial Quiz 1 (Suggested Solution)
Name: Student ID: Week 2, 10 Sep 2008

1.
A bus company is charging a flat rate of 50 cents per rider to any part of the city has a patronage of 500,000 per day. It has been decided to raise the fare to 60 cents per rider and it is estimated that 470,000 people will ride the buses. Calculate:


a.
Price Elasticities:


i.
Shrinkage ratio




.

ii.
Arc elasticity






iii.
Log-arc elasticity







* Note: Earc ~ Elog-arc and Eshr > Earc and Elog-arc

b.
Change in total revenue per day (in dollar)






2.
A bus company found that the price elasticity of demand for bus trips during peak hours is -0.40. Management of the company would like to raise the current fare but dont know if this action will (a) lead to a reduction in patronage, and (b) result in a loss of revenue for the company. Are these fear justified? Discuss. What if the price elasticity of -1.30.


a.
Reduction in Patronage?


i.
ep = -0.40



Patronage decrease as price elasticity is negative.
ii.
ep = -1.30



Patronage decrease as price elasticity is negative.
b.
Loss in revenue (Indicate whether the company is operating in elastic range or inelastic range)?


i.
ep = -0.40



Revenue increases. As -1<ep<0, the service is operating in inelastic region. 1% increase in price induces just 0.4% reduction in patronage, so revenue would increase


ii.
ep = -1.30



Revenue decreases. As ep<-1, the service is operating in elastic region. 1% increase in price would induce 1.3% drop in patronage, so revenue would decrease.




3.
The ferry service from a city to a recreational island is currently served by regular ferries and luxury boat. 5000 passengers per day use regular ferries and 7000 use the luxury boat. Travel times (min) and fares ($) are as follows:


4.





Travel Time (min)
Fare ($)

Regular
45
1

Luxury
30
2




The demand elasticities (shrinkage ratios) are:

Regular
Luxury


Time
Fare
Time
Fare

Regular
-0.03
-0.04
+0.02
+0.05

Luxury
+0.05
+0.02
-0.07
-0.20





Calculate (no need to show calculation):

Ridership
Change in Revenue


Regular
Luxury
Regular
Luxury

a) Fare of luxury boat raised to $2.50




+62.5
+2625

b) Travel time on luxury boat reduced to 25 min




-17
+164

c) Travel time of regular ferry increase to 50 min




-17
+78