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
10
0
0
470,000 500,000
50
0.30
60 50
500,000
shr
QQP
E
PPQ
−
−
==
=
−−
−
ii.
Arc elasticity
1
0
470,000 500,000
60 50
0.3402
60 50
470,000 500,000
arc
QQPP
E
PPQQ
−+
−
+
=
−
−
+
iii.
Logarc elasticity
logarc
ln
ln
ln 470,000 ln500,000
0.3394
ln
ln
ln 60 ln 50
QQ
E
PP
−
−
=
−
* Note: E
arc
~ E
logarc
and E
shr
> E
arc
and E
logarc
b.
Change in total revenue per day (in dollar)
$0.60 470,000 $0.50 500,000
$32,000
=×
−×
=
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 don’t 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.
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 Spring '09
 Lee
 Price Elasticity, Arc elasticity, Earc, ln Q0 ln

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