Problem Set 3 Solutions
Chapter 5
2.
a.
For business travelers, the price elasticity of demand when the price of
tickets rises from $200 to $250 is [(2,000 - 1,900)/1,950]/[(250 - 200)/225]
= 0.05/0.22 = 0.23.
For vacationers, the price elasticity of demand when
the price of tickets rises from $200 to $250 is [(800 - 600)/700] / [(250 -
200)/225] = 0.29/0.22 = 1.32.
b.
The price elasticity of demand for vacationers is higher than the elasticity
for business travelers because vacationers can choose more easily a
different mode of transportation (like driving or taking the train).
Business travelers are less likely to do so since time is more important to
them and their schedules are less adaptable.
3.
a.
If your income is $10,000, your price elasticity of demand as the price of
compact discs rises from $8 to $10 is [(40 - 32)/36]/[(10 - 8)/9] =0.22/0.22
=
1.
If your income is $12,000, the elasticity is [(50 - 45)/47.5]/[(10 - 8)/
9] = 0.11/0.22 = 0.5.
b.
If the price is $12, your income elasticity of demand as your income
increases from $10,000 to $12,000 is [(30 - 24)/27] / [(12,000 -
10,000)/11,000] = 0.22/0.18 = 1.22.
If the price is $16, your income
elasticity of demand as your income increases from $10,000 to $12,000 is
[(12 - 8)/10] / [(12,000 - 10,000)/11,000] = 0.40/0.18 = 2.2.
4.
a.
If Emily always spends one-third of her income on clothing, then her
income elasticity of demand is one, since maintaining her clothing
expenditures as a constant fraction of her income means the percentage
change in her quantity of clothing must equal her percentage change in
income.
For example, suppose the price of clothing is $30, her income is
$9,000, and she purchases 100 clothing items.
If her income rose 10
percent to $9,900, she'd spend a total of $3,300 on clothing, which is 110
clothing items, a 10 percent increase.
b.
Emily's price elasticity of clothing demand is also one, since every
percentage point increase in the price of clothing would lead her to reduce
her quantity purchased by the same percentage.
Again, suppose the price
of clothing is $30, her income is $9,000, and she purchases 100 clothing
items.
If the price of clothing rose 1 percent to $30.30, she would
purchase 99 clothing items, a 1 percent reduction.
[Note:
This part of the
problem can be confusing to students if they have an example with a
larger percentage change and they use the point elasticity.
Only for a
small percentage change will the answer work with an elasticity of one.
Alternatively, they can get the second part if they use the midpoint method
for any size change.]