Download CHAPTER 5 ELASTICITY PROBLEM SET

CHAPTER 5
ELASTICITY
PROBLEM SET
1.
a. When the price of gasoline rises from $2 per gallon to $3 per gallon, the price
elasticity of demand for gasoline over 1 month is 0.26.
$3 − $2
$1
% change in price =
=
= 0.4 or 40%
⎛ $3 + $2 ⎞ $2.5
⎜
⎟
⎝ 2 ⎠
400 − 360
40
% change in quantity =
=
= 0.105 or 10.5%
⎛ 400 + 360 ⎞ 380
⎜
⎟
2
⎝
⎠
%ΔQ 10.5%
E=
=
= 0.26
%ΔP
40%
b. When the price of gasoline rises from $2 per gallon to $3 per gallon, the price
elasticity of demand for gasoline over 1 month is 0.40.
% change in quantity =
E=
400 − 340
60
=
= 0.162 or 16.2%
⎛ 400 + 340 ⎞ 370
⎜
⎟
2
⎝
⎠
%ΔQ 16.2%
=
= 0.40
%ΔP
40%
b. When the price of gasoline rises from $2 per gallon to $3 per gallon, the price
elasticity of demand for gasoline over 1 month is 0.56.
% change in quantity =
E=
2.
400 − 320
80
=
= 0.222 or 22.2%
⎛ 400 + 320 ⎞ 360
⎜
⎟
2
⎝
⎠
%ΔQ 22.2%
=
= 0.56
%ΔP
40%
Long-run elasticity of demand for cigarettes is larger than the short-run elasticity
and this is what we would expect. In general, our demand for goods becomes more
elastic over time and cigarettes are no exception. In the short-run, when the price
of cigarettes rises, smokers may decrease their cigarette consumption only slightly
because smoking is addictive. But over time, they could transition to smoking
significantly fewer cigarettes per day or even quit smoking altogether.
3.
We would use income elasticity to determine if “tooth extraction” is an inferior
good. If income elasticity of “tooth extraction” is negative, then we would
conclude that it is an inferior good. Alternatively, if it is positive, we would
conclude that it is a normal good.
4.
For the poor, expenditure on Kellogg’s cornflakes is likely a higher share of their
budget, than for the rich. When spending on a good makes up a larger proportion
of families’ budgets, the demand tends to be more elastic, so the poor would have
elasticity of 4.05 and the rich 2.93.
5.
a. This is a straight line demand curve since for every $0.50 increase in price, the
quantity of bottles demanded falls by the same amount (100 units).
b. Demand is inelastic for this price change.
500 − 400
1 − 1.50
÷
⎛ 500 + 400 ⎞ ⎛ 1 + 1.50 ⎞
⎜
⎟ ⎜
⎟
2
⎝
⎠ ⎝ 2 ⎠
100 0.50
=
÷
450 1.25
= 0.55
E=
c. Demand is elastic for this price change.
200 − 100
2.50 − 3
÷
⎛ 200 + 100 ⎞ ⎛ 2.50 + 3 ⎞
⎜
⎟ ⎜
⎟
2
⎝
⎠ ⎝ 2 ⎠
100 0.50
=
÷
150 2.75
= 3.66
d.
As we slide down the demand curve, the price elasticity of demand changes
from 3.66 to 0.55, that is, demand becomes less elastic.
E=
e.
P
1.00
1.50
2.00
Qd
500
400
300
Total Revenue
500
600
600
2.50
3.00
200
100
500
300
f. From the table in part e, we can confirm that an increase in price in the inelastic
range (from $1 to $1.50) led to an increase in total revenue from $500 to $600,
while an increase in price in the elastic range (from $2.50 to $3.00) led to a
decrease in total revenue (from $500 to $300).
6.
For the demand curve to be unit elastic, there would have to be no change in revenue
as a result of a price change. In the initial situation, 110 units are sold at a price of $9
per unit, so revenue is $9 x 110 = $990. If demand is unit elastic, and the price rises to
$11 per unit, a constant revenue implies that the new quantity demanded would have
to be $990/$11 = 90 units.
Now we know two points on the demand curves. To find other points, try to
come up with price quantity combinations such that p x q = $990. Once you’ve found
one or two more, plot them and connect them to find that the demand curve must be
curved.
Price Per
Unit ($)
$11
$9
D
7.
Given that the short-run elasticity of demand is 0.35, a 25 percent
increase
fares
Quantity
perinyear
90
110
would lead to a 25 x 0.35 = 8.75 percent decrease in ridership. Since New Yorker’s
take about 2 billion trips per year, an 8.75% decrease would amount to (1-0.0875)*2
billion = 1.825 billion trips per year (a decrease of 175 million trips per year). The
new revenue would be 1.825 billion*$2.5 = 4.5625 billion. Since demand is inelastic,
a rise in price lead to an increase in revenue, as expected. Furthermore, since demand
is more inelastic in the short run than in the long run, we observe that the revenue
increase in the short run (4.5625 billion – 4 billion = 562.5 million) is higher than the
revenue increase in the long run, calculated in the chapter.
8.
We learned that about 25 percent of the world’s oil is produced in the Persian Gulf. If
half the Gulf’s capacity was wiped out, that would amount to a 12.5 percent drop in
production. In the long run, with a long-run demand elasticity of 0.45, the price would
have to rise by 12.5/0.45 = 27.78 percent. From an initial price of $60 per barrel, the
price would rise by 0.2778 x 60 = $16.67 per barrel to a new price of $76.67 per
barrel. (Note that here we did not use the midpoint rule when we increased the price
by a certain percentage. If we used the midpoint rule the resulting price would be
$79.36 per barrel)
9.
a. It is not a straight line demand curve since quantity demanded does not fall by the
same amounts following repeated price rises by a fixed amount.
c. Demand is elastic for this price change.
230 − 150
11 − 10
÷
⎛ 230 + 150 ⎞ ⎛ 11 + 10 ⎞
⎜
⎟ ⎜
⎟
2
⎝
⎠ ⎝ 2 ⎠
80
1
=
÷
190 9.5
=4
E=
c. Demand is elastic for this price change.
90 − 40
13 − 12
÷
⎛ 90 + 40 ⎞ ⎛ 13 + 12 ⎞
⎜
⎟ ⎜
⎟
⎝ 2 ⎠ ⎝ 2 ⎠
50
1
=
÷
65 12.5
= 9.61
E=
10. a. The demand for pork is more elastic than the demand for cigarettes because the
estimated elasticity for pork is greater than the highest estimated elasticity for
cigarettes, i.e. 0.78 > 0.7. This is because there are more substitutes for pork (e.g.,
beef, chicken) than there are for cigarettes.
b. If the price of milk rises by 5 percent, then the quantity of milk demanded will fall
by 2.7 percent (5 × 0.54).
11. a. More elastic.
b. Quantity demanded will fall by 2,190 bottles. To find this answer, first use the
mid-point rule to calculate that the price of Pepsi increased by 10%. Then,
substitute this value and the value of the price elasticity of demand into the
equation for price elasticity of demand, and solve for the change in quantity
demanded:
2.08 = x ÷ 10%
x = 20.8%.
Hence, the quantity of Pepsi demanded falls by 20.8% due to a price increase of
10%.
c. The price of ground beef will have to increase by 4.9%. Find this by substituting
what is known into the equation for price elasticity of demand and solving for x:
1.02 = 5% ÷ x
x = 4.9%
12.
a. They should increase their price to $30/hour. Given that the price elasticity of
demand for their service is 0.5 (i.e. it is inelastic), their revenue will increase when
they increase their price to $30/hour because the increase in their price will be
larger (in percentage terms) than the decrease in their demand. (Also note: They
will be doing less moving at a higher price, so their other costs will go down as
well, and they will enjoy more leisure.)
b. Demand is likely to become more elastic. The availability of substitutes is one of
the primary determinants of price elasticity of demand. Increased competition from
companies providing essentially the same service will make demand for “Three
Guys” services more sensitive to changes in price, hence, more elastic.
MORE CHALLENGING QUESTION
13.
Either the supply of PCs in Europe is perfectly inelastic, or the demand for PCs in
Europe is perfectly elastic. Neither of these statements is likely to be true, or even
close to true.
EXPERIENTIAL EXERCISES
Cross-price elasticities are important in the computer industry. Read the “Personal
Technology” column in Thursday’s Wall Street Journal and find a story that describes a
hardware or software product. Make a list of other products that you think would be
substitutes (positive cross-price elasticity) for the product in the article. Arrange the items in
your list from very close substitutes (very large cross-price elasticity) to more distant
substitutes (smaller cross-price elasticity). For each item on the list, make your best guess
about the numerical value of the elasticity. Using the guess, what would happen if the price of
each item on your list rose by 10%? When you’ve finished, follow the same steps for a list of
complements to the product in question. In this case, the cross-price elasticities will be
negative.