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Suppose that during a given year: (1) the price of TV sets increases by 4 percent in Japan, (2) the dollar depreciates by 5 percent with respect to the yen (the Japanese currency), (3) consumer incomes in the United States increase by 3 percent, (4) the price elasticity of demand for imported TV sets in the United States is -1.5, and (5) consumers' income elasticity of demand for TV sets in the United States is 2. (a)* If the price of the imported TV set was \$300 in the United States at the beginning of the year, approximately how much would you expect the price of the same imported TV set to be in the United States at the end of the year? (b)** By how much would the quantity demanded of imported TV sets in the United States change as a result of the change in price only? (c) By how much would the demand for imported TV sets in the United States change as a result of the increase in consumer income alone? (d) By how much would the demand for imported TV sets in the United States change as a result of both the change in price and in income?

Note: (a)* the 4 percent increase in the price of TV sets in Japan and the 5 percent depreciation of the dollar lead to a total increase of 9 percent in the dollar price of imported TV sets in the United States, from \$300 to \$327, and (b)** the change in price only?" refers to the import price.

https://brainmass.com/economics/elasticity/consumer-income-change-339168

#### Solution Preview

See the attached file. Thanks

Suppose that during a given year:
(1) the price of TV sets increases by 4 percent in Japan,
(2) the dollar depreciates by 5 percent with respect to the yen (the Japanese currency),
(3) consumer incomes in the United States increase by 3 percent,
(4) the price elasticity of demand for imported TV sets in the United States is -1.5, and
(5) consumers' income elasticity of demand for TV sets in the United States is 2.

(a)* If the price of ...

#### Solution Summary

This post examines consumer income change.

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## The demand curve

1. Illustrate the following demand on a graph:

Price (per pair) \$100 \$80 \$60 \$40 \$20
Quantity demanded (pairs per day) 10 14 18 22 26

(a) How many pairs will be demanded when the price is \$70?

(b) How much money will be spent on shoes at a price of (i) \$50
(ii) \$90

3. According to the News stories on pages 95 and 96 (see below), by how much would cigarette prices have
to rise to get a 50 percent reduction in smoking by

(a) Teenagers?

4. Suppose consumers buy 20 million packs of cigarettes per month at a price of \$2 per pack. If a
\$1 tax is added to that price,

(a) By what percent does price change? (Use midpoint formula on p. 92.) %

(b) By what percent will cigarette sales decline in the short run? (See Table 5.1 for clue.) %

(c) According to Gary Becker, by how much will sales decline in the long run?
(See News, page 96.)(see below)

7. According to the calculation on page 100 (see below), by how much will popcorn sales increase if
average income goes up by 5 percent?

8. Use the following table to compute the income elasticity of the demand for air travel:

Income Vacations Income Elasticity
(per year) (per year) of Demand
a. \$ 20,000 0
b. 50,000 1 b to c __________
c. 100,000 3 c to d __________
d. 200,000 5

10. Use the following data to illustrate the (a) demand curve and (b) total revenue curve:

Price \$1 2 3 4 5 6 7 8 9 10
Quantity 18 16 14 12 10 8 6 4 2 0

(a) At what price is total revenue maximized? \$

(b) At that price what is the elasticity of demand? E _

(c) Indicate the elastic and inelastic regions of each curve on the graphs.

Page 95
Dramatic Rise in Teenage Smoking
Smoking among youths in the United States rose precipitously
starting in 1992 after declining for the previous 15 years. By
1997, the proportion of teenage smokers had risen by onethird
from its 1991 trough.
A prominent explanation for the rise in youth smoking over
the 1990s was a sharp decline in cigarette prices in the early
1990s, caused by a price war between the tobacco companies.
Gruber and Zinman find that young people are very sensitive
to the price of cigarettes in their smoking decisions. The
authors estimate that for every 10 percent decline in the price,
youth smoking rises by almost 7 percent, a much stronger
price sensitivity than is typically found for adult smokers. As a
result, the price decline of the early 1990s can explain about a
quarter of the smoking rise from 1992 through 1997. Similarly,
the significant decline in youth smoking observed in 1998 is at
least partially explainable by the first steep rise in cigarette
prices since the early 1990s. The authors also find that black
youths and those with less-educated parents are much more
responsive to changes in cigarette prices than are white teens
and those with more-educated parents.
However, price does not appear to be an important determinant
of smoking by younger teens. This may be because they
are more experimental smokers.
Source: National Bureau of Economic Research, NBER Digest, October
2000. www.nber.org/digest
Analysis: The effectiveness of higher cigarette prices in curbing teen smoking depends on the price elasticity of demand.

Page 96
New York City's Costly Smokes
New York City has the nation's costliest smokes. NYC Mayor
Michael Bloomberg raised the city's excise tax from 8 cents a
pack to \$1.50 effective July 2002. Together with state and federal
taxes, that raised the retail price of smokes in NYC to
nearly \$8 a pack.
Mayor Bloomberg expected the city to reap a tax bonanza
from the 350 million packs of cigarettes sold annually in
NYC. What he got instead was a lesson in elasticity. NYC
smokers can buy cigarettes for a lot less money outside the
city limits. Or they can stay home and buy cigarettes on the
Internet from (untaxed) Indian reservations, delivered by
UPS. They can also buy cigarettes smuggled in from low-tax
states like Kentucky, Virginia, and North Carolina. What matters
isn't the price elasticity of demand for cigarettes in general
(around 0.4), but the elasticity of demand for NYC-taxed
cigarettes. That turned out to be quite high. Unit sales of
NYC cigarettes plummeted by 44 percent after the "Bloomberg
tax" was imposed.
Source: "NewsFlash," Economy Today, October 2002.
Analysis: If demand is price-elastic, a price increase will lead to a disproportionate drop in unit sales. In this case, the ready
availability of substitutes (cigarettes from other jurisdictions) made demand highly price-elastic.

Page 100

FIGURE 5.7
Income Elasticity
If income changes, the demand
curve shifts. In this case, an increase
in income enables consumers to
buy more popcorn at every price. At
a price of 25 cents, the quantity
demanded increases from 12 ounces
(point F) to 16 ounces (point N).
The income elasticity of demand measures
this response of demand to a
change in income.

When the underlying determinants of demand change, the entire demand curve shifts.
These shifts also alter consumer behavior. The price elasticity of demand is of no use in
gauging these behavioral responses, since it refers to price changes (movements along a
constant demand curve) for that good only.
A change in any determinant of demand will shift the demand curve. Suppose consumer
incomes were to increase. How would popcorn consumption be affected? Figure 5.7 pro-
vides an answer. Before the change in income, consumers demanded 12 ounces of popcorn
at a price of 25 cents per ounce. With more income to spend, the new demand curve ( D 2)
suggests that consumers will now purchase a greater quantity of popcorn at every price.
The increase in income has caused a rightward shift in demand. If popcorn continues to
sell for 25 cents per ounce, consumers will now buy 16 ounces per show (point N ) rather
than only 12 ounces (point F ).
It appears that changes in income have a substantial impact on consumer demand for
popcorn. The graph in Figure 5.7 doesn't tell us, however, how large the change in income
was. Will a small increase in income cause such a shift, or does popcorn demand increase
only when moviegoers have a lot more money to spend?
Figure 5.7 doesn't answer these questions. But a little math will. Specifically, the income
elasticity of demand relates the percentage change in quantity demanded to the percentage
change in income—that is,
Income elasticity
of demand _
% change in
quantity demanded
(at given price)
% change in
income
The similarity to the price elasticity of demand is apparent. In this case, however, the
denominator is income (a determinant of demand), not price.
Computing Income Elasticity. As was the case with price elasticity, we compute income
elasticity with average values for the changes in quantity and income. Suppose that the shift
in popcorn demand illustrated in Figure 5.7 occurred when income increased from \$110 per
week to \$120 per week. We would then compute
Income elasticity _
change in quantity demanded
average quantity
change in income
average income
_
16 ounces - 12 ounces
14 ounces
\$120 - \$110
\$115

1. Illustrate the following demand on a graph:

Price (per pair) \$100 \$80 \$60 \$40 \$20
Quantity demanded (pairs per day) 10 14 18 22 26

(a) How many pairs will be demanded when the price is \$70?

(b) How much money will be spent on shoes at a price of (i) \$50
(ii) \$90

3. According to the News stories on pages 95 and 96 (see below), by how much would cigarette prices have
to rise to get a 50 percent reduction in smoking by

(a) Teenagers?

4. Suppose consumers buy 20 million packs of cigarettes per month at a price of \$2 per pack. If a
\$1 tax is added to that price,

(a) By what percent does price change? (Use midpoint formula on p. 92.) %

(b) By what percent will cigarette sales decline in the short run? (See Table 5.1 for clue.) %

(c) According to Gary Becker, by how much will sales decline in the long run?
(See News, page 96.)(see below)

7. According to the calculation on page 100 (see below), by how much will popcorn sales increase if
average income goes up by 5 percent?

8. Use the following table to compute the income elasticity of the demand for air travel:

Income Vacations Income Elasticity
(per year) (per year) of Demand
a. \$ 20,000 0
b. 50,000 1 b to c __________
c. 100,000 3 c to d __________
d. 200,000 5

10. Use the following data to illustrate the (a) demand curve and (b) total revenue curve:

Price \$1 2 3 4 5 6 7 8 9 10
Quantity 18 16 14 12 10 8 6 4 2 0

(a) At what price is total revenue maximized? \$

(b) At that price what is the elasticity of demand? E _

(c) Indicate the elastic and inelastic regions of each curve on the graphs.

Page 95
Dramatic Rise in Teenage Smoking
Smoking among youths in the United States rose precipitously
starting in 1992 after declining for the previous 15 years. By
1997, the proportion of teenage smokers had risen by onethird
from its 1991 trough.
A prominent explanation for the rise in youth smoking over
the 1990s was a sharp decline in cigarette prices in the early
1990s, caused by a price war between the tobacco companies.
Gruber and Zinman find that young people are very sensitive
to the price of cigarettes in their smoking decisions. The
authors estimate that for every 10 percent decline in the price,
youth smoking rises by almost 7 percent, a much stronger
price sensitivity than is typically found for adult smokers. As a
result, the price decline of the early 1990s can explain about a
quarter of the smoking rise from 1992 through 1997. Similarly,
the significant decline in youth smoking observed in 1998 is at
least partially explainable by the first steep rise in cigarette
prices since the early 1990s. The authors also find that black
youths and those with less-educated parents are much more
responsive to changes in cigarette prices than are white teens
and those with more-educated parents.
However, price does not appear to be an important determinant
of smoking by younger teens. This may be because they
are more experimental smokers.
Source: National Bureau of Economic Research, NBER Digest, October
2000. www.nber.org/digest
Analysis: The effectiveness of higher cigarette prices in curbing teen smoking depends on the price elasticity of demand.

Page 96
New York City's Costly Smokes
New York City has the nation's costliest smokes. NYC Mayor
Michael Bloomberg raised the city's excise tax from 8 cents a
pack to \$1.50 effective July 2002. Together with state and federal
taxes, that raised the retail price of smokes in NYC to
nearly \$8 a pack.
Mayor Bloomberg expected the city to reap a tax bonanza
from the 350 million packs of cigarettes sold annually in
NYC. What he got instead was a lesson in elasticity. NYC
smokers can buy cigarettes for a lot less money outside the
city limits. Or they can stay home and buy cigarettes on the
Internet from (untaxed) Indian reservations, delivered by
UPS. They can also buy cigarettes smuggled in from low-tax
states like Kentucky, Virginia, and North Carolina. What matters
isn't the price elasticity of demand for cigarettes in general
(around 0.4), but the elasticity of demand for NYC-taxed
cigarettes. That turned out to be quite high. Unit sales of
NYC cigarettes plummeted by 44 percent after the "Bloomberg
tax" was imposed.
Source: "NewsFlash," Economy Today, October 2002.
Analysis: If demand is price-elastic, a price increase will lead to a disproportionate drop in unit sales. In this case, the ready
availability of substitutes (cigarettes from other jurisdictions) made demand highly price-elastic.

Page 100

FIGURE 5.7
Income Elasticity
If income changes, the demand
curve shifts. In this case, an increase
in income enables consumers to
buy more popcorn at every price. At
a price of 25 cents, the quantity
demanded increases from 12 ounces
(point F) to 16 ounces (point N).
The income elasticity of demand measures
this response of demand to a
change in income.

When the underlying determinants of demand change, the entire demand curve shifts.
These shifts also alter consumer behavior. The price elasticity of demand is of no use in
gauging these behavioral responses, since it refers to price changes (movements along a
constant demand curve) for that good only.
A change in any determinant of demand will shift the demand curve. Suppose consumer
incomes were to increase. How would popcorn consumption be affected? Figure 5.7 pro-
vides an answer. Before the change in income, consumers demanded 12 ounces of popcorn
at a price of 25 cents per ounce. With more income to spend, the new demand curve ( D 2)
suggests that consumers will now purchase a greater quantity of popcorn at every price.
The increase in income has caused a rightward shift in demand. If popcorn continues to
sell for 25 cents per ounce, consumers will now buy 16 ounces per show (point N ) rather
than only 12 ounces (point F ).
It appears that changes in income have a substantial impact on consumer demand for
popcorn. The graph in Figure 5.7 doesn't tell us, however, how large the change in income
was. Will a small increase in income cause such a shift, or does popcorn demand increase
only when moviegoers have a lot more money to spend?
Figure 5.7 doesn't answer these questions. But a little math will. Specifically, the income
elasticity of demand relates the percentage change in quantity demanded to the percentage
change in income—that is,
Income elasticity
of demand _
% change in
quantity demanded
(at given price)
% change in
income
The similarity to the price elasticity of demand is apparent. In this case, however, the
denominator is income (a determinant of demand), not price.
Computing Income Elasticity. As was the case with price elasticity, we compute income
elasticity with average values for the changes in quantity and income. Suppose that the shift
in popcorn demand illustrated in Figure 5.7 occurred when income increased from \$110 per
week to \$120 per week. We would then compute
Income elasticity _
change in quantity demanded
average quantity
change in income
average income
_
16 ounces - 12 ounces
14 ounces
\$120 - \$110
\$115

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