Explore BrainMass
Share

Explore BrainMass

    The demand curve

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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?
    (b) Adults (short-run)?

    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?
    (b) Adults (short-run)?

    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

    © BrainMass Inc. brainmass.com October 10, 2019, 12:10 am ad1c9bdddf
    https://brainmass.com/economics/short-and-long-run-cost-functions/demand-curve-281707

    Attachments

    Solution Preview

    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

    The demand curve can be drawn as follows:

    What we have done here is just plotted the quantity and price pairs. The top left point is the point representing price 100 and quantity 10, and the next one is price 80 quantity 14 and so on.

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

    When the price is $70 it is between $60 and $80. We know at $60 consumers demand 18 units and at $80 they demand 14 units. The line is a straight line, and so changes are uniform across the line. When going from $60 to $80 the price changes by $20 and the quantity changes by 4, so we can say that when price changes by $10 quantity will change by 4/2 = 2 units. Hence, at $70 the quantity demanded is 16 units.

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

    Following the last example we can say that quantity demanded at $50 is 20, since quantity demanded at $40 is 22 and that at $60 is 18. Similarly the quantity demanded at $90 is 12. Therefore, total money spent when price is $50 is Price * Quantity Demanded = $50 * 20 = $1000. When price is $90, the total amount spent is Price * Quantity Demanded = $90 * 12 = $1080.

    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?

    This will depend on the elasticity of demand. It is given that for every 10% decline in price, the quantity demanded amongst teenagers increased by 7%. Thus we can say that the elasticity of demand amongst teenagers is
    Elasticity = (% Change in Quantity)/(% Change in Price) = 7/10 = 0.7.

    To get a 50% reduction in usage we need % Change in Quantity to be 50. Using the formula again we have

    Elasticity = (% Change in Quantity)/(% Change in Price)
    or 0.7 = 50/(% Change in Price)
    or (% Change in Price) * 0.7 = [50/(% Change in Price)] * (% Change in Price)
    or (% Change in Price) * 0.7 = 50
    or (% Change in Price) * 0.7 / 0.7 = 50/0.7
    or (% Change in Price) = 71.428

    Hence price should rise by at least 71.428% for quantity demanded to fall by 50%.

    (b) Adults (short-run)?

    It is also mentioned that the short-run price elasticity of demand for smokes is 0.4. Using the same method as above we can say that

    Elasticity = (% Change in Quantity)/(% Change in Price)
    or 0.4 = 50/(% Change in Price)
    or (% Change in Price) * 0.4 = [50/(% Change in Price)] * (% Change in Price)
    or (% Change in Price) * 0.4 = 50
    or (% Change in Price) * 0.4 / 0.4 = 50/0.4
    or (% Change in Price) = 125

    Hence price should rise by at least 125% for the quantity demanded to fall by 50%.

    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.) %

    The mid-point formula states that

    % Change in Price = [(Change in Price)/(Average Price)] * 100

    Using it with the data above we can say that

    % Change in Price = [(1)/(Average of 2 and 3)] * 100 = [(1)/(2.5)]*100 = ...

    Solution Summary

    The demand curve is depicted for the change in quantity.

    $2.19