Transcript
Chapter06 - Elasticity
Chapter06 - Elasticity
McConnell Brue Flynn Barbiero 14ce
DISCUSSION QUESTIONS
1. Explain why the choice between 1, 2, 3, 4, 5, 6, 7, and 8 “units,” or 1,000, 2,000, 3,000, 4,000, 5,000, 6,000, 7,000 and 8,000 movie tickets, makes no difference in determining elasticity in Table 6.1. LO6.1
Answer: Price elasticity of demand is determined by comparing the percentage change in price and the percentage change in quantity demanded. The percentage change in quantity will remain the same regardless of whether the difference is between 1 unit and 2 units or 1000 units and 2000 units.
To see this note that the percentage change between 1 and 2 equals ((2-1)/1) x 100 = 100%. The percentage change between 1000 and 2000 equals ((2000-1000)/1000) x 100=100%. Since these are the same for a given percentage change in price the elasticities will be the same.
This is also true if you use the midpoints formula. In this case, that the percentage change between 1 and 2 equals ((2-1)/((1+2)/2)) x 100(1/1.5) x 100 = 67%. The percentage change between 1000 and 2000 equals ((2000-1000)/((1000+2000)/2) x 100 = (1000/1500) x 100 = 67%.
2. What effect would a rule stating that university students must live in university dormitories have on the price elasticity of demand for dormitory space? What impact might this in turn have on room rates? LO6.1
Answer: The ruling would make the price elasticity of demand more inelastic than if there were no such rule, assuming that there is not another equivalent university nearby to which students could transfer. Although universities are nonprofit organizations, the rule would certainly allow them to raise rates without worrying so much about students moving out to live elsewhere.
3. The income elasticities of demand for movies, dental services, and clothing have been estimated to be +3.4, +1, and +.5, respectively. Interpret these coefficients. What does it mean if an income elasticity coefficient is negative? LO6.5
Answer: All are normal goods—income and quantity demanded move in the same direction. These coefficients reveal that a 1 percent increase in income will increase the quantity of movies demanded by 3.4 percent, of dental services by 1 percent, and of clothing by 0.5 percent. A negative coefficient indicates an inferior good—income and quantity demanded move in the opposite direction.
4. Research has found that an increase in the price of beer would reduce the amount of marijuana consumed. Is cross elasticity of demand between the two products positive or negative? Are these products substitutes or complements? What might be the logic behind this relationship?LO6.5
Answer: If the cross elasticity is negative, this implies that an increase in the price of one good results in a decrease in the quantity purchased of another good. This implies that the goods are compliments; as the price of one good increases, it reduces the consumption of other goods (purchased less). The cross elasticity of the two products above is negative. Thus, the products appear to be complementary. As one drinks beer, one also smokes marijuana.
What is the tax incidence of a sales tax when demand is highly inelastic? Highly elastic? What effect does the elasticity of supply have on the incidence of a sales tax? LO6.6
Answer: The incidence of a tax is likely to be primarily on consumers when demand is highly inelastic and primarily on producers when demand is elastic. The more elastic the supply, the greater the incidence of a tax on consumers and the less on producers.
The LAST WORD What is the purpose of charging different groups of customers different prices? Supplement the three broad examples in the Last Word with two additional examples of your own. Hint: Think of price discounts based on group characteristics or time of purchase.
Answer: The primary purpose for charging different prices is to increase revenue and, in turn, profits. Other examples include student and senior citizen discounts (group characteristics based on age or activity), and movies and golf courses (discounts for consumption during “off-peak” times in order to spread out consumption and increase revenue).
REVIEW QUESTIONS
1. Graph the accompanying demand data, and then use the midpoint formula for Ed to determine price elasticity of demand for each of the four possible $1 price changes. What can you conclude about the relationship between the slope of a curve and its elasticity? Explain in a nontechnical way why demand is elastic in the northwest segment of the demand curve and inelastic in the southeast segment. LO6.1
Answer: The graph of the data is:
To calculate the elasticity, we use the midpoint formula.
First we calculate the percentage change in quantity. Second we calculate the percentage change in price. Then we divide the percentage change in quantity by the percentage change in price. To report the values as positive numbers we then take the absolute value of the answer. For example, we have the following elasticities as we move down the demand schedule (demand elasticities are reported as positive values).
Moving from $5 to $4:
Moving from $4 to $3:
The same process applies to further reductions in price (and increase in quantity): As we move from $3 to $2 the elasticity is 0.714. As we move from $2 to $1 the elasticity is 0.333.
This demand curve has a constant slope of -1 (= -1/1), but elasticity declines as we move down the curve. When the initial price is high and initial quantity is low, a unit change in price is a low percentage while a unit change in quantity is a high percentage change. The percentage change in quantity exceeds the percentage change in price, making demand elastic. When the initial price is low and initial quantity is high, a unit change in price is a high percentage change while a unit change in quantity is a low percentage change. The percentage change in quantity is less than the percentage change in price, making demand inelastic.
2. What are the major determinants of price elasticity of demand? Use those determinants and your own reasoning in judging whether demand for each of the following products is probably elastic or inelastic: (a) bottled water; (b) toothpaste; (c) Crest toothpaste; (d) ketchup; (e) diamond bracelets; (f) Microsoft’s Windows operating system.LO6.1
Answer: The key determinants of price elasticity are substitutability, proportion of income; luxury versus necessity, and time. The larger the number of substitutes available, the more elastic the demand. The higher the price of a good is relative to a consumer's income, the more elastic the demand. Generally, goods seen as luxury items have a more elastic demand. The longer time duration, the more elastic the demand.
(a) bottled water. This good is likely elastic because there are a number of substitutes (water fountains, cans of soda, etc...)
(b) toothpaste. This good is likely inelastic because there aren't many substitutes and it is a necessity (in economic terms).
(c) Crest toothpaste. This specific brand of the good is likely elastic. There are a number of substitutes for this specific brand of the good.
(d) ketchup. This good is likely inelastic. There aren't many substitutes for ketchup (for people who like ketchup) and it makes up a small percentage of income.
(e) diamond bracelets. This good is likely elastic because it is a luxury good and may make up a large fraction of income (more than ketchup).
(f) Microsoft's Windows operating system. This good is likely inelastic because there aren't many substitutes for this good and it has become a necessity in a number of workplaces.
3. Calculate total-revenue data from the demand schedule in review question 1. Graph total revenue below your demand curve. Generalize about the relationship between price elasticity and total revenue.LO6.2
Answer:
To calculate total revenue, multiply price and quantity. At the price of $5 one unit is sold. Thus, total revenue is $5x1 = $5. At the price of $2 total revenue is $4x2 = 8, at $3 total revenue is $3x3 = 9, at $4 total revenue is $4x2 = 8, and at $1 total revenue is $1x5 = 5.
When demand is elastic, price and total revenue move in the opposite direction. This is because the percentage change in quantity is greater than the percentage change in price. When demand is inelastic, price and total revenue move in the same direction because the percentage change in quantity is less than the percentage change in price.
4. How would the following changes in price affect total revenue? That is, would total revenue increase, decrease, or remain unchanged?LO6.2
a. Price falls and demand is inelastic.
b. Price rises and demand is elastic.
c. Price rises and supply is elastic.
d. Price rises and supply is inelastic.
e. Price rises and demand is inelastic.
f. Price falls and demand is elastic.
g. Price falls and demand is of unit elasticity.
Answer: When demand is elastic, price and total revenue move in the opposite direction. This is because the percentage change in quantity is greater than the percentage change in price. When demand is inelastic, price and total revenue move in the same direction because the percentage change in quantity is less than the percentage change in price.
Supply is a simpler story. Since price and quantity move in the same direction an increase in price will result in an increase in total revenue (a higher price and selling more) and a decrease in price will result in a decrease in total revenue (a lower price and selling less).
Using these rules, we have the following answers.
(a) Total revenue decreases (As the price falls individuals purchase more of the good. However, the decrease in price on the previous units sold outweighs the gains from selling more units.)
(b) Total revenue decreases (As the price increases individuals purchase less of the good reducing total revenue. However, the increase in price on the previous units sold increases total revenue. Here the loss in quantity sold outweighs the increase in price effect.)
(c) Total revenue increases
(d) Total revenue increases
(e) Total revenue increases
(f) Total revenue increases
(g) No change. (Here the decrease in total revenue that results from the decrease in price is offset by the increase in total revenue from selling more units.)
5. In 2006, Willem De Kooning’s abstract painting Woman III sold for $137.5 million. Portray this sale in a demand and supply diagram and comment on the elasticity of supply. Comedian George Carlin once mused, “If a painting can be forged well enough to fool some experts, why is the original so valuable?” Provide an answer. LO6.4
Answer: The supply is perfectly inelastic—vertical—at a quantity of 1 unit. The $137.5 million price is determined where the downward sloping demand curve intersected this supply curve.
If more than one picture were available (all but one having to be a copy), the demand would likely decrease enormously.
6. Suppose the cross elasticity of demand for products A and B is +3.6 and for products C and D is - 5.4. What can you conclude about how products A and B are related? Products C and D? LO6.5
Answer: The cross elasticity relates the percentage change in quantity to the percentage change in price of a different good. If the cross elasticity is positive this implies that and increase in the price of one good results in an increase in the quantity purchased of another good. This implies the goods are substitutes, as the price of one good increases substitute into the other good (purchase more).
This implies that goods A and B are substitutes and that goods C and D are compliments.
For reference, if the cross elasticity is negative this implies that and increase in the price of one good results in a decrease in the quantity purchased of another good. This implies that the goods are compliments; as the price of one good increases, reduce the consumption of the other good (purchase less).
True or false. The incidence of property taxes that are levied on rented houses and apartments is high—meaning that they are paid almost entirely by the landlords, who are billed by the government for those taxes. LO 6.6
Answer: false. The incidence of property taxes levied on rented properties is in fact low—meaning that very little is paid by the landlords who are billed by the government.
This is true because the landlords simply pass the property taxes on to their tenants by boosting rents.
PROBLEMS
1. Look at the demand curve in Figure 6.2a. Use the midpoint formula and points a and b to calculate the elasticity of demand for that range of the demand curve. Do the same for the demand curves in Figures 6.2b and 6.2c using, respectively, points c and d for Figure 6.2b and points e and f for Figure 6.2c. LO6.1
Answers: 9/5 = 1.8; 5/9 = .5556; 1.
Feedback: Consider the following figures taken from the textbook (Figures 6.2a, 6.2b, and 6.2c).
To calculate the elasticity, we use the midpoint formulas. Recall that the elasticity is percentage change in quantity divided by the percentage change in price. We take the absolute value to convert the elasticity to a positive number.
Given the two points in Figure 6.2a (10,2) and (40,1), note that the ordered pair is (Q,P), we can calculate the elasticity.
Given the two points in Figure 6.2b (10,4) and (20,1), we can calculate the elasticity.
Given the two points in Figure 6.2c (10,3) and (30,1), we can calculate the elasticity. (Note this is an approximation of the nonlinear schedule.)
2. Investigate how demand elasticities are affected by increases in demand. Shift each of the demand curves in Figures 6.2a, 6.2b, and 6.2c to the right by 10 units. For example, point a in Figure 6.2a would shift rightward from location (10 units, $2) to (20 units, $2) while point b would shift rightward from location (40 units, $1) to (50 units, $1). After making these shifts, apply the midpoint formula to calculate the demand elasticities for the shifted points. Are they larger or smaller than the elasticities you calculated in Problem 1 for the original points? In terms of the midpoint formula, what explains the change in elasticities? LO6.1
Answers: 1.29; 1/3 = .3333; 2/3 = .6667; smaller; everything in the midpoint formula stays the same except the reference point for quantity, which increases—that increase reduces the elasticity.
Feedback: Once again, consider the following figures taken from the textbook (Figures 6.2a, 6.2b, and 6.2c).
Here everything remains the same, but the quantity units in the ordered pairs (Q,P) increase by 10 units.
Given the initial two points in Figure 6.2a (10,2) and (40,1), we now have the two points (20,2) and (50,1).
Given the two points in Figure 6.2b (10,4) and (20,1), we now have (20,4) and (30,1).
Given the two points in Figure 6.2c (10,3) and (30,1), we now have (20,3) and (40,1).
If we compare the elasticities in this problem to those found in problem 1, we can see that an increase in quantity at every price (shift the demand schedule to the right) reduces the elasticity. The percentage change in quantity is smaller given the higher quantity purchased at every price.
3. Suppose that the total revenue received by a company selling basketballs is $600 when the price is set at $30 per basketball and $600 when the price is set at $20 per basketball. Without using the midpoint formula, can you tell whether demand is elastic, inelastic, or unit-elastic over this price range? LO6.2
Answer: Unit elastic
Feedback: Consider the following values: Total revenue received by a company selling basketballs is $600 when the price is set at $30 per basketball and $600 when the price is set at $20 per basketball.
The company is initially selling 20 basketballs at a price of $30, which results in a total revenue of $600. The company then decreases its price to $20 a ball and still has a total revenue of $600. This implies that the company is now selling 30 basketballs. The decrease in price of $10 on the previous balls sold resulted in a decrease in revenue of ($200 = $10x20). However the company sells 10 more balls at the lower price resulting in a $200 increase in revenue (= $20 x 10). Thus, we know that demand is unit-elastic over this range because there is no change in total revenue.
4. Danny “Dimes” Donahue is a neighborhood’s 9-year-old entrepreneur. His most recent venture is selling homemade brownies that he bakes himself. At a price of $1.50 each, he sells 100. At a price of $1.00 each, he sells 300. Is demand elastic or inelastic over this price range? If demand had the same elasticity for a price decline from $1.00 to $0.50 as it does for the decline from $1.50 to $1.00, would cutting the price from $1.00 to $0.50 increase or decrease Danny’s total revenue? LO6.2
Answers: Elastic; cutting price would increase Danny’s total revenue.
Feedback: The total revenue rule implies that demand is elastic when revenue and price move in opposite directions. In other words, a decrease in price results in an increase in total revenue. We can use this rule to answer this question.
Consider the following values: At a price of $1.50 each, Danny sells 100. At a price of $1.00 each, he sells 300. Is demand elastic or inelastic over this price range?
Total revenue at the price $1.50 and the quantity of 100 equals $150 (= $1.50x100). Danny then decreases his price to $1.00 and sells 300 brownies now. Total revenue at this new price equals $300 (= $1.00x300). Since total revenue increased after Danny decreased his price we know from the rule above that demand is elastic over this range.
We can also answer the following question now: If demand had the same elasticity for a price decline from $1.00 to $0.50 as it does for the decline from $1.50 to $1.00, would cutting the price from $1.00 to $0.50 increase or decrease Danny’s total revenue?
The answer is obviously yes. A decrease in price would increase total revenue because demand is elastic over this range as well.
5. What is the formula for measuring the price elasticity of supply? Suppose the price of apples goes up from $20 to $22 a box. In direct response, Goldsboro Farms supplies 1,200 boxes of apples instead of 1,000 boxes. Compute the coefficient of price elasticity (midpoints approach) for Goldsboro’s supply. Is its supply elastic, or is it inelastic? LO6.4
Answers: elasticity of supply = percentage change in quantity supplied
percentage change in price
Es = 1.91; supply is elastic
Feedback: The formula for measuring the elasticity of supply is the same as the formula for measuring the elasticity of demand. Divide the percentage change in quantity by the percentage change in price. The only difference is that we do not need to take absolute value here because the price and quantity will move in the same direction (implying the elasticity is already positive).
Consider the following values: Suppose the price of apples goes up from $20 to $22 a box. In direct response, Goldsboro Farms supplies 1200 boxes of apples instead of 1000 boxes. Here we have two ordered pairs (1000, 20) and (1200, 22), note the form is (Q,P).
The same interpretation also applies. Supply is elastic if greater than 1, inelastic if less than 1, and is unit elastic if the elasticity equals 1. Thus, in this case, supply is elastic.
6. ADVANCED ANALYSIS Currently, at a price of $1 each, 100 popsicles are sold per day in the perpetually hot town of Rostin. Consider the elasticity of supply. In the short run, a price increase from $1 to $2 is unit elastic (Es = 1.0). So how many popsicles will be sold each day in the short run if the price rises to $2 each? In the long run, a price increase from $1 to $2 has an elasticity of supply of 1.50. So how many popsicles will be sold per day in the long run if the price rises to $2 each? (Hint: Apply the midpoints approach to the elasticity of supply.) LO6.4
Answers: 200 per day in the short run; 300 per day in the long run.
Feedback: To answer this question we need to use the midpoint formula. Assume we have the two ordered pairs (Q1,P1) and (Q2,P2).
We can then solve this equation to determine the quantity sold as a result of a price increase.
Consider the following values: At a price of $1 each, 100 popsicles are sold per day in Rostin. In the short run, a price increase from $1 to $2 is unit elastic (Es = 1.0). So how many popsicles will be sold each day in the short run if the price rises to $2 each? In the long run, a price increase from $1 to $2 has an elasticity of 1.50. So how many popsicles will be sold per day in the long run if the price rises to $2 each?
For the short run we have the following information. with the ordered pairs of (100,1) and (Q2,2). Here we need to solve for Q2. Substituting the values into the above formula, we have:
This implies,
Solving for Q2 we have the following:
We can do the same exercise for the long run. Here we have the following information. with the ordered pairs of (100,1) and (Q2,2). Here we need to solve for Q2.
This implies:
Thus, we sell 200 popsicles in the short run and 300 in the long run when price increases from $1 to $2. (Note, this implies an increase in demand (shift right)).
7. Lorena likes to play golf. The number of times per year that she plays depends on both the price of playing a round of golf as well as Lorena’s income and the cost of other types of entertainment—in particular, how much it costs to go see a movie instead of playing golf. The three demand schedules in the table below show how many rounds of golf per year Lorena will demand at each price under three different scenarios. In scenario D1, Lorena’s income is $50,000 per year and movies cost $9 each. In scenario D2, Lorena’s income is also $50,000 per year, but the price of seeing a movie rises to $11. And in scenario D3, Lorena’s income goes up to $70,000 per year while movies cost $11. LO6.5
a. Using the data under D1 and D2, calculate the cross elasticity of Lorena’s demand for golf at all three prices. (To do this, apply the midpoints approach to the cross elasticity of demand.) Is the cross elasticity the same at all three prices? Are movies and golf substitute goods, complementary goods, or independent goods?
b. Using the data under D2 and D3, calculate the income elasticity of Lorena’s demand for golf at all three prices. (To do this, apply the midpoints approach to the income elasticity of demand.) Is the income elasticity the same at all three prices? Is golf an inferior good?
Answers: (a) -2.00, -2.50, -3.33; No, the cross price elasticity is not the same at the three prices; Movies and golf are complementary goods. (b) 1.20, 2.00, 2.57; No, the income elasticity is different at each of the three prices; No, golf is not an inferior good—it is a normal good.
Feedback: Consider the following values and table: In scenario D1, Lorena’s income is $50,000 per year and movies cost $9 each. In scenario D2, Lorena’s income is also $50,000 per year, but the price of seeing a movie rises to $11. And in scenario D3, Lorena’s income goes up to $70,000 per year while movies cost $11.
Part (a): To calculate the cross elasticity we use the percentage change in quantity of one good divided by the percentage change in the price of another good. For the current problem we will look at the percentage in the quantity of golf games divided by the percentage change in the price of movies.
At the price of $50 for a golf game (hold constant for this calculation because we are looking at how golf games respond to a change in the price of movies) we have the following ordered pairs (15, 9) and (10, 11). Note that the ordered pair is (golf games, price of a movie).
Here we use the same formula:
We do the same exercise for $35. Here we have the ordered pairs (25, 9) and (15, 11).
Finally we have the ordered pair of (40, 9) and (20, 11) at the price of $20 for a game of golf.
The cross elasticities are not the same at all three golf game prices. The percentage change in quantity is larger the lower the price.
To determine if movies and golf are substitute goods, complementary goods, or independent goods we have the following rule.
If the cross elasticity is negative then the goods are complements. The logic underlying this rule is as follows. If the price of a movie increases we know that we will see fewer movies. This implies that the quantity of movies declines. Also, given the negative cross elasticity we know that golf games decline as the price of a movie increases. This implies that as the price of movies goes up we consume less movies and golf games. This implies the goods are complements.
Thus, our answer is golf and movies are complements.
A similar logic applies to substitute goods. If the price of good A increases then the quantity demanded of good A goes down. If the cross elasticity is positive then this implies the demand for the good B increases as a result of the price increase for good A. Thus, the quantity of good A decreases and the quantity of good B increases. This implies good A and good B are substitutes.
Finally two goods are independent if the cross elasticity is zero. A price change in one good does not change the quantity of the other good.
Part (b): To calculate the income elasticity we use a similar approach. Here we divide the percentage change in quantity by the percentage change in income. We do this at every price for the good.
For our golf example we have the following income elasticities.
At the price of $50 for a golf game (hold constant for this calculation because we are looking at how golf games respond to a change in income) we have the following ordered pairs (10, 50000) and (15, 70000). Note that the ordered pair is (golf games, income).
We do the same exercise for $35. Here we have the ordered pairs (15, 50000) and (30, 70000).
Finally we have the ordered pair of (20, 50000) and (50, 70000) at the price of $20 for a game of golf.
The income elasticity is not the same at each price of a game of golf. Golf games are more responsive to changes in income the lower the price of golf.
To determine if golf is a normal good or inferior good we have the following rule.
If the income elasticity is positive then the good is a normal good. The higher an individual's income the more of the good they consume.
Thus, golf is a normal good.
If the income elasticity is negative, then the good is an inferior good. The higher an individual's income the less of the good they consume.
8. ADVANCED ANALYSIS Suppose the equation for the demand curve for some product X is P = 8 ? 0.6Q and the supply curve is P = 2 + 0.4Q. What are the equilibrium price and quantity? Now suppose an excise tax is imposed on X such that the new supply equation is P = 4 + 0.4Q. How much tax revenue will this excise tax yield the government? LO6.6
Answer: To determine the equilibrium quantity we equate the supply schedule with the demand schedule (in equilibrium the price must be the same for both schedules).
8 ? 0.6Q = 2 + 0.4Q or 8 - 2 = 0.6Q + 0.4Q, thus Q*=6
We can solve for the equilibrium price by substituting the equilibrium quantity back into the supply or demand schedule.
Supply: P = 2+.4x6 = 4.4 (or $4.40)
Demand: P = 8 -0.6x6 = 4.4 (or $4.40)
If the government imposes an excise tax on the firm of $2 the new supply schedule will be P = 4 + 0.4Q. The firm must now charge an additional $2 per unit to cover the cost of the tax. Thus, the additional $2 shows up in the intercept.
Again, to determine the equilibrium quantity we equate the NEW supply schedule with the demand schedule.
8 ? 0.6Q = 4 + 0.4Q or 8 - 4 = 0.6Q + 0.4Q, thus Q*=4
We can solve for the equilibrium price by substituting the equilibrium quantity back into the NEW supply or demand schedule.
Supply: P = 4+0.4x4 = 5.6 (or $5.60)
Demand: P = 8 -0.6x4 = 5.6 (or $5.60)
Since the government collects $2 per unit sold, government revenue equals $8 (=$2x4).
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