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CHAPTER 4ELASTICITY

CHAPTER OVERVIEWBoth the elasticity coefficient and the total receipts test for measuring price elasticity of demand are presented in the chapter. The text attempts to sharpen students’ ability to estimate price elasticity by discussing its major determinants. The chapter reviews a number of applications and presents empirical estimates for a variety of products. Cross and income elasticities of demand and price elasticity of supply are also addressed.

WHAT’S NEWThe title has been changed. The title in the 12 th edition was “Elasticity, Consumer Surplus, and Producer Surplus.”

Discussion of consumer and producer surplus has been moved to chapter 5 in the 13th edition.

“Terms and Concepts” at the end of the chapter has been updated to exclude the following: consumer surplus, producer surplus, and efficiency losses (or deadweight loss) since this information was moved to chapter 5.

INSTRUCTIONAL OBJECTIVESAfter completing this chapter, students should be able to:

1. Define demand and supply and state the laws of demand and supply (review from Chapter 3).

2. Determine equilibrium price and quantity from supply and demand graphs and schedules (from Chapter 3).

3. Define price elasticity of demand and compute the coefficient of elasticity given appropriate data on prices and quantities.

4. Explain the meaning of elastic, inelastic, and unitary price elasticity of demand.

5. Recognize graphs of perfectly elastic and perfectly inelastic demand.

6. Use the total-revenue test to determine whether elasticity of demand is elastic, inelastic, or unitary.

7. List four major determinants of price elasticity of demand.

8. Explain how a change in each of the determinants of price elasticity would affect the elasticity coefficient.

9. Define price elasticity of supply and explain how the producer’s ability to shift resources to alternative uses and time affect price elasticity of supply.

10. Explain cross elasticity of demand and how it is used to determine substitute or complementary products.

11. Define income elasticity and its relationship to normal and inferior goods.

12. Define and identify the terms and concepts listed at end of the chapter.

COMMENTS AND TEACHING SUGGESTIONS1. Suggestions given for chapter 3 are also pertinent to this chapter, as an understanding of demand

and supply is essential to understanding this chapter.

2. Find, or have the students find, real-world examples of changing prices to explore the forces of the changing demand and supply. Any daily newspaper or business periodical should have such articles. Articles on impacts of a drought, freeze, strike, or a new fad product would provide such examples. Use the examples to differentiate between changes in quantity demanded and change in demand.

3. Draw demand curves that illustrate relatively elastic, relatively inelastic and unitary elastic. When discussing the idea that every downward sloping demand curve has all three properties, use salt as an example. Ask the students if anyone knows what a box of salt costs. Probably no one will. Then ask them if anyone cares what a box of salt costs and if they would hesitate buying a box if the price were to increase from 30 cents to 33 cents. Then ask if they would answer the same way if the price were to increase from $100 per box to $110.

4. Emphasize the total revenue test for elasticity. Many important applications turn on whether a price change is directly or inversely related to the change in total revenue. Most students assume that if you raise the price of a product or service, more money will be collected. Ask students how the theatre department could increase revenue from ticket sales. The following discussion illustrates the point that they must know the coefficient of elasticity in order to make the correct choice to raise or lower the price for more revenue. It also will give you an opportunity to explain why economists often give more than one answer to a question.

5. The discussion on income elasticity and cross elasticity provides an opportunity to review the difference between “change in demand” and “change in quantity demanded” and substitute good and complementary goods.

STUDENT STUMBLING BLOCKS1. The general concept of price elasticity of demand is relative easy for the students to understand

particularly if they have a good grasp of the demand concepts in chapter 3. Where students run into problems is when they are introduced to the calculation of the coefficient of elasticity of demand. Use an example of an elastic demand schedule and a demand curve. Calculate the percentage changes in both price and quantity and ask them to identify whether the demand is elastic or inelastic by comparing the two percentages. Repeat the process with an inelastic demand schedule and demand curve.

2. A related problem is for the students to remember whether the percentage change in quantity or the percentage price is the numerator or the denominator of the coefficient ratio. A way of overcoming this problem is to explain that the coefficient is greater than “1” when the demand is elastic, and thus the larger of the two percentages (percentage change in quantity demanded) must be divided by the smaller of the two percentages (percentage in change in price). Use the same analysis for the inelastic demand.

3. Some students, especially those with a stronger math background, will want to calculate percentage changes in quantity demanded and price from the starting values rather than using the midpoint formula. To help them understand why it is important to use the midpoint formula, have them calculate the elasticity over a given range first when the price is rising and then when it is falling. The different coefficients they find should help convince them as to why they need the midpoint formula at this point.

4. There are many clever ways to help students remember the difference between elastic and inelastic. The perfectly inelastic curve looks like an “I” for “inelastic,” the perfectly elastic curve resembles


an “E” for “elastic.” A trampoline (horizontal like a perfectly elastic curve) has a lot of bounce; a wall (vertical like a perfectly inelastic curve) moves little when force is applied.

LECTURE NOTES

I. Introduction

A. Learning objectives – After reading this chapter, students should be able to:

1. Discuss the price elasticity of demand and how it can be applied.

2. Explain the usefulness of the total revenue test for price elasticity of demand.

3. Describe the price elasticity of supply and how it can be applied.

4. Apply cross elasticity of demand and income elasticity of demand.

5. Apply the concept of elasticity to real-world situations.

B. Elasticity of demand measures how much the quantity demanded changes with a given change in price of the item, change in consumers’ income, or change in price of related product.

C. Price elasticity is a concept that also relates to supply.

D. The chapter explores both elasticity of supply and demand and applications of the concept.

II. Price Elasticity of Demand

A. Law of demand tells us that consumers will respond to a price decrease by buying more of a product (other things remaining constant), but it does not tell us how much more.

B. The degree of responsiveness or sensitivity of consumers to a change in price is measured by the concept of price elasticity of demand.

1. If consumers are relatively responsive to price changes, demand is said to be elastic.

2. If consumers are relatively unresponsive to price changes, demand is said to be inelastic.

3. Note that with both elastic and inelastic demand, consumers behave according to the law of demand; that is, they are responsive to price changes. The terms elastic or inelastic describe the degree of responsiveness. A precise definition of what we mean by “responsive” or “unresponsive” follows.

4. CONSIDER THIS … A Bit of a Stretch

The Ace bandage stretches a lot when force is applied (elastic); the rubber tie-down (not to be confused with a rubber band) moves stretches little when force is applied (inelastic).

C. Price elasticity coefficient and formula:

Quantitative measure of elasticity, Ed = percentage change in quantity/ percentage change in price.

1. Using two price-quantity combinations of a demand schedule, calculate the percentage change in quantity by dividing the absolute change in quantity by one of the two original quantities. Then calculate the percentage change in price by dividing the absolute change in price by one of the two original prices.

2. Estimate the elasticity of this region of the demand schedule by comparing the percentage change in quantity and the percentage change in price. Do not use the ratio

formula at this time. Emphasize that it is the two percentage changes that are being compared when determining elasticity.

3. Show that if the other original quantity and price were used as the denominator that the percentage changes would be different. Explain that a way to deal with this problem is to use the average of the two quantities and the average of the two prices.

4. Using averages – the midpoint formula

a. Using traditional calculations, the measured elasticity over a given range of prices is sensitive to whether one starts at the higher price and goes down, or the lower price and goes up. The midpoint formula calculates the average elasticity over a range of prices to alleviate that problem.

b. The midpoint formula for elasticity is:

Ed = [(change in Q)/(sum of Q’s/2)] divided by [(change in P)/(sum of P’s/2)]

c. Have the students calculate each of the percentage changes separately to determine whether the demand is elastic or inelastic. After the students have determined the type of elasticity, then have them insert the percentage changes into the formula.

d. Students should practice the exercise in Table 4.1. (Key Question 2)

5. Emphasis: The percentages changes are compared, not the absolute changes.

a. Absolute changes depend on choice of units. For example, a change in the price of a $10,000 car by $1 and is very different than a change in the price of a $1 can of beer by $1. The auto’s price is rising by a fraction of a percent while the beer rice is rising 100 percent.

b. Percentages also make it possible to compare elasticities of demand for different products.

6. Because of the inverse relationship between price and quantity demanded, the actual elasticity of demand will be a negative number. However, we ignore the minus sign and use absolute value of both percentage changes.

7. If the coefficient of elasticity of demand is a number greater than one, we say demand is elastic; if the coefficient is less than one, we say demand is inelastic. In other words, the quantity demanded is “relatively responsive” when Ed is greater than 1 and “relatively unresponsive” when Ed is less than 1. A special case is if the coefficient equals one; this is called unit elasticity.

8. Note: Inelastic demand does not mean that consumers are completely unresponsive. This extreme situation called perfectly inelastic demand would be very rare, and the demand curve would be vertical.

9. Likewise, elastic demand does not mean consumers are completely responsive to a price change. This extreme situation, in which a small price reduction would cause buyers to increase their purchases from zero to all that it is possible to obtain, is perfectly elastic demand, and the demand curve would be horizontal.

D. Graphical analysis:

1. Illustrate graphically perfectly elastic, relatively elastic, unitary elastic, relative inelastic, and perfectly inelastic. (Figures 4.1 and 4.2)


2. Using Figure 4.2, explain that elasticity varies over range of prices.

a. Demand is more elastic in upper left portion of curve (because price is higher, quantity smaller).

b. Demand is more inelastic in lower right portion of curve (because price is lower, quantity larger).

3. It is impossible to judge elasticity of a single demand curve by its flatness or steepness, since demand elasticity can measure both elastic and inelastic at different points on the same demand curve.

E. Total-revenue test is the easiest way to judge whether demand is elastic or inelastic. This test can be used in place of elasticity formula, unless there is a need to determine the elasticity coefficient.

1. Elastic demand and the total-revenue test: Demand is elastic if a decrease in price results in a rise in total revenue, or if an increase in price results in a decline in total revenue. (Price and revenue move in opposite directions).

2. Inelastic demand and the total-revenue test: Demand is inelastic if a decrease in price results in a fall in total revenue, or an increase in price results in a rise in total revenue. (Price and revenue move in same direction).

3. Unit elasticity and the total-revenue test: Demand has unit elasticity if total revenue does not change when the price changes.

4. The graphical representation of the relationship between total revenue and price elasticity is shown in Figure 4.2.

5. Table 4.2 provides a summary of the rules and concepts related to elasticity of demand.

F. There are several determinants of the price elasticity of demand.

1. Substitutes for the product: Generally, the more substitutes, the more elastic the demand.

2. The proportion of price relative to income: Generally, the larger the expenditure relative to one’s budget, the more elastic the demand, because buyers notice the change in price more.

3. Whether the product is a luxury or a necessity: Generally, the less necessary the item, the more elastic the demand.

4. The amount of time involved: Generally, the longer the time period involved, the more elastic the demand becomes.

G. Table 4.3 presents some real-world price elasticities. Use the determinants discussed to see if the actual elasticities are equivalent to what one would predict.

H. There are many practical applications of the price elasticity of demand.

1. Inelastic demand for agricultural products helps to explain why bumper crops depress the prices and total revenues for farmers.

2. Governments look at elasticity of demand when levying excise taxes. Excise taxes on products with inelastic demand will raise the most revenue and have the least impact on quantity demanded for those products.

3. Demand for cocaine is highly inelastic and presents problems for law enforcement. Stricter enforcement reduces supply, raises prices and revenues for sellers, and provides more incentives for sellers to remain in business. Crime may also increase as buyers have to find more money to buy their drugs.

a. Opponents of legalization think that occasional users or “dabblers” have a more elastic demand and would increase their use at lower, legal prices.

b. Removal of the legal prohibitions might make drug use more socially acceptable and shift demand to the right.

III. Price Elasticity of Supply

A. The concept of price elasticity also applies to supply. The elasticity formula is the same as that for demand, but we must substitute the word “supplied” for the word “demanded” everywhere in the formula.

Es = percentage change in quantity supplied / percentage change in price

As with price elasticity of demand, the midpoints formula is more accurate.

B. The ease of shifting resources between alternative uses is very important in price elasticity of supply because it will determine how much flexibility a producer has to adjust his/her output to a change in the price. The degree of flexibility, and therefore the time period, will be different in different industries. (Figure 4.4)

1. The market period is so short that elasticity of supply is inelastic; it could be almost perfectly inelastic or vertical. In this situation, it is virtually impossible for producers to adjust their resources and change the quantity supplied. (Think of adjustments on a farm once the crop has been planted.)

2. The short-run supply elasticity is more elastic than the market period and will depend on the ability of producers to respond to price change. Industrial producers are able to make some output changes by having workers work overtime or by bringing on an extra shift.

3. The long-run supply elasticity is the most elastic, because more adjustments can be made over time and quantity can be changed more relative to a small change in price, as in Figure 4.4c. The producer has time to build a new plant.

C. Applications of the price elasticity of supply.

1. Antiques and other non-reproducible commodities are inelastic in supply, sometimes the supply is perfectly inelastic. This makes their prices highly susceptible to

fluctuations in demand.

2. Gold prices are volatile because the supply of gold is highly inelastic, and unstable demand resulting from speculation causes prices to fluctuate significantly.

IV. Cross elasticity and income elasticity of demand:

A. Cross elasticity of demand refers to the effect of a change in a product’s price on the quantity demanded for another product. Numerically, the formula is shown for products X and Y.

Exy = (percentage change in quantity of X) / (percentage change in price of Y)

1. If cross elasticity is positive, then X and Y are substitutes.

2. If cross elasticity is negative, then X and Y are complements.

3. Note: if cross elasticity is zero, then X and Y are unrelated, independent products.

B. Income elasticity of demand refers to the percentage change in quantity demanded that results from some percentage change in consumer incomes.

Ei = (percentage change in quantity demanded) / (percentage change in income)

1. A positive income elasticity indicates a normal or superior good.


2. A negative income elasticity indicates an inferior good.

3. Those industries that are income elastic will expand at a higher rate as the economy grows.

V. Elasticity and Real World Applications

A. Tax incidence refers to who actually bears the economic burden of a tax (see Figure 4-5).

1. The division of the burden is not obvious. Figure 4-5 shows the impact of a $2 per-bottle tax on wine that was priced at $8 per bottle before the tax.

2. S is the no-tax supply situation and S t is the after-tax supply curve. The new equilibrium price rises to $9, not $10 as one might expect with the $2 tax.

a. Consumers pay $1 more per bottle.

b. Producers receive $1 less per bottle.

3. In this example, consumers and producers share the burden of the tax equally. The incidence is not completely on either one.

B. Elasticities of demand and supply explain the incidence of an excise or sales tax.

1. Given supply, the more inelastic the demand for the product, the larger the portion of the tax is shifted forward to consumers (Figure 4-6b). Figure 4-6a shows the situation if demand is more elastic.

2. Given demand, the more inelastic the supply (Figure 4-7b), the larger the portion of the tax borne by producers or sellers. Figure 4-7a shows the situation if supply is more elastic.

3. Rent controls also create special problems because they make it less attractive for landlords to offer housing and so shortages of housing will develop.

VI. LAST WORD: Elasticity and Pricing Power: Why Different Consumers Pay Different Prices

A. Sellers often charge different prices for goods based on differences in price elasticity of demand.

B. The ability to charge different prices depends on some market power; that is, some ability to control price (unlike the competitive model where all buyers and sellers exchange at exactly the same price).

C. Customers are grouped according to elasticities. Business travelers have more inelastic demand for air travel, and thus can be charged a higher price than the more price elastic tourist. The low budgets of children make their demand more price elastic, explaining why they receive discounts for movies or sporting events. In a like manner, colleges and universities recognize that income differences cause students to have different elasticities of demand for higher education, and schools attempt to discount prices (through financial aid) based on price sensitivity.

D. The above are examples of price discrimination, a topic covered in more detail in Chapter 8.

QUIZ1. A perfectly inelastic demand schedule:

A. rises upward and to the right, but has a constant slope.

B. can be represented by a line parallel to the vertical axis.

C. cannot be shown on a two-dimensional graph.

D. can be represented by a line parallel to the horizontal axis.

Answer: B

2. When the percentage change in price is greater than the resulting percentage change in quantity demanded:

A. a decrease in price will increase total revenue.

B. demand may be either elastic or inelastic.

C. an increase in price will increase total revenue.

D. demand is elastic.

Answer: C

3. Block's sells 500 bottles of perfume a month when the price is $7. A huge increase in resource costs causes price to rise to $9 and Block's only manages to sell 460 bottles of perfume. The price elasticity of demand is:

A. .33 and elastic

B. 3.0 and elastic

C. .33 and inelastic

D. 3.0 and inelastic

Answer: C

4. Demand is said to be inelastic when:

A. An increase in price results in a reduction in total revenue

B. A reduction in price results in an increase in total revenue

C. A reduction in price results in a decrease in total revenue

D. The elasticity coefficient exceeds one

Answer: C

5. In which of the following instances will total revenue decline?

A. price rises and supply is elastic

B. price falls and demand is elastic

C. price rises and demand is inelastic

D. price rises and demand is elastic

Answer: D


6. The main determinant of elasticity of supply is the:

A. number of close substitutes for the product available to consumers.

B. amount of time the producer has to adjust inputs in response to a price change.

C. urgency of consumer wants for the product.

D. number of uses for the product.

Answer: B

7. Price elasticity of supply is:

A. positive in the short run but negative in the long run.

B. greater in the long run than in the short run.

C. greater in the short run than in the long run.

D. independent of time.

Answer: B

8. Cross elasticity of demand measures how sensitive purchases of a specific product are to changes in:

A. the price of some other product.

B. the price of that same product.

C. income.

D. the general price level.

Answer: A

9. A remote island nation is discovered, and on this island the cross elasticity of demand for coconut milk and fruit punch is 1.0. This indicates that these two goods are:

A. Normal

B. Inferior

C. Complements

D. Substitutes

Answer: D

10. The supply of product X is elastic if the price of X rises by:

A. 5 percent and quantity supplied rises by 7 percent.

B. 8 percent and quantity supplied rises by 8 percent.

C. 10 percent and quantity supplied remains the same.

D. 7 percent and quantity supplied rises by 5 percent.

Answer: A

Questions

1. Explain why the choice between 1, 2, 3, 4, 5, 6, 7, and 8 “units,” or 1000, 2000, 3000, 4000, 5000, 6000, 7000, and 8000 movie tickets, makes no difference in determining elasticity in Table 4.1. LO 4.1

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. 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 upper left segment of the demand curve and inelastic in the lower right segment. LO 4.1


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.

3. 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. LO 4.2

Answer: The key determinants of price elasticity are substitutability, proportion of income; luxury versus necessity, and time. (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.

4. 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? LO 4.2

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.

5. Calculate total-revenue data from the demand schedule in question 2. Graph total revenue below your demand curve. Generalize about the relationship between price elasticity and total revenue. LO 4.2


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.

6. How would the following changes in price affect total revenue? That is, would total revenue increase, decrease, or remain unchanged? LO 4.2a. 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.)

7. 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. LO 4.3

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.

8. 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? LO 4.4

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).

9. The income elasticities of demand for movies, dental services, and clothing have been estimated to be +3.4, +1.0, and +0.5, respectively. Interpret these coefficients. What does it mean if an income elasticity coefficient is negative? LO 4.4

Answer: All are normal goods—income and quantity demanded move in the same direction. The positive coefficients indicates a normal good. 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.

10. 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? LO 4.4

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, reduce the consumption of other good (purchase 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.

11. What is the tax incidence of a tax when demand is highly inelastic? Highly elastic? What effect does the elasticity of supply have on the incidence of a tax? LO 4.5

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.

12. 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? LO 4.5

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*=6We 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).

The LAST WORD What is the purpose of charging different groups of customers different prices? Supplement the three broad examples in this 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).

PROBLEMS

1. Look at the demand curve in Figure 4.2a. 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 4.2b and 4.2c using, respectively, points c and d for Figure 4.2b and points e and f for Figure 4.2c. LO 4.1

Answers: 9/5 = 1.8; 5/9 = .5556; 1.

Feedback: Consider the following figures taken from the textbook (Figures 4.2a, 4.2b, and 4.2c).

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 4.2a (10,2) and (40,1), note that the ordered pair is (Q,P), we can calculate the elasticity.

Given the two points in Figure 4.2b (10,4) and (20,1), we can calculate the elasticity.


Given the two points in Figure 4.2c (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 4.2a, 4.2b, and 4.2c to the right by 10 units. For example, point a in Figure 4.2a would shift right from location (10 units, $2) to (20 units, $2) while point b would shift right 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? LO 4.1

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 4.2a, 4.2b, and 4.2c).

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 4.2a (10,2) and (40,1), we now have the two points (20,2) and (50,1).

Given the two points in Figure 4.2b (10,4) and (20,1), we now have (20,4) and (30,1).


Given the two points in Figure 4.2c (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? LO 4.2

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 that demand is unit-elastic over this range because there is no change in total revenue.

4. Danny “Dimes” Donahue is a neighborhood’s nine -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? LO 4.2

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 1200 boxes of apples instead of 1000 boxes. Compute the coefficient of price elasticity (midpoints approach) for Goldsboro’s supply. Is its supply elastic, or is it inelastic? LO 4.3

Es = 1.91; supply is elasticFeedback: 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. 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.) LO 4.3

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. How many times per year she plays depends on two things: (1) the price of playing a round of golf, and (2) Lorena’s income and the cost of other types of entertainment—in particular, how much it costs to 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 in 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. LO 4.4

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.

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