QUESTION TWO [2 marks]:

Read the paper below:

Child Safety Seats on Commercial Airliners:

A Demonstration of Cross-Price Elasticities

Abstract: The cross-price elasticity concept can be a difficult one for microeconomics

students to grasp. We provide a real-life application of cross-price elasticities in

policymaking. After a debate that spanned more than a decade and included input from

safety engineers, medical personnel, politicians and economists, the Federal Aviation

Administration (FAA) recently announced that it would not mandate the use of child

safety seats on commercial airliners.The FAA's analysis revealed that if families were

forced to purchase additional airline tickets, they might opt to drive rather than fly and

driving represents a far more dangerous mode of travel.Given the relatively high cross-

price elasticity between automobile travel and air travel, the FAA concluded that the

mandatory child safety seat policy fails to pass the cost-benefit testthe policy would

lead to a net increase in the number of fatalities.We review the FAA's decision-making

process and highlight the role of economic analysis in developing public policy.

Keywords:cross-price elasticities, cost-benefit analysis, public policy

JEL classification: A20; A22

The concept of a cross-price elasticity is an important one in microeconomics, and our

collective experience is that students frequently have difficulty understanding and

applying this concept. In addition, there is a tendency for students to treat cross-price

elasticities as merely a theoretical concept that is of limited practical value. We examine

the child safety seat (CSS) mandate proposal on commercial airplanes as a real-life

example that illustrates the use of cross-price elasticities in policymaking. A CSS

mandate would raise the price of flying for passengers with children because seats must

be purchased separately for infants less than two years of age. This increase in pricereduces the quantity demanded of air travel and increases the quantity of automobile

travel, a riskier substitute for air travel.If the substitution effectthat is, the cross-price

elasticityis sufficiently large, mandatory CSS may increase the number of fatalities.

Through this example, we demonstrate that the cross-price elasticity concept is not only

an important one in microeconomics, but also an important tool for policy analysis.

On August 25, 2005, the Federal Aviation Administration (FAA) announced that it

would not mandate the use of CSS on airplanes. The FAA (2005) indicated in its

analysis that if families were forced to purchase additional airline tickets, they may opt to

drive rather than fly and driving represents a far more dangerous mode of travel.In other

words, given the effective cross-price elasticities, the increase in the price of airfare for

families would cause them to substitute relatively risky automobile travel for relatively

safe air travel. As shown in Tables 1 and 2, fatalities per 100 million passenger miles

traveled are approximately .03 for air travel and .97 for highway travel during the period

from 1995 through 2003.1See also Figure 1.It is estimated that a CSS mandate would

save 0.3 infant lives per year in the air.Specifying demand functions for air travel and

highway travel and adopting the cross-price elasticity estimate used in Windle and

Dresner (1991), we estimate that a CSS mandate would cause an additional 11.5 deaths

per year on the nation's roadways.Thus, a mandatory CSS policy would be expected to

lead to a net increase in the number of fatalities.

To the casual observer, it may seem that a policy mandating CSS on commercial

airliners is a "no-brainer."After all, if we require CSS in automobiles traveling 60 miles

per hour, it stands to reason that we should also require CSS on airplanes traveling 600

miles per hour. And yet, as Thomas Sowell (1995) has previously observed, whether

mandating CSS on commercial aircraft constitutes good public policy, in the sense that itresults in a net reduction in fatalities, is first and foremost an empirical issue.To wit, if

the cross-price elasticity between automobile travel and air travel is sufficiently large, the

effective higher price of air travel will induce a large number of families to substitute

risky automobile travel for relatively-safe air travel resulting in a net increase in the

number of fatalities.

We use the mandatory CSS policy proposal as an avenue through which to highlight

the importance of cross-price elasticities and their role in developing public policy.To

illustrate the relevant tradeoffs, we first review the cost-benefit analysis conducted by the

FAA in arriving at its decision not to implement the CSS policy. We then proceed to

develop the key demand concepts underlying the relevant tradeoffs. To further

underscore the instructional nature of this material, classroom discussion questions and

quantitative exercises are provided to enhance student learning.

OVERVIEW OF FAA ANALYSIS

From the time of its inception in 1958, the FAA has permitted children under two

years of age on commercial flights to sit on the lap of an accompanying adult.2From a

safety standpoint, the practice was noncontroversial over most of its history because of

the absence of effective CSS for airplanes.This technological constraint dissipated over

the ensuing decades, however, to the point that in 1982 the FAA issued its first regulation

defining performance standards for CSS used on airlines. This regulation essentially

approved those safety seats that pass the FAA's dynamic test.3In 1985, the FAA updated

standards to ensure that approved CSS performed satisfactorily in a rollover test.

By 1990, three econometric studies had been undertaken to explore the overall safety

implications should the FAA require use of CSS on commercial aircraft (McKenzie and

Lee 1990; Windle and Dresner 1991; U.S. Department of Transportation 1990).Each ofthese studies, including one commissioned by the FAA itself, concluded that such a

policy would result in a net loss of lives.The basis for this result was that some families,

if required to purchase an extra seat for their young child, would substitute highway

travel for air travel.4 Because the highway mortality rate per passenger mile is

significantly greater than the corresponding mortality rate for air travel, the FAA's 1990

study estimated a net loss of 8.2 lives during the ensuing 10 years should CSS be

mandated on commercial aircraft. Additionally, the study projected 52 more serious

injuries and 2,300 more minor injuries over the same period should a CSS mandate be

enacted.The essence of this result, that such a policy would have negative overall safety

consequences, was further corroborated by an updated 1993 econometric study prepared

for the FAA (Apogee Research 1993).

Notably, the central conclusion of these studies formed the basis for the FAA's de

facto decision during the early 1990s not to mandate CSS on commercial airlines despite

strong pressure from the National Transportation Safety Board, members of Congress,

and the Association of Flight Attendants.5

Reacting to a 1997 recommendation from the White House Commission on Aviation

Safety and Security that the FAA create such a mandate, the FAA issued an Advanced

Notice of Proposed Rulemaking on February 18, 1998, concerning the requirement of

CSS on commercial airplanes.This notice allowed for a period in which the public could

voice opinions on the issue.After years of public feedback, the FAA officially withdrew

the notice on August 26, 2005, in order "to pursue other options that will mitigate the risk

of child injuries and fatalities in aircraft" (Federal Register 2005). The FAA justified

this policy decision with essentially the same argument that it had provided when the

issue first became public in 1990.During the early years of the CSS debate, major United States airlines, as represented

by the Air Transport Association (ATA), supported an FAA mandate.On February 22,

1990, the ATA issued a petition to the FAA requesting that the FAA act accordingly.

Following the FAA's 1995 Report to Congress, which departed from previous studies in

predicting an adverse market outcome for the airline industry should a CSS mandate take

effect, the ATA relinquished its initial position by withdrawing the 1990 petition.

Subsequently, the ATA has publicly supported a non-regulatory solution to the child

safety issue (U.S. Cong. House of Representatives 1996).

DEMAND CONCEPTS

In this section, we develop the basic demand concepts required for students to

understand the economic analysis that the FAA conducted in arriving at its public policy

decision not to mandate CSS.

Suppose the demand functions for air travel and automobile travel are given,

respectively, by:

(1) ln(QA)= 1 + 2 ln(PA) + 3 ln(PM) + 4 ln(I), and

(2) ln(QM)= 1 + 2 ln(PM) + 3 ln(PA) + 4 ln(I),

where PA and QA are prices and quantities of family travel units (FTUs) by air travel, PM

and QM are prices and quantities of FTUs by automobile travel, I is income and ln() is

the natural logarithm function.A typical FTU consists of 4 members, including one child

under 2 years of age and one between 2 and 5 years of age.6 Given the double-log

functional form, the coefficients in the demand equations represent elasticities.

According to the Law of Demand, we expect the own-price elasticities, 2 and 2, to be

negative. Generally, air travel and automobile travel are considered to be substitute modes of long-distance travel, so 3 and 3 are expected to be positive.As both goods are

generally considered to be normal goods, 4 and 4 are expected to be positive.

The demand function for automobile travel in (2) is of particular interest for the CSS

policy. The cross-price elasticity of QM with respect to PA is 3. This represents the

percentage change of FTUs that will choose to travel by automobile if the price of air

travel rises by 1 percent, ceteris paribus.If the cross-price elasticity is zero (3 = 0), the

adoption of the CSS policy would reduce the number of fatalities associated with air

travel without increasing the number of fatalities associated with automobile travel.

Conversely, if the cross-price elasticity is positive, the implementation of the CSS policy

would reduce the risk associated with air travel, but would simultaneously increase the

number of families who choose to drive and thereby increase the number of families at

risk through automobile travel.

We adopt the assumptions in Windle and Dresner (1991) in our numerical analysis.

The mortality rate for air travel is 0.264 per billion passenger-miles and that of auto travel

is 12.80 per billion passenger-miles.The price of air travel per FTU is $295.75 before

the CSS policy is implemented and $357.90 afterwards, a 21 percent increase in price.

The cross-price elasticity (3) is 0.356.This implies that a 1 percent increase in the price

of air travel leads to a 0.356 percent increase in FTUs by automobile, ceteris paribus.

Hence, a 21 percent increase in the price of air travel leads to a 7.48 percent increase in

FTUs by automobile, which translates into 300,000 FTUs.The increase in automobile

fatalities induced by the CSS policy is 11.5 fatalities per year. It is estimated that 0.3

lives can be saved in air travel per year from the CSS policy.The implementation of the

CSS policy would divert many FTUs to travel by automobile, a far more dangerous modeof travel, and thus increase the net number of fatalities.It was on the basis of just such an

analysis that the FAA declined to implement the CSS policy.

To further demonstrate the relationship between the cross-price elasticity and the

change in fatalities, we use Figure 2 to illustrate the additional fatalities from automobile

travel and the decrease in fatalities by air travel when the CSS policy is implemented.

The flat line shows the reduced number of air travel fatalities resulting from the CSS

policy0.3 per year. The dotted line shows the relationship between the additional

automobile travel fatalities and the cross-price elasticity upon implementation of the CSS

policy. For example, if the cross-price elasticity is 0.20, the increase in automobile

fatalities is 6.5. The breakeven cross-price elasticity is 3 = 0.01.Hence, when 3 < 0.01,

the number of air travel fatalities avoided as a result of the CSS policy exceeds the

increased number of automobile fatalities and vice versa.

Based on the demand function for air travel in (1), the own-price elasticity for air

travel is 2.According to Windle and Dresner (1991), 2 = -0.381, which implies that a 1

percent increase in price of air travel leads to a 0.381 percent decrease in FTUs.Because

the price of air travel would be expected to increase by 21 percent, the number of FTUs

by air travel will decrease by 8 percent or 321,000 FTUs.If the own-price elasticity is

sufficiently large in absolute value, implementing the CSS policy would result in lower

profits for the airlines.7, 8 CONCLUSION

This discussion highlights the role of economic analysis and cross-price elasticities in

particular in informing the FAA's decision-making concerning the merits of the CSS

policy.After extensive analysis over more than a decade, the FAA concluded that the

mandatory CSS policy failed to pass the cost-benefit test in that the expected number of

lives saved in the air from the implementation of the CSS policy was considerably less

than the number of lives that would be lost as a result of diverting families to the nation's

relatively risky highways.In this case, cross-price elasticities, given their prominent role

in developing public policy, are indeed a matter of life and death.FURTHER READING

Interested readers can find additional discussion on this topic in Windle and Dresner

(1991), McKenzie and Warner (1987), and U.S. Department of Transportation (1990).It

should be noted, however, that the last two articles are technical in nature and may only

be appropriate for undergraduate students with a strong quantitative background. For

other applications of cross-price elasticities, see Bask and Melkersson (2003) and Ault et

al. (2005) for an interesting exchange on cross-price elasticities and the cessation of

smoking. See Davis and Wohlgenant (1993) for the first estimate of the cross-price

elasticity of natural Christmas trees with respect to artificial Christmas trees. See

Abraham et al. (2002) for estimates of cross-price elasticities of different health insurance

plans. See Decker and Schwartz (2000) for an interesting analysis of the asymmetrical

demand relationship between cigarettes and alcohol.See Diamond and Fayed (1998) for

an analysis of the substitutability between adult labor and child labor.TABLE 1:U.S. Highway Fatalities per 100 Million Passenger-Miles

Year

1995 1996 1997 1998 1999 2000 2001 2002 2003

Rate 1.0811 1.0600 1.0274 0.9880 0.9692 0.9555 0.9087 0.9215 0.9082

Calculated using U.S. highway fatalities and U.S. highway passenger-miles for each year.

Source: U.S. Department of Transportation, Bureau of Transportation Statistics, National Transportation

Statistics, annual.

TABLE 2:U.S. Air Carrier Fatalities per 100 Million Passenger-Miles

Year

1995 1996 1997 1998 1999 2000 2001 2002 2003

Rate 0.0416 0.0874 0.0018 0.0002 0.0025 0.0178 0.1091 0.0000 0.0044

Calculated using U.S. air carrier fatalities and U.S. air carrier passenger-miles for each year.

Source: U.S. Department of Transportation, Bureau of Transportation Statistics, National Transportation

Statistics, annual.

The paper discusses why the FAA decided not to mandate the use of Child Safety Seats (CSS) on commercial airliners. Suppose the cross-price elasticity of QM with respect to PA (3 in equation 2) was found to be negative instead.

(a). What would this mean about the relationship between air travel and automobile travel? Give a simple practical example of a situation when a negative cross price elasticity might make sense [1 mark].

(b). In this situation of a negative cross price elasticity, would you recommend the use of child safety seats? Clearly state Yes or No, and provide an explanation for your choice (computation not necessary) [1 mark]