6|

Elasticity:

The Responsiveness

of Demand and

Supply

SOLUTIONS TO END-OF-CHAPTER EXERCISES

Answers to Thinking Critically Questions

1. Even if the overall demand for gasoline is inelastic, a revenue increase for Joe’s Gas-and-Go will occur only if the percentage increase in price is greater than the percentage decrease in quantity demanded. If Joe’s price increase is too large and Joe has other competitors who do not raise their prices, then it is possible that the percentage decrease in quantity demanded will result in a decrease in total revenue. 2. If Wal-Mart and Sam’s Club begin selling gasoline at lower prices than the conventional service stations, this will cause the demand curves faced by the conventional service stations to shift left and become more elastic, which will lower the equilibrium price of gasoline at these stations.

6.1

The Price Elasticity of Demand and its Measurement

Learning Objective: Define price elasticity of demand and understand how to measure it.

Review Questions

1.1

Price elasticity of demand = (percentage change in quantity demanded)/(percentage change in price). It isn’t measured by the slope of the demand curve because the slope depends arbitrarily on what units you are using. Slope will change by a factor of 100 if you use cents instead of dollars, for example. Or, for another example, consider six-packs of soda versus cans of soda: If the price drops by $1.00 per six-pack and this causes quantity demanded to increase by two six-packs, then that is the same thing as quantity demanded going up by 12 cans. So, you could calculate the slope either as −1/2 six-packs, or as −1/12 cans. In addition, using percentage changes in the elasticity formula allows for meaningful comparisons of demand responsiveness between very different kinds of goods: for example, breakfast cereal versus health care. Because the slope uses physical units of quantities, such comparisons are impossible.

1.2

The price elasticity = (percentage change in quantity demanded)/(percentage change in price) = –25%/10% = –2.5. This is elastic.

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CHAPTER 6 | Elasticity: The Responsiveness of Demand and Supply

1.3

In calculating the percentage change in price and quantity, the midpoint formula divides by the average of the starting and ending values.

(Q 2 − Q1)

( P 2 − P1)

÷

Q1 + Q 2 P1 + P 2

Midpoint formula:

2

2

Percentage changes can also be calculated by using the starting or ending value without averaging, but this gives different results depending on whether the starting or ending value is used. 1.4

A perfectly inelastic demand curve is shown by a vertical line, as shown at the bottom of Table 6–1. Such a good will have no substitutes—for example, a life-saving drug.

Problems and Applications

1.5

a.

12 ,000 ,000 −8,000 ,000

= − ,000 ,000

4

$2.00 −$3.00

b.

12 −8

= − . This is a much smaller value than in a.

4

$2.00 −$3.00

c. We can calculate the price elasticity using the midpoint formula as follows: Percentage change in quantity demanded =

Percentage change in price =

12 ,000 ,000 −8,000 ,000

×100 = 40 %

10 ,000 ,000

$2.00 − $3.00

×100 = −40 %

$2.50

So, the price elasticity of demand =

40%

= −1

− 40%

Notice that this value is significantly different from the ones calculated in a. and b.

1.6

For D1:

Percentage change in quantity demanded =

$2 − $3

×100 = −40 %

$ 2 .5

Percentage change in price =

Elasticity =

60 − 30

×100 = 66 .7%

45

66 .7%

= −1.7

− 40 .0%

For D2:

Percentage change in quantity demanded =

$2 − $3

×100 = −40 %

$2.5

Percentage change in price =

Elasticity =

1.7

40 − 30

×100 = 28 .6%

35

28 .6%

= −0.7

− 40 .0%

Step 1: Calculating average quantity and average price:

Average quantity =

Average price =

1,469 +1,131

=1,300

2

$24 ,751 + $29 ,454

= $27 ,102 .5

2

Step 2: Calculating percentage change in quantity...