chapter four elasticity and its uses. 4 | 2 copyright © houghton mifflin company. all rights...

Chapter Four

Elasticity and Its Uses

Copyright © Houghton Mifflin Company. All rights reserved. 4 | 2

Elasticity of Demand

• Price elasticity of demand - the percentage change in the quantity demanded of a good divided by the percentage of the price of that good. It is a measure of the sensitivity of the quantity demanded or changes in the price of the good.

Price Elasticity of Demand priceinchangepercentage

demandedquantityinchangepercentage

___

____


Percentage Change

• We calculate percentage change using the formula:

• For example, if prices go up from an old value of $20 to a new value of $25, then the percentage change in price is:

100_

__

valueold

valueoldvaluenewPercentage change

%2510020

5100

20

2025

Prices went up by 25 percent.


Percentage Change (cont’d)

• However, if prices go down from an old value of $25 to a new value of $20, then the percentage change in price is:

%2010025

5100

25

2520

In this case, prices went up by negative 20 percent, or more appropriately, it went down by 20 percent. Note that incorrectly labeling the starting value and the end value will result in an incorrectly calculated percentage change.


High Elasticity vs. Low

ElasticityFigure 4.1


High Elasticity vs. Low Elasticity (cont’d)

• Figure 4.1 depicts two demand curves, one with high elasticity and another with low elasticity. The graph on the top shows a demand curve with a high price elasticity of demand, since a small increase in the price (10 percent, from $20 to $22) results in a large decrease in the quantity demanded (20 percent, from 60 million barrels to 48 million barrels), or:



Percentage change in price

percent1010020

2100

20

2022

Percentage

change in

Qty. demanded

percent20100

60

12100

60

6048



The elasticity of demand for the top graph is:

Price Elasticity of Demand

22%10

%20

Note: Since the demand curve shows a negative relationship between price and quantity demanded, we can ignore the negative sign, and just take the absolute value of the price elasticity of demand. In this particular example, the price elasticity of demand is 2.


High Elasticity vs. Low

Elasticity (cont’d)



• The bottom graph on Figure 4.1 shows a demand curve with a lower price elasticity of demand. For the same price increase (10 percent, from $20 to $22), the decrease in the quantity demanded is much smaller (5 percent, from 60 million barrels to 57 million barrels), or:



Percentage

change in price percent1010020

2100

20

2022

Percentage

change in

Qty. demanded

57 60

60100

3

60100 5percent



The elasticity of demand for the bottom graph is:

Price Elasticity of Demand 2

1

2

1

%10

%5

Note: The top graph in Figure 4.1 had a higher price elasticity of demand (elasticity = 2) than the price elasticity of demand for the bottom graph (elasticity =1/2).


• One application of knowing the price elasticity of demand is in analyzing the impact of a change in supply of a good. Fig. 4.2 analyzes the effect of an decrease in the supply of oil on the equilibrium price of oil.

Impact of a Price Change in Oil


Impact of a Price

Change in Oil (cont’d) Figure 14.2


• The same shift in the supply of oil to the right results in a higher equilibrium price in the bottom graph, where the demand curve has a lower price elasticity, than in the top graph, which has a higher price elasticity.

Impact of a Price Change in Oil (cont’d)


Working with Demand Elasticities

• The general formula that we will use for demand elasticity (ed) will be:

d

dd

d

d Q

P

P

Q

PPQ

Q

e


• One attractive feature of the price elasticity of demand is that it is a unit-free measure; it does not depend on the units of measurement of quantity demanded.

• Unit-free measure – A measure that does not depend on the unit of measurement.

Working with Demand Elasticities (cont’d)


• For example, we can convert the barrels of oil into liters of oil– One American barrel of

oil = 158.984 liters




60 million barrels of oil is equal to :

60 million X Lbarrel

L04.9539

984.158

48 million barrels of oil is equal to :

48 million X Lbarrel

L232.7361

984.158



Percentage

change in

Qty. demanded

percent2010004.9539

81.1907

10004.9539

04.9539232.7361

The percentage change in price is still -20 percent, whether in barrels or in liters. The value of the elasticity of demand the elasticity will also be unaffected by changes in units.


Elasticity vs. Slope

• One common mistake made when dealing with elasticity is that students tend to interchange the elasticity of the demand curve with its slope. These concepts are similar, but not the same.

d

dd

d

d Q

P

P

Q

PPQ

Q

e

Elasticity of demand =

Slope of the demand curve = P

Qslope d


Elasticity vs. Slope (cont’d)

• The slope of the demand curve, unlike the price elasticity of demand, is sensitive to changes in units.

• From Figure 4.1, the slope of the demand curve in the top graph (between points A and B) is:

62

12

2022

6048

P

Qslope d



691.9532$

81.19072022$

04.9539232.7361

Lslope

LL

P

Qslope d

If we convert barrels into liters, as we have done in the previous slides, then the slope will now be

Changing the units changes the slope of the demand curve.


• One more thing to remember with elasticity and slopes is that with a straight line demand curve, the slope is constant but the elasticity varies.



Elastic vs. Inelastic Demand

• Elastic demand - Demand (or part of the demand curve) where the price elasticity is greater than one.

• Unit Elastic demand - Demand (or part of the demand curve) where the price elasticity is exactly equal to one.


• Perfectly inelastic demand - Demand (or part of the demand curve) where the price elasticity is zero, indicating no response to a change in price. A perfectly inelastic demand curve is a vertical line.

• Perfectly elastic demand - Demand (or part of the demand curve) where the price elasticity is infinite, indicating an infinite response to a change in price. A perfectly elastic demand curve is a horizontal line.

Elastic vs. Inelastic Demand (cont’d)


Elastic vs. Inelastic Demand (cont’d) Figure 4.4


The Midpoint Formula

• As shown in some of our examples, the calculated values of the percentage change and the price elasticity of demand will vary depending on the starting and the end value. For example, an increase from $10 to $12 will give a different percentage change (and hence, a price elasticity of demand) from a decrease in price from $12 to $10.


The Midpoint Formula (cont’d)

• The most common convention is by taking the average of the starting and ending values, or using the midpoint formula.

Midpoint Formula

2/)(

2/)(

12

12

12

12

PPPP

QQQQ

ed

Where Q1 and P1 are starting values for price and quantity, and Q2 and P2 are end values for price and quantity.


Revenue and the Price Elasticity of Demand

Revenue of a firm

= (P X Q)

= (price of a good) X (quantity of the good sold)

• From the formula above, a change in the price of a good will have two effects on the revenue that a firm receives

1) A change in the price changes the payment per unit that a firm receives and;

2) A change in the prices changes the quantity of units sold.


1. In some situations, increasing the price will increase revenue if the effect of the increase in price on revenue is greater than the effect of the drop in quantity on revenue. If the effect of the increase in price on revenue is less than the effect of the drop in quantity on revenue, then raising prices may reduce revenue.

Revenue and the Price Elasticity of Demand (cont’d)

Note: Our discussion focuses on revenue, not profits. Higher revenues may not always lead to an increase in profits.


• Fig. 4.5 illustrates two related points. The top graph shows that with a straight line demand curve, elasticity is not constant. Specifically, points on the demand curve above the midpoint have price elasticities greater than one, and are elastic. Points on the demand curve below the midpoint have price elasticities less than one, and are inelastic.



Revenue and the Price Elasticity of

Demand (cont’d)

Figure 4.5


• The bottom graph on the previous figure shows that the revenue that a firm receives is not constant. At the midpoint of the demand curve, the revenue that a firm expects is highest. Any quantity to the left or to the right of the midpoint of the demand curve yields a lower total revenue.



• Putting the top graph in the previous figure together with the bottom graph, we can see that if the calculated (absolute) value of the price elasticity of demand is greater than one, the demand curve is elastic, and lowering the price will yield a higher revenue. If the calculated (absolute) value of the price elasticity of demand is less than one, the demand curve is inelastic, and raising the price will yield a higher revenue.



What Determines the Size of the

Price Elasticity of Demand?


• Determinants of the Price Elasticity of Demand

1) Degree of substitutability

2) Big-ticket vs. little-ticket Items

3) Temporary vs. permanent price change

4) Differences in preferences

5) Long run vs. Short run elasticity

What Determines the Size of the Price Elasticity of Demand? (cont’d)


• The presence of other goods that can easily act as a substitute will affect the price elasticity of demand for that good. If the price of a good changes, the quantity demanded will change a lot if there are a lot of substitutes (hence, a very elastic demand curve). On the other hand, with goods that had few good substitutes (for example, eggs), if the price of a good changes, the quantity demanded will change very little (hence, a very inelastic demand curve).

Degree of Substitutability


• If a good represents a large share fraction of people’s income, then the price elasticity will be high (some families do a lot of research before making a decision to buy a house or a car).

• If a good represents a small share fraction of people’s income, then the price elasticity will be low (when was the last time you compared prices of salt across different stores?).

Big-Ticket vs. Little-Ticket Items


Temporary vs. Permanent Price Change

• If the price change is perceived to be temporary, then the price elasticity of demand will be high. For example, when Wal-Mart sold laptop computers for $398 only for the first 30 buyers, many people stood in line hoping to get a chance to buy it.

• If the price change is perceived to be permanent, then the price elasticity of demand will be low. For example, when your local furniture store advertises a “liquidation sale, this weekend only” every week for the last 2 years, few people find it advantageous to buy sooner rather than later.


Differences in Preferences

• Some goods have varying price elasticity of demand across different consumer groups.

For example

1) New smokers have a higher price elasticity of demand for cigarettes than long time smokers.

2) Retired persons have a lower price elasticity of demand for motor homes than persons in the 18-26 age group.


Long Run vs. Short Run

• The length of time elapsed since a price change affects the price elasticity of demand. For example, if the price of gasoline rises, the price elasticity of demand for gasoline may be lower for SUV owners in the short run (just immediately after the price change) than in the long run. This is because it may take time to find substitutes for gasoline, or change cars in response to a higher price for gasoline.


Income Elasticity of Demand

• Income Elasticity of Demand – the percentage change in the quantity demanded of a good divided by the percentage change in the income. This measures the sensitivity of quantity demanded of a good to a change in income. Income Elasticity of Demand

incomeinchangepercentage

demandedquantityinchangepercentage

___

____


Income Elasticity of Demand (cont’d)


• If the income elasticity of demand is positive (i.e., you buy more as income increases), then the good is a normal good.

• If the income elasticity of demand is negative (i.e., you buy less as income increases), then the good is an inferior good.

• Note: With income elasticity of demand, it is incorrect to take the absolute value of the computed elasticity. Remember that taking the absolute value of elasticity is only applicable to the price elasticity of demand.

Income Elasticity of Demand (cont’d)


• Cross Price Elasticity of Demand – The percentage change in the quantity demanded of a good divided by the percentage change in the price of a related good (a substitute or a complement). This measures the sensitivity of quantity demanded of a good to a change in the price of another good.

Cross-Price Elasticity of Demand


Cross-Price Elasticity of Demand (cont’d)

• If the cross-price elasticity of demand is positive (i.e., you buy more as price of the other good increases), then the two related goods are substitutes.

• If the cross-price elasticity of demand is negative (i.e., you buy less as price of the other good increases), then the two related goods are complements.


Elasticity of Supply

• Elasticity of Supply – The percentage change in the quantity supplied of a good divided by the percentage change in the price of the same good. This measures the sensitivity of quantity supplied of a good to a change in the price of that good.

Price Elasticity of Supply priceinchangepercentage

pliedquantityinchangepercentage

___

sup____


Elasticity of Supply (cont’d)

• The general formula that we will use for price elasticity of supply (es) will be:

s

ss

s

s Q

P

P

Q

PPQ

Q

e

Note that the equation used to calculate the price elasticity of supply is very similar to the equation for the price elasticity of demand. The only difference is that the quantity we are now using is the quantity supplied (Qs), not the quantity demanded (Qd).


Elastic vs. Inelastic Supply

• Elastic supply - Supply (or part of the supply curve) where the price elasticity is greater than one

• Inelastic supply - Supply (or part of the supply curve) where the price elasticity is less than one

• Unit Elastic supply - Supply (or part of the supply curve) where the price elasticity is exactly equal to 1


Perfectly Elastic vs. Perfectly Inelastic Supply

• Perfectly inelastic supply - Supply (or part of the supply curve) where the price elasticity is zero, indicating no response to a change in price. A perfectly inelastic supply curve is a vertical line

• Perfectly elastic supply - Supply (or part of the supply curve) where the price elasticity is infinite, indicating an infinite response to a change in price. A perfectly elastic supply curve is a horizontal line


Perfectly Elastic vs. Perfectly Inelastic Supply (cont’d)

Figure 4.7


• One application of knowing the price elasticity of supply is in analyzing the impact of a change in demand for a good. The next figure illustrates the effect of an decrease in the demand of oil on the equilibrium price of oil.

Elastic vs. Inelastic Supply


Elastic vs. Inelastic Supply (cont’d)

Figure 4.9


Elastic vs. Inelastic Supply (cont’d)

• The same shift in the demand for oil to the left results in a lower equilibrium price in the bottom graph, where the supply curve has a lower price elasticity, than in the top graph, which has a higher price elasticity.


Key Terms

• Price elasticity of demand• Unit-free measure• Elastic and inelastic demand• Perfectly elastic and inelastic demand• Income elasticity of demand• Cross-price elasticity of demand• Price elasticity of supply• Elastic and inelastic supply• Perfectly elastic and inelastic supply

chapter four elasticity and its uses. 4 | 2 copyright © houghton mifflin company. all rights...

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