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Elasticity of Demand and Supply

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Elasticity of Demand and Supply. CHAPTER 5. © 2003 South-Western/Thomson Learning. Price Elasticity of Demand. Thus far we have talked about the impact of changes in prices, incomes, costs, on demand and supply in rather general terms In fact, in real world, more precision is needed

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Price Elasticity of Demand

- Thus far we have talked about the impact of changes in prices, incomes, costs, on demand and supply in rather general terms
- In fact, in real world, more precision is needed
- Law of demand says that a higher price will reduce quantity demanded, BUT BY HOW MUCH that is, will the number sold decline by only a little or by a lot?

Price Elasticity of Demand

- Price elasticity of demand measures in a standardized way how responsive consumers are to price change elasticity is another word for responsiveness
- In simplest terms, the price elasticity of demand measures the percent change in quantity demanded divided by the percent change in price

Price Elasticity of Demand

- To illustrate this process, consider the demand curve for tacos in Exhibit 1

Exhibit 1: Demand Curve for Tacos

For the price elasticity to be a useful measure, we should come up with the same result between points a and b as we get between b and a. To do this we must take the average of the initial price and the new price and use that as the base in computing the percent change in price in our example the base used for price is the average of $1.10 and $0.90 = $1.00 the change in price is -$0.20 divided by $1.00 -20%

a

$1.10

b

0.90

Price per taco

D

The same process should be used for changes in quantity demanded the average quantity demanded is 100,000 and the change in quantity demanded is 10,000 10% change

Thousands per day

0

95

105

Price elasticity between a and b = 10% / - 20% = - 0.5

Price Elasticity of Demand

- Generalize the price elasticity formula
- If the price drops from p to p’, other things constant, the quantity demanded increases from q to q’
- The change in price can be represented as Δp and the change in quantity as Δq

Price Elasticity of Demand

- Because the average quantity and average price are used as a base for computing percent change, the same elasticity results whether going from the higher price to the lower price or the other way around
- Since the focus is on the percent change, we need not be concerned with how output or price is measured

Price Elasticity of Demand

- Elasticity expresses a relationship between two amounts
- The percent change in quantity demanded
- The percent change in price

- Because the law of demand states that price and quantity demanded are inversely related, the change in price and the change in quantity demanded have opposite signs the price elasticity of demand has a negative sign

Price Elasticity of Demand

- Since constantly referring to elasticity as a negative number gets cumbersome, we will discuss the price elasticity of demand as an absolute value positive number
- For example, absolute value of the elasticity for tacos computed earlier will be referred to as 0.5 rather than –0.5

Categories

- The price elasticity of demand can be divided into three general categories depending on how responsive quantity demanded is to a change in price
- If the percent change in quantity demanded is smaller than the percent change in price, the resulting price elasticity has an absolute value between 0 and 1.0 demand is inelastic quantity demanded is relatively unresponsive to a change in price
- If the percent change in quantity demanded just equals the percent change in price a price elasticity with an absolute value of 1.0 unit-elastic demand

Categories Summary

- If the percent change in quantity demanded exceeds the percent change in price, the resulting price elasticity has an absolute value exceeding 1.0 demand is said to be elastic quantity is responsive to changes in price

- Inelastic absolute value between 0 and 1.0 unresponsive
- Unit elastic absolute value equal to 1.0
- Elastic absolute value greater than 1.0 responsive

Elasticity and Total Revenue

- Knowledge of price elasticity is especially valuable because it indicates the effect of a price change on total revenue
- Total revenue (TR) is the price (p) multiplied by the quantity demanded (q) at that price TR = p x q
- What happens to total revenue when price decreases?

Elasticity and Total Revenue

- A lower price means producers get less for each unit sold which tends to decrease total revenue
- However, a lower price increases quantity demanded which tends to increase total revenue
- Thus, the overall impact of a lower price on total revenue depends on the net result of these opposite effects

Elasticity and Total Revenue

- Specifically
- When demand is elastic, the percent increase in quantity demanded exceeds the percent decrease in price total revenue increases
- When demand is unit elastic, the two are equal total revenue remains unchanged
- When demand is inelastic, the percent increase in quantity demanded is more than offset by the percent decrease in price total revenue decreases

Elasticity and Total Revenue

- These relationships can be tied together by looking at a linear demand curve
- A linear demand curve is simply a straight-line demand curve
- Exhibit 2 presents these ideas

(a) Demand and Price Elasticity

e

u

n

e

v

e

r

l

a

t

o

T

Exhibit 2: Demand, Price Elasticity and Total Revenue$100

Panel (a) shows the linear demand curve and panel (b) shows the total revenue generated by each price-quantity combination along the demand curve.

90

80

70

60

50

Price per unit

40

30

20

10

D

Since the demand curve is linear, its slope is constant a given decrease in price always causes the same unit increase in quantity demanded.

0

100

200

500

800

900

1,000

Quality per period

(b) Total Revenue

TR = p x q

$25,000

The price elasticity of demand is greater on the higher-price end of the demand curve than on the lower-price end.

Total

revenue

500

1,000

0

Quantity per period

(a) Demand and Price Elasticity

e

u

n

e

v

e

r

l

a

t

o

T

Exhibit 2: Demand, Price Elasticity and Total Revenue$100

Consider a movement from point a to point b on the demand curve. The 100-unit increase in quantity demanded is a percent change of 100/150 = 0.67 while the $10 drop in price is a percent change of 10/85 = 12% the price elasticity of demand here is 5.6

90

a

80

b

70

60

50

c

Price per unit

40

30

20

d

10

e

D

0

100

200

500

800

900

1,000

Quality per period

(b) Total Revenue

TR = p x q

Between points d and e on the lower end, the 100-unit quantity increase is a percent change of 100/850 = 12% and the $10 price decrease is a percent decline of 10/15 = 67% a price elasticity of 0.2

$25,000

Total

revenue

500

1,000

0

Quantity per period

(a) Demand and Price Elasticity

e

u

n

e

v

e

r

l

a

t

o

T

Demand becomes less elastic as we move down the curve. Halfway down, the elasticity equals 1.0. Since we have a linear demand curve, the slope is constant but the elasticity varies slope is not the same thing as elasticity.

Exhibit 2: Demand, Price Elasticity and Total Revenue$100

90

Elastic ED > 1

a

80

b

70

Unit elastic ED = 1

60

50

c

Price per unit

40

Inelastic ED < 1

30

20

d

10

Where demand is elastic, a decrease in price will increase total revenue because the gain in revenue from selling more units exceeds the loss in revenue from selling at the lower price.

e

D

0

100

200

500

800

900

1,000

Quality per period

(b) Total Revenue

TR = p x q

$25,000

Where demand is inelastic, a price decrease reduces total revenue because the gain in revenue from selling more units is less than the loss in revenue at the lower price.

Total

revenue

500

1,000

0

Quantity per period

Exhibit 3: Constant Elasticity Demand Curves

(a) Perfectly elastic

(b) Perfectly inelastic

(c) Unit elastic

D'

t

t

t

i

i

i

n

n

n

u

E =

1

u

u

¥

D

r

r

r

E =

e

e

e

D

p

p

p

D

p

E =

0

e

e

e

D

a

$10

c

c

c

i

i

i

r

r

r

P

P

P

b

6

D"

0

Q

0 60 100

0

Quantity

Quantity

Quantity

per period

per period

per period

Demand curve in (a) indicates consumers will demand all that is offered at the given price, p. If the price rises above p, quantity demanded drops to zero perfectly elastic demand curve.

Demand curve in (b) is vertical, quantity demanded does not vary when the price changes no matter how high the price, consumers will purchase the same quantity perfectly inelastic demand curve.

(c) shows a unit-elastic demand curve where any percent change in price results in an identical offsetting percent change in quantity demanded.

Determinants

- Time to turn to the issue of why price elasticities of demand vary for different goods
- Three basic determinants
- Availability of substitutes
- Proportion of the consumer’s budget spent on the good
- A matter of time

Availability of Substitutes

- The greater the availability of substitutes for a good and the closer the substitutes, the greater the good’s price elasticity of demand
- The number and similarity of substitutes depend on how we define the good the more broadly we define a good, the fewer the substitutes and the less elastic the demand

Proportion of Consumer’s Budget

- Because spending on some goods represents a large share of the consumer’s budget, a change in the price of such a good has a substantial impact on the amount consumers are able to purchase
- Generally, the more important the item is as a share of the consumer’s budget, other things constant, the greater will be the income effect of a change in price the more price elastic will be the demand for the item

A Matter of Time

- The process of finding substitutes takes time
- Thus, the longer the adjustment period, the greater the consumers’ ability to substitute away from relatively higher-priced products toward lower-priced substitutes the more responsive the change in quantity demanded is to a given change in price
- Exhibit 5 demonstrates this

Exhibit 5: Demand Becomes More Elastic over Time

Initial price = $1.00

Dw = the demand curve one week after the price change

Dm = one month after

Dy, = one year after.

$1.25

Suppose the price now increases to $1.25. The more time for consumers to respond to price increase, the greater the reduction in quantity demanded.

1.00

Dw

Price per unit

Dw shows that one week after the price increase, the quantity demanded has not changed much – in this case from 100 to 95 per day. Conversely, after one month, the quantity demanded has declined to 75, and after one year to 50 per day.

Dm

Dw

0

Quantity per period

50

75

95

100

Note that among these demand curves and over the range starting from the point where the demand curves intersect, the flatter the demand curve, the more price elastic the demand.

Elasticity Estimates

- When estimating price elasticity, economists often distinguish between a period during which consumers have little time to adjust – the short run – and a period during which consumers can more fully adjust to a price change – the long run.
- Exhibit 6 provides some short-run and long-run price elasticity estimates for selected products

Exhibit 6: Selected Price Elasticities of Demand

Product Short Run Long Run

Cigarettes (among adults) — 0.4

Electricity (residential) 0.1 1.9

Air travel 0.1 2.4

Medical care and hospitalization 0.3 0.9

Gasoline 0.4 1.5

Milk 0.4 —

Fish (cod) 0.5 —

Wine 0.7 1.2

Movies 0.9 3.7

Natural gas (residential) 1.4 2.1

Automobiles 1.9 2.2

Chevrolets — 4.0

Price Elasticity of Supply

- Prices are signals to both sides of the market about the relative scarcity of products
- High prices discourage consumption but encourage production
- The price elasticity of supply measures how responsive producers are to a price change

Price Elasticity of Supply

- The price elasticity of supply equals the percent change in quantity supplied divided by the percent change in price
- Since the higher price usually results in an increased quantity supplied, the percent change in price and the percent change in quantity supplied move in the same direction the price elasticity of supply is usually a positive number
- Exhibit 7 depicts a typical upward-sloping supply curve

Exhibit 7: Price Elasticity of Supply

S

If the price increases from p to p', the quantity supplied increases from q to q'

p'

p

The price elasticity of Es, is

Price per unit

Where q is the change in quantity supplied and p is the change in price.

q

q'

Quantity per period

0

Categories of Supply Elasticity

- The terminology for supply elasticity is the same as for demand elasticity
- If supply elasticity is less than 1.0, supply is inelastic
- If it equals 1.0, supply is unit elastic
- If it exceeds 1.0, supply is elastic

- Exhibit 8 illustrates some special cases of supply elasticity to consider

Exhibit 8: Constant-Elasticity Supply Curves

(a) Perfectly elastic

(b) Perfectly inelastic

(c) Unit elastic

S'

t

t

t

i

i

i

n

n

n

S"

u

u

u

¥

E =

1

r

r

r

S

E =

e

e

e

S

p

p

p

$10

S

p

E =

0

e

e

e

S

c

c

c

i

i

i

r

r

r

P

P

P

5

Quantity per period

Quantity per period

Quantity per period

0

0

0

10

20

Q

At one extreme is the horizontal supply curve. Here producers will supply none of the good at a price below p, but will supply any amount at a price of p, as in (a).

The most unresponsive relationship is where there is no change in the quantity supplied regardless of the price, as shown in (b) where the supply curve is perfectly vertical.

Any supply curve that is a straight line from the origin such as shown in (c) is a

unit-elastic supply curve.

Determinants

- The elasticity of supply indicates how responsive producers are to a change in price
- Their responsiveness depends on how easy it is to alter output when price changes
- If the cost of supplying additional units rises sharply as output expands, then a higher price will elicit little increase in quantity supplied
- But if the marginal cost rises slowly as output expands, the lure of a higher price will prompt a large increase in output

Length of Time

- Just as demand becomes more elastic over time as consumers adjust to price changes, supply also becomes more elastic over time as producers adjust to price changes
- The longer the time period under consideration, the more able producers are to adjust to changes in relative prices
- Exhibit 9 illustrates this

S

w

m

S

y

Price per unit

0

100

140

200

Quantity per period

110

Exhibit 9: Supply Becomes More Elastic over TimeSw is the supply curve when the period of adjustment is a week. In this situation, the higher price does not elicit much of a response in quantity supplied because firms have little time to adjust supply curve is inelastic if the price increases from $1.00 to $1.25

$1.25

1.00

Sm is the supply curve when the adjustment period is one month. Here the firms have a greater ability to vary output supply is more elastic

Supply is even more elastic when the adjustment period is a year as shown by Sy

Income Elasticity of Demand

- The income elasticity of demand measures how responsive demand is to a change in income
- Measures the percent change in demand divided by the percent change in income
- Categories
- Goods with income elasticities less than zero are called inferior goods demand declines when income increases

Income Elasticity of Demand Exhibit 10 presents some income elasticity estimates for various goods and services

- Normal goods have income elasticities greater than zero demand increases when income increases
- Normal goods with income elasticities greater than zero but less than 1 are called income inelastic goods demand increases but not as much as does income
- Goods with income elasticity greater than 1 are called income elastic demand not only increases when income increases but increases by more than does income

Exhibit 10: Selected Income Elasticities of Demand

Income IncomeProduct Elasticity Product Elasticity

Private education 2.46 Physicians’ services 0.75

Automobiles 2.45 Coca-Cola 0.68

Wine 2.45 Beef 0.62

Owner-occupied housing 1.49 Food 0.51

Furniture 1.48 Coffee 0.51

Dental service 1.42 Cigarettes 0.50

Restaurant meals 1.40 Gasoline and oil 0.48

Shoes 1.10 Rental housing 0.43

Chicken 1.06 Beer 0.27

Spirits (“hard” liquor) 1.02 Pork 0.18

Clothing 0.92 Flour –0.36

Exhibit 12: The Effect of Increases in Supply and Demand on Farm Revenue

Cross-Price Elasticity of Demand

- Since firms often produce an entire line of products, it has a special interest in how a change in the price of one product will affect the demand for another
- The responsiveness of the demand for one good to changes in the price of another good is called the cross-price elasticity of demand

Cross-Price Elasticity of Demand

- Defined as the percent change in the demand of one good divided by the percent change in the price of another good
- Its numerical value can be positive, negative, or zero depending on whether the goods are substitutes, complements, or unrelated, respectively

Substitutes and Complements

- If an increase in the price of one good leads to an increase in the demand for another good, their cross-price elasticity is positive the two goods are substitutes
- If an increase in the price of one good leads to a decrease in the demand for another, their cross-price elasticity is negative the two goods are complements

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