Market Demand and Elasticity

Chapter 4

Market

2

Market Demand Curves

 The market demand is the total quantity of a

good or service demanded by all potential

buyers.

 The market demand curve is the relationship

3

Construction of the Market Demand

Curve

 The market demand curve is constructed by

horizontally summing the demands of the individual consumers

 Assume the market consists of only two buyers

as shown in Figure 4.1

– At any given price, such as P*_X, individual 1 demands X*

4

(a) Individual 1 PX

X P*

X* 1 0

5

(a) Individual 1 P_X

X P*

X* 1 0

(b) Individual 2 X*

2 0

FIGURE 4.1: Constructing a Market Demand Curve from Individual Demand Curves

6

Construction of the Market Demand

Curve

– The total quantity demanded at the market at P*_X is the sum of the two amounts:

X* = X*

1 + X*2 .

 The point X*, P*_X is one point on the market

demand curve.

 The other points on the curve are similarly

7

(a) Individual 1 PX X P* X* 1 0

(b) Individual 2 X*

2 0

(c) Market Demand X D

X* 0

FIGURE 4.1: Constructing a Market Demand Curve from Individual Demand Curves

P_{X P}

8

Shifts in the Market Demand Curve

 To discover how some event might shift a

market demand curve, we must first find out how this event causes individual demand

9

Shifts in the Market Demand Curve

 For example consider the two buyer case

where both consumers regard X as a normal good.

 An increase in income for each consumer

would shift their individual demand curves out so that the market demand curve, would also shift out

10

(a) Individual 1 PX X P* X* 1 0

(b) Individual 2 X*

2 0

(c) Market Demand X D

X* 0

FIGURE 4.2: Increases in Each individual’s Income Cause the Market Demand Curve to Shift Outward

P_{X P}

11

(a) Individual 1 P_X X P* X* 1 0

(b) Individual 2 X*

2 0

(c) Market Demand X D

X* 0

FIGURE 4.2: Increases in Each individual’s Income Cause the Market Demand Curve to Shift Outward

P_{X P}

X

X** X** X**

D’

12

Shifts in the Market Demand Curve

 However, some events result in ambiguous

outcomes.

– If one consumer’s demand curve shifts out while another’s shifts in, the net effect depends on the size of the relative shifts.

 An increase in income for pizza lovers would

increase the market demand for pizza so

13

Shifts in the Market Demand Curve

 On the other hand, if the increase in income

was for people who don’t like pizza, there

would be no significant effect on the market

demand curve for pizza.

 Changes in the prices of related goods,

14

Shifts in the Market Demand Curve

 If goods X and Y are substitutes, an increase in

the price of Y will increase the demand for X. Similarly, a decrease in the price of Y will

decrease the demand for X.

 If goods X and Y are complements, an

increase in the price of Y will decrease the

15

A Word on Notation and Terms

 When looking at only one market, Q is used for

the quantity of the good demanded, and P is used for its price.

 When drawing the demand curve, all non-price

factors are assumed to not change.

 Movements along the curve are changes in

16

Elasticity

 Goods are often measured in different units

(steak is measured in pounds while oranges are measured in dozens).

 It can be difficult to make simple comparisons

17

Elasticity

 Elasticity is a measure of the percentage

change in one variable brought about by a 1 percent change in some other variable.

 Since it is measured in percentages, the units

18

Price Elasticity of Demand

 The price elasticity of demand is the

percentage change in the quantity demanded of a good in response to a 1 percent change in its price P in change Percentage Q in change Percentage demand of elasticity

Price _ e_{Q,P }

Q P P Q P P Q Q

e_{Q P} 

19

Price Elasticity of Demand

 The price elasticity records how Q changes in

percentage terms in response to a percentage change in P.

 Since, on a typical demand curve, P and Q

move oppositely, e_Q,P will be negative.

 For example, if e_Q,P = -2, a 1 percent increase

20

Values of the Price Elasticity of

Demand

 When e_Q,P < -1, the quantity demanded is

relatively unresponsive to changes in price

inelastic

 When e_Q,P = -1, a price increase causes a

proportional quantity decrease, and the curve is called unit elastic.

 When e_Q,P > -1, a price increase causes more

21

TABLE 4.1: Terminology for the

Ranges of

e

_Q,P

Value of eQ,P at a Point

on Demand Curve

Terminology for Curve at This Point

eQ,P < -1 Inelastic

eQ,P = -1 Unit elastic

22

Price Elasticity and the Shape of

the Demand Curve

 We often classify market demand curves by

their elasticities

– For example, the market demand curve for

medical services is inelastic (nearly vertical) since there is little quantity response to changes in price. – Alternatively, the market demand curve for a

23

Price Elasticity and the

Substitution Effect

 Goods which have many close substitutes

are subject to large substitution effects from a price change so their market demand curve is likely to be relatively elastic.

 Goods with few close substitutes, on the other

24

Price Elasticity and the

Substitution Effect

 There is also an income effect that will

determine how responsive quantity demanded is to changes in price.

 However, since changes in the prices of

most goods have a small effect on

individuals’ real incomes, the income effect

will likely not have as large an impact on

25

Price Elasticity and Time

 Some items can be quickly substituted for,

such as a brand of breakfast cereal, others, such as heating fuel, may take several years.

 Thus, in some situations, it is important to

make the distinction between the short-term

26

APPLICATION 4.2: Brand Loyalty

 Substitution due to price changes will likely

take a longer time if individual’s develop

spending habits.

 Such brand loyalties are rational since they

reduce decision making costs.

 Over the long term, however, price differences

27

APPLICATION 4.2: Brand Loyalty

 It took several years, but by the 1970s the

price differences between U.S. and Japanese cars eventually convinced Americans to buy the Japanese cars.

 Brand name Licensing, such as Coca-Cola

sweatshirts and Mickey Mouse watches,

28

Price Elasticity and Total

Expenditures

 Total expenditures on a good are found by

multiplying the good’s price (P) times the quantity purchased (Q).

 When demand is elastic, price increases will

cause total expenditures to fall.

29

Price Elasticity and Total

Expenditures

 For example suppose price elasticity = -1.5.

– Suppose a family buys 100 pounds of chicken per year at a price of $2 per pound. The price elasticity of demand for chicken is -1.5. If the price of chicken increases to $2.20 (a 10% increase). What is the difference between new family’s expenditures on chicken and the old one? The family’s consumption of chicken falls to 85 pounds a year (a 15%

decrease). Total expenditure on chicken will also

30

Price Elasticity and Total

Expenditures

 Of course, when demand is inelastic and prices

increase, total expenditures increase.

– A family currently uses 1000 gallons of gasoline a year when the price is $1 per gallon;

Suppose that the price elasticity of demand for gasoline is -0.5. If the price of gasoline increases to $1.10 (10% increase). What happen to expenditure on gasoline? The Consumption of gasoline falls to 950 gallons (5% decrease). Total expenditure on gasoline increase from $1000 (1000 gallons x $1/ gallon) to $1045 (950 gallons x $1.1/ gallon)

 With unit elasticity, total expenditures remain

the same with a price change.

– The movement in one direction by the price is fully offset by the movement in the other

31

TABLE 4.2: Relationship between Price

Changes and Changes in Total Expenditure

If Demand Is

In Response to an Increase in Price, Expenditures will

In Response to a Decrease in Price, Expenditures will

Elastic Fall Rise

Unit elastic Not change Not change

32

APPLICATION 4.3: Volatile Farm Prices

 The demand for many basic agricultural

products (wheat, corn, etc.) is relatively inelastic.

 Even modest changes in supply, brought about

33

Demand Curves and Price Elasticity

 The relationship between a particular demand

curve and the price elasticity it exhibits can be complicated.

 For some curves, the elasticity remains

constant everywhere, but for others it is different at every point.

 A more accurate way to describe it would be to

34

Linear Demand Curves and Price

Elasticity

 The price elasticity of demand is always

changing along a straight line demand curve.

– Demand is elastic at prices above the midpoint price.

– Demand is unit elastic at the midpoint price.

35

Numerical Example of Elasticity on

a Straight Line Demand Curve

 Assume a straight-line demand curve for

Walkman cassette tape players is Q = 100 - 2P

– where Q is the quantity of players demanded per week and P is their price.

 This demand curve is illustrated in Figure 4.3

36

Price (dollars)

10 50

40

30 25 20

Quantity of tape players per week Demand

20 405060 80 100 0

37

TABLE 4.3: Price, Quantity, and Total

Expenditures on Walkmans for the Demand Function Q = 100 - 2P

Price (P) Quantity (Q) _{Total Expenditures (P}



_Q)

$50 0 $0

40 20 800

30 40 1,200

25 50 1,250

20 60 1,200

10 80 800

38

Numerical Example of Elasticity on

a Straight Line Demand Curve

 For prices of $50 or more, nothing is bought so

total expenditures are $0.

 As prices fall between $50 and $25, the

midpoint, total expenditures increase.

 At the midpoint, total expenditures reach a

maximum.

 As prices fall below $25, total expenditures

39

Elasticity of a Straight Line Demand

Curve

.

, ,

Q

P

b

e

Q

P

P

Q

P

P

Q

Q

e

P Q P Q





















 More generally, for a linear demand curve of

40

A Unitary Elastic Curve

 Suppose the demand for tape players took the

form

P

Q



1

,

200

• The graph of this equation, shown in Figure 4.4,

is a hyperbola.

• _{P·Q = $1,200 regardless of price so demand is}

41

General Formula for the Elasticity

of a Hyperbola

 If the demand curve takes the following form,

the price elasticity of demand is equal to b everywhere on the curve.

0)

(b





aP

b

42

Price (dollars)

20 60 50 40 30

Quantity of tape players per week

20 24 30 40 60

43

Income Elasticity of Demand

 The income elasticity of demand equals the

percentage change in the quantity demanded of a good in response to a 1 percent change in income.

 The formula is given by (where I represents

income):

.

I

in

change

Percentage

Q

in

change

Percentage

,I



Q

44

Income Elasticity of Demand

 For normal goods, e_Q,I is positive because

increases in income lead to increases in purchases of the good.

 For inferior goods e_Q,I is negative.

 If e_Q,I > 1, the purchase of the good increases

45

APPLICATION 4.4: An Experiment in

Health Insurance

 Most developed countries have some form of

national health insurance.

– In the U.S. Medicare covers the elderly and Medicaid is available for many of the poor.

 Recently a number of comprehensive

46

The Moral Hazard Problem

 A “moral hazard” problem occurs because

insurance misleadingly lowers the

out-of-pocket expenses to patients, greatly increasing their demand for medical services.

 An important question, in considering

47

The Rand Experiment

 The Rand Corporation conducted a

government-funded large-scale experiment in four cities.

 People were assigned to different insurance

plans that varied in the generosity of coverage they offered.

48

The Rand Experiment

 A rough estimate of the elasticity of demand

can be obtained by averaging the percentage changes across the various plans in Table 1

49

Table 1: Results of the Rand Health

Insurance Experiment

Coinsurance rate

Percent change in price

Average total spending

Percent change in quantity

0.95 540.00

0.50 -47% 573.00 6.10% 0.25 -50 617.00 7.7 0.00 -100 750.00 21.6

50

Low Elasticities for Hospital and

Doctors’ Visits

 Using the estimate of -0.22 found in Table 4.4,

and based on other studies suggests only a small increase in hospital and doctor visits

would result from the lower prices provided by insurance.

 Alternatively, researchers have found greater

51

Cross-Price Elasticity of Demand

 The cross-price elasticity of demand

measures the percentage change in the

quantity demanded of a good in response to a 1 percent change in the price of another good. Letting P’ be the price of another good,

.

P'

in

change

Percentage

Q

in

change

Percentage

,P



Q

52

Cross-Price Elasticity of Demand

 If the goods are substitutes, an increase in

the price of one will cause buyers to

purchase more of the substitute, so the

elasticity will be positive.

 If the goods are complements, an increase

in the price of one will cause buyers to buy

less of that good and also less of the good they use with it, so the elasticity will be

53

Empirical Studies of Demand:

Estimating Demand Curves

 Estimating a demand curve for a product is one

of the more difficult but important problems in econometrics.

 Empirical studies are useful because they a

provide a more precise estimate of the amount of change in quantity demanded that results

54

Problems Estimating Demand

Curves

 The first problem is how to derive an estimate

holding all other factors (the ceteris paribus assumption) constant.

 This problem is often solved, as discussed in

55

Problems Estimating Demand

Curves

 The second problem deals with what is

observed in the data. The data points

represent quantity and price outcomes that are simultaneously determined by both the

demand and the supply curves.

 The econometric problem is to “identify” from

56

Some Elasticity Estimates

 Table 4.4 gathers a number of estimated

income and price elasticities of demand.

 Some things to note

– All of the estimated price elasticities are less than zero as predicted by a negatively sloped demand curve.

57

TABLE 4.4: Representative Price and

Income Elasticities of Demand

Price Elasticity Income Elasticity

Food -0.21 +0.28

Medical services -0.22 +0.22

Rental housing -0.18 +1.00

Owner-occupied

housing -1.20 +1.20

Electricity -1.14 +0.61

Automobiles -1.20 +3.00

Beer -0.26 +0.38

Wine -0.88 +0.97

Marijuana -1.50 0.00

Cigarettes -0.35 +0.50

Abortions -0.81 +0.79

Transatlantic air travel -1.30 +1.40

Imports -0.58 +2.73

58

Some Elasticity Estimates

 The income elasticities of automobiles and

transatlantic travel exceed 1 (luxuries).

 The high income elasticities are balanced by

goods such as food and medical care which

are less than 1 (necessities).

 There is no evidence of Giffen’s paradox in the

59

Some Cross-price Elasticity

Estimates

 Table 4.5 shows a few cross-price elasticity

estimates

 All of the goods appear to be substitutes and

60

TABLE 4.5: Representative Cross-Price

Elasticities of Demand

Demand for Effect of Price of Elasticity Estimate

Butter Margarine 1.53

Electricity Natural gas 0.50