Chapter 4Chapter 4

Market Demand

And Elasticity

© 2006 Thomson Learning/South-Western

2

Market Demand Curves

Market demand: total quantity of good or service demanded by all potential buyers.

Market demand curve shows relationship between the total quantity demanded of a single good or service and its price, holding all other factors constant.

3

Constructing the Market Demand Curve

We construct a market demand curve (D) by horizontally summing the all individual consumers’ demand for the good or service.

Fig. 4-1: Assume market consists of only two buyers At any given price, such as P*

X, individual 1 demands X*

1 and individual 2 demands X*2.

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(a) Individual 1

PX

XP*

X*1

0

FIGURE 4-1: Constructing a Market Demand Curve from Individual Demand Curves

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(a) Individual 1

PX

XP*

X*1

0

(b) Individual 2

X*2

0

FIGURE 4-1: Constructing a Market Demand Curve from Individual Demand Curves

PX

Area AEB the consumer surplus area in Figure 3-11.

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(a) Individual 1

PX

XP*

X*1

0

(b) Individual 2

X*2

0

(c) Market Demand

X

D

X*0

FIGURE 4-1: Constructing Market Demand Curve from Individual Demand Curves

PX PX

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Construction of Market Demand Curve

The total QX demanded at market P*X is sum of

two amounts:

X* = X*1 + X*

2 .

Point X*, P*X provides one point on market

demand curve.

Other points on D curve similarly plotted based on all QX demanded at other PX.

8

Shifts in Market Demand Curve: Income

An increase in income for each consumer would shift their individual demand curves out so that the market demand curve would also shift out from the origin.

Shown in Figure 4-2

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(a) Individual 1

PX

XP*

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: Market Demand Curve Shifts Outward

PX PX

X** X** X**

D’

1 2

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Shifts in Market Demand Curve: Income

Some events result in ambiguous demand curve 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.

Income increases for pizza lovers would increase market demand for pizza, so long as pizza is normal good.

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Shifts in Market Demand Curve: Income

If only people who don’t like pizza enjoyed income increases, the market demand curve for pizza would not change.

Changes in prices of related goods-- substitutes or complements--will also shift individual and market demand curves.

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Shifts in Market Demand Curve: Related Goods

If goods X and Y are substitutes, an increase in PY will increase DX. Similarly, a decrease in PY will decrease DX.

If goods X and Y are complements, an increase in PY will decrease DX. A decrease in PY will increase DX.

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Elasticity

Elasticity: measures percentage change in one variable brought about by a 1 percent change in some other variable.

Because it’s measured in percentages, units cancel out-- elasticity is a unit-less measure of responsiveness.

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Price Elasticity of Demand

Price elasticity of demand: percentage change in quantity of a good demanded in response to a 1 percent change in its price

Pin change Percentage

Q in change Percentagedemand of elasticity Price , PQe

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Price Elasticity of Demand

Price elasticity of demand records how QX changes (in percentage terms) given a percentage change in PX.

On typical demand curve, P and Q move oppositely: eQ,P will be negative.

For example, if eQ,P = -2, a 1 percent increase in price leads to a 2 percent decrease in quantity demanded.

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TABLE 4.1: Terminology for the Ranges of eQ,P

Value of eQ,P at a Pointon Demand Curve

Terminology for Curveat This Point

eQ,P < -1 Elastic

eQ,P = -1 Unit elastic

eQ,P > -1 Inelastic

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Price Elasticity: Substitutes Effect

Goods that have many close substitutes are strongly affected by price changes, so their market demand curve is likely to be relatively elastic (flat).

Goods with few close substitutes will likely be relatively inelastic (demand curve will be more steep).

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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 elasticity as the substitution effect.

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Price Elasticity and Time

For some items, substitutes can be quickly developed--such as brands of breakfast cereal. Other goods, such as heating fuel, are much less subject to being copied.

We must thus make the distinction between short-term and long-term price elasticities of demand.

20

Price Elasticity and Total Expenditures

Total expenditures on a good are found by multiplying the good’s price (PX) times the quantity purchased (QX).

When demand is price elastic, price increases will cause total expenditures to fall. Given percentage increase in price more than

counterbalanced by decrease in quantity demanded.

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Price Elasticity and Total Expenditures

Suppose price elasticity of demand = -2. Initially people buy 1 million automobiles at

$10,000 each-- total expenditure of $10 billion.

10% price increase to $11,000 would cause 20 percent decline in cars purchased to 800,000 vehicles.

Total expenditures after price increase would be only $8.8 billion

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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

Inelastic Rise Fall

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(a) Inelastic Demand

Price

0

(b) Elastic Demand

Q00

FIGURE 4-3: Relationship between Price Elasticity and Total Revenue

PX

Quantity per period

Quantity per periodQ1Q1 Q0

P0

P0

P1

P1

DD

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Demand Curves and Price Elasticity

Relationship between particular demand curve and price elasticity it exhibits can be complicated.

For some curves, elasticity remains constant everywhere (unit elastic); for others, it differs at every point along curve.

More accurate to describe elasticity at current price—specifies point on curve.

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Linear Demand Curves and Price Elasticity

Price elasticity of demand changes continuously along linear demand curves.

Demand elastic at prices above midpoint price.

Demand unit elastic at midpoint price. Demand inelastic at prices below midpoint

price.

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Numerical Example: Elasticity along Linear

Demand Curve

Assume a straight-line demand curve for Walkman cassette tape players is Q = 100 - 2Pwhere Q is the quantity of players demanded

per week and P is their price. Figure 4-4 shows this demand curve;

Table 4-3 shows several price-quantity combinations.

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Price

(dollars)

10

50

40

30

25

20

Quantity of CD players per week

Demand

20 405060 80 1000

FIGURE 4-4: Elasticity Varies along a Linear Demand Curve

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TABLE 4-3: Price, Quantity, and Total Expenditures on Walkmans for 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 0 100 0

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Elasticity of a Straight Line Demand Curve

.,

,

Q

Pbe

Q

P

P

Q

P

PQ

Q

e

PQ

PQ

More generally, for linear demand curve of form Q = a - bP,

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A Unitary Elastic Curve

Suppose demand for tape players took form

PQ

200,1

• Figure 4.5 shows graph of this equation--a hyperbola.

• P·Q = $1,200 regardless of price so demand is unit elastic (-1) everywhere on the curve.

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General Formula: Elasticity of Hyperbola Demand Curves

If demand curve takes the following form, price elasticity of demand equals b everywhere along curve:

0) (b baPQ

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Price(dollars)

20

60

50

40

30

Quantity ofCD players

per week

20 24 30 40 60

FIGURE 4-5: Unitary Elastic Demand Curve

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Income Elasticity of Demand

Income elasticity of demand: percentage change in quantity demanded of a good in response to 1 percent change in income.

The formula is given by (I represents income):

.Iin change Percentage

Qin change Percentage, IQe

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Income Elasticity of Demand Normal goods: eQ,I positive--income

increases lead to increased purchases of good.

Inferior goods: eQ,I negative

eQ,I > 1, purchase of good increases more on percentage basis than income--good is called luxury good.

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Cross-Price Elasticity of Demand

Cross-price elasticity of demand: measures percentage change in quantity demanded of one good in response to a 1 percent change in price of another good. Letting P’ be the price of another good,

. P'in change Percentage

Q in change Percentage, PQe

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Cross-Price Elasticity of Demand If goods are substitutes, increase in

price of one good will cause buyers to purchase more of substitute: Cross-price elasticity positive.

If goods are complements, increase in price of one good will cause buyers to buy less of that good as well as less of the complementary good: Cross-price elasticity negative.

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Problems Estimating Demand Curves

First problem: how to derive estimate holding all other factors constant (the ceteris paribus assumption).

As discussed in Appendix to Chapter 1, ceteris paribus problem often solved using multiple regression analysis.

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Problems Estimating Demand Curves

Second problem: what is observed in the data. Data points represent quantity and price outcomes simultaneously determined by both demand and supply curves.

Econometric problem here is to “identify” the demand curve from equilibrium points that generated curve.

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Some Elasticity Estimates

Table 4-4 gathers estimated income and price elasticities of demand.

Note: All estimated price elasticities are less than

zero--as predicted by negatively sloped demand curve.

Most price elasticity estimates indicate that goods are price inelastic.

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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 Money -0.40 +1.00

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Some Cross-price Elasticity Estimates

Table 4-5 shows cross-price elasticity estimates

All goods appear to be substitutes and have positive cross-price elasticities.

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TABLE 4-5: Representative Cross-Price Elasticities of Demand

Demand for Elasticity Estimate

Butter Margarine 1.53

Electricity Natural gas 0.50

Coffee Tea 0.15