4. individual and market demand...income and substitution effects •a fall in the price of a good...


Chapter outline

1. Individual Demand

2. Income and Substitution Effects

3. Market Demand

4. Consumer Surplus

5. Empirical Estimation of Demand


Individual Demand

• Price Changes

– With the help of the illustrations developed in the previous

chapter, the effects of a change in the price of food can be

illustrated by using indifference curves.


Effects of Price Changes

Food

(units per month)

Clothing

(units per month)

4

5

6

U2

U3

A

B D U1

4 12 20

Three separate

indifference curves

touching their respective

budget lines.

Assume:

•I = €20

•PC = €2

•PF = €2, €1, €0.50 10



Price-Consumption Curve

Clothing

(units per month)

4

5

6

U2

U3

A

B D U1

4 12 20

Price-consumption

curve: a curve tracing

the utility-maximizing

combinations of two

goods as the price of

one changes (in this

case food).

Food

(units per month)



Demand Curve

Individual demand curve: a

curve relating the quantity of a

good-that a single consumer

will buy-to its price.

Food

(units per month)

Price of Food

H

E

G

€2.00

4 12 20

€1.00

€0.50


Individual Demand

• The individual demand curve has two important properties:

1) The level of utility that can be attained changes as we move

along the curve.

2) At every point on the demand curve, the consumer is

maximizing utility by satisfying the condition that the

marginal rate of substitution (MRS) of food for clothing

equals the price ratio of food and clothing.



Food

(units per month)

Food Price

H

E

G

€2.00

4 12 20

€1.00

€0.50

Demand Curve

•E: Pf /Pc = 2/2 = 1 = MRS

•G: Pf /Pc = 1/2 = 0.5 = MRS

•H:Pf /Pc = 5/2 = 0.25 = MRS

If price falls, then Pf /Pc & MRS decrease as well.


Individual Demand

• Income Changes

– Taking our example on food and clothing, the effects of a

change in income can be illustrated using indifference

curves.


Effect of Income Change

Food (units per month)

Clothing

(units per month)

A change in income, with prices

of all goods fixed, causes

consumers to alter their choice

of market baskets.

Income-Consumption

Curve

3

4

A U1

5

10

B

U2

D 7

16

U3

Assume:

Pf = €1

Pc = €2

I = €10, €20, €30


Effect of Income Change

Food (units

per month)

Food-

price An increase in income from €10

to €20 and €20 to €30, with the

prices for all goods fixed, shifts

the demand curve to the right.

€1.00

4

D1

E

10

D2

G

16

D3

H


Individual Demand

• Change in income:

– Income consumption curve: Curve tracing the utility-

maximizing combinations of two goods as a consumer’s

income changes.

– An increase in income causes a rightward shift in the

budget line. This leads to having higher consumption

along the income consumption curve.

– At the same time, due to the increase in income, the

demand curve shifts to the right.


Individual Demand

• Changes in income

– if the Income-consumption curve has a positive slope, then

demand decreases as income increases;

income elasticity of demand is positive,

and the good is a normal Good.

Normal versus Inferior Goods


Individual Demand

• Changes in income

– if the Income-consumption curve has a negative slope, then

demand decreases with increasing income;

income elasticity of demand is negative,

and the good is an inferior Good.

Normal versus Inferior Goods


Inferior Good

Hamburgers

(units per month)

Steaks

(units

per month)

15

30

U3

C

Income-Consumption Curve

…but hamburgers become

an inferior good when the

income-consumption curve

bends backwards between

points B and C.

10 5 20

5

10

A

U1

B

U2

Here, hamburger and steaks

are normal goods between points

A and B…


Individual Demand

• Engel curves

– Curve relating the quantity of a good consumed to

income.

– If the good is a normal good, the Engel curve is upward

sloping.

– If the good is an inferior good, the Engel curve is

negatively sloped.


Engel Curves

30

4 8 12

10

Income

(€ per

month)

20

16 0

With a normal good, the

Engel curve is positively

sloped.

Food (units per

month)


Engel curves

With inferior goods,

the Engel curve is

negatively sloped.

inferior

normal

30

4 8 12

10

Income

(€ per

month)

20

16 0 Food

(units per month)


Individual Demand

1) Two goods are substitutes if an increase in the price

of one leads to an increase in the quantity demanded of

the other.

For example: cinema tickets and movie rentals.

2) Two goods are complements if an increase in the

price of one good leads to a decrease in the quantity

demanded of the other.

For example: gasoline and motor oil.

Substitutes and Complements


Individual Demand

3) Two goods are independent if a change in the price

of one good has no effect on the quantity demanded of

the other.


If the price-consumption curve is negatively sloped

then we consider the goods to be substitutes.

However, if the price consumption curve is positively

sloped then we consider the goods to be

complements.



Income and Substitution Effects

• A fall in the price of a good has two effects: the substitution & the income effect.

1. Consumers will tend to buy more of the good that has

become cheaper and less of those goods that are now

relatively more expensive. This response to a change in

the relative prices of goods is called the substitution effect.

2. Because one of the goods is now cheaper, consumers

enjoy an increase in real purchasing power. The change in

demand resulting from this change in real purchasing

power is called the income effect.


Income and Substitution Effects

Substitution effect

Change in consumption of a good associated with a change

in its price, with the level of utility held constant.

If the price of the good decreases, the substitution effect

leads to increased demand for this good.


Income and Substitution Effect

• Income effect:

– Change in consumption of a good resulting from an

increase in purchasing power, with relative prices held

constant.

– If the income of the individual increases, this causes the

demanded quantity to either increase or decrease.

– Even when we have inferior goods, the income effect is

rarely large enough to compensate for the substitution

effect.


Income and Substitution Effects: Normal Goods

Food

(units per month) O

Clothing

(units per

month) R

F1 S

C1 A

U1

The income effect EF2

(associated with a move from

D to B) keeps relative prices

constant but increases

purchasing power.

Income effect

C2

F2 T

U2

B

When the price of food falls,

consumption increases by F1F2,

as the consumer moves from A

to B.

E Total effect

Substitution

effect

D

The substitution effect F1E

(associated with a move from A to D)

changes the relative prices of food and

clothing but keeps real income

(satisfaction) constant.


Income and Substitution Effect: Inferior Goods

Food

(units per month) O

R

Clothing

(units per

month)

F1 S F2 T

A

U1

E

Substitution-

effect

D

Total effect

In this case, food is an

inferior good because the

income effect is negative.

However, because the

substitution effect exceeds

the income effect, the

decrease in the price of food

leads to an increase in the

quantity of food demanded

B

Income effect

U2


Income and Substitution Effect:

• A Special Case - the Giffen Good

– Theoretically, the income effect can be so large that the

demand curve of a good is positively sloped.

– This rarely occurs and is of little practical interest.


The Effects of a Gasoline Tax

• Assume:

– The taxes on gasoline are €0.5

– Income = €9,000

– Price of gasoline = €1

– Elasticity of demand = -0.5

– Income elasticity = 0.3

– Demand without tax 1200l

• We will see that the tax makes the consumer worse off

even when the consumer gets a tax rebate.


The Effect of a Gasoline Tax with a Tax Rebate.

Gasoline consumption (gallons per year)

Expenditure on other goods(€)

A

C •Gasoline = 1200 Liter

•Other expenses= €7,800

U2

1200

Original Budget Line

B D

U1

900

After Gasoline

Tax

E

•€0.50 consumer taxes

•Gasoline = 900 Liter

J

F

H

913.5

After Gasoline Tax plus Rebate

U3

•€450 Tax Rebate

•New budget line

•Consumer worse off


• As for other goods and services, the prices of gasoline and diesel are

freely formed on the basis of supply and demand. As regular

investigations show, the prices for petrol and diesel at the petrol

stations in Germany are fundamentally in line with the wholesale prices

for fuels on the Rotterdam petroleum market. These, in turn, usually

follow the crude oil price, but may, depending on the supply and

demand of the product in question, detach to some extent from the

crude oil price in the short term.

• In addition to the price for the respective product, further cost items are

also included in the final consumer prices. These include the energy

tax, which has been 47.04 cents per liter for diesel and 65.45 cents per

liter for petrol and the value added tax 19 percent of the total value of

the goods (including energy tax).

(BMWi https://www.bmwi.de/Redaktion/DE/Textsammlungen/Energie/mineraloelversorgung.html )


Market Demand

• Market Demand Curve

– Curve relating the quantity of a good,

that all consumers in a market will buy, to its

price.

From Individual to Market Demand


Determining the Market Demand Curve

1 6 10 16 32

2 4 8 13 25

3 2 6 10 18

4 0 4 7 11

5 0 2 4 6

Price Person A Person B Person C Market

(€) (units) (units) (units) (units)


Summing to Obtain a Market Demand Curve

Quantity

1

2

3

4

Price

0

5

5 10 15 20 25 30

DB DC

Market Demand

DA

The market demand curve is

obtained by summing our

three consumer demand

curves DA, DB, and DC.


Market Demand

• Two points should be noted:

1. The market demand curve will shift to the right as more

consumers enter the market.

2. Factors that influence the demands of many consumers

will also affect market demand.

• The aggregation of individual demands into a market demand becomes important in practice when market demands are built up from the demands of different demographic groups or from consumers located in different areas.


Market Demand

/

/

Q / Q Q P Q PEP

P / P Q P P Q

• Elasticity of Demand

Remember that the price elasticity of demand

measures the percentage change in the

demanded quantity resulting from a one percent

change in the price:


Price Elasticity and Consumer Expenditures

Inelastic (Ep <1) Increase Decrease

Unit elastic (Ep = 1) Are unchanged Are unchanged

Elastic (Ep >1) Decrease Increase

Demand If price increases, If price decreases,

expenditures expenditures


Point Elasticities

• Point elasticity of demand

– For significant price changes (e.g., 20%), the elasticity

value depends on the pount at which we measure price

and the quantity along the demand curve.

• Point elasticity of demand

Price elasticity at a particular point on the demand

curve.

Point elasticity:

PE (P / Q)(1 / Slope)


Point Elasticities

• Issues when using point elasticity:

– We may need to calculate the price elasticity over a

certain range of points on the demand curve and not only

at a single point.

– The price and quantity used for calculating the elasticity

affects the price elasticity of demand.


Point Elasticities

• Assume:

– The price increases from €8 to €10, and the quantity demanded decreases from 6 to 4.

– Is the percentage change in price €2/€8 = 25% or €2/€10 = 20%

– Is the percentage change in quantity -2/6 = -33.33% or -2/4 = -50%

Point elasticity of demand (example)


Point Elasticities

• The elasticity is equal to

-33.33/25 = -1.33 or rather -50/20 = -2.5

• Which one is correct?

Point elasticity of demand (Example)


• Arc elasticity of demand

• Price elasticity calculated over a range of prices.

– The formula for the arc elasticity:

Arc Elasticities

/ )

average price

average quantity

EP ( Q / P)( P Q

P

Q


Market Demand

• Arc elasticity of demand (example)

/ ) PE ( Q / P)( P Q

1 2

1 2

10 88 10 9

2

6 46 4 5

2

P P P

Q Q Q

( 2 / €2)(€9 / 5) 1,8PE .


The aggregated Demand for Wheat

• The total world demand for US wheat is the sum of the

domestic demand and the export demand.

• Domestic demand for wheat is given by the equation

QDD = 1700 - 107P

• Export demand for wheat is given by

QDE = 1544 – 176P

• The domestic demand is relatively price inelastic (-0.2),

the export demand is more price elastic (-0.4).


The Aggregate Demand for Wheat

C

D

Export

Demand

A

B

Domestic

Demand

The total world demand for wheat

is the horizontal sum of the

domestic demand AB and the

export demand CD.

F

Total Demand

E

Price

($/bushel)

2

4

6

8

10

12

14

16

18

20

Wheat

(millions of bushels/yr)

1700 1544 3244


Consumer Surplus

• Consumer Surplus:

Difference between what a consumer is willing to pay for a

good and the amount actually paid.


Consumer Surplus

The consumer surplus associated with

purchasing six concert tickets (at $14

per ticket) is given by the yellow-shaded

area: 6+5+4+3+2+1 = 21

Consumer surplus

6 + 5 + 4 + 3 + 2 + 1 = 21

Rock concert tickets

Price

(€ per

ticket)

2 3 4 5 6

13

0 1

14

15

16

17

18

19

20

Market price


Consumer Surplus

Demand curve

Consumer

Surplus

Actual Expenditure

€19.50014)x6.5001/2x(20

Consumer surplus in the market

Rock concert

tickets (thousand)

Price

(€ per

ticket)

2 3 4 5 6

13

0 1

14

15

16

17

18

19

20

Market price

The staircase shaped demand curve can be converted

into a straight demand curve by a reduction in the units of

the goods.


Consumer Surplus

• When we combine consumer surplus with the aggregate

profits that producers obtain, we can

1) evaluate both the costs and benefits of

alternative market structures

2) and public policies that alter the behavior of

consumers and firms in those markets.


The Value of Clean Air

• Although there is no actual market for clean air, people do

pay more for houses where the air is clean than for

comparable houses in areas with more smog.

• Question: Are the benefits of clear air worth the costs?

• Example: Nitrogen oxides and diesel cars


Another Example: Noise Pollution and the A46

• Consumers pay more for houses located in quiet areas.

• Data on real estate prices in Wuppertal can be compared

while taking the degree of street-traffic noise into account.

• Using the data on real estate prices in Wuppertal we can

check the effect of noise on house prices.


Assessment of Noise Reduction (Plausibility Check!!!!!)

The shaded triangle is the consumer

surplus when noise pollution at a price of

€1,000 per reduced db is reduced by 20

dbs to 60 dbs.

2000

80 0

1000

40

A

Decibel

Reduction

Value

(€ per decibel)


Empirical Estimation of Demand

• The most direct method to determine information about

demand, is to conduct interviews in which consumers are

asked what quantity of a product they are willing to buy at a

certain price.

• Problem:

– Consumers may be lacking information, interest, or may

even want to mislead the interviewer.



• In direct marketing experiments, actual sales offers are

posed to potential customers and customer’s responses

are monitored.

• The statistical approach to estimate demand.

– Properly applied, the statistical approach to estimating

demand can enable us to determine the effects of

variables on the demanded quantity of a product.

– The "least squares" regression method is such an

approach.


Data on the Demand of Raspberries

Year Quantity (Q) Price (P) Income (I)

1995 4 24 10

1996 7 20 10

1997 8 17 10

1998 13 17 17

1999 16 10 17

2000 15 15 17

2001 19 12 20

2002 20 9 20

2003 22 5 20



• Assume price is the only determinant for demand:

Q = a - bP

Q = 28.2 –1.00P


Estimating Demand

Quantity

Price

0 5 10 15 20 25

15

10

5

25

20

d1

d2

d3

D

D is the demand curve,

when only price P

determines the demand;

from the data we know

that Q = 28.2 – 1.00P


Estimating Demand

Quantity

Price

0 5 10 15 20 25

15

10

5

25

20

D

d1

d2

d3

d1, d2, and d3 are the demand curves for each

income level. By substituting income in the

demand equation we get Q = a – bP + cI or

Q = 8.08 – 0.49P + 0.81I

Adjustments to income changes



• For the demand equation: Q = a – bP

• Elasticity:

Estimation of the Elasticities

)/()/)(/( QPbQPPQEP



)log()log()log( IcPbaQ

• Assume that price & income elasticity are constant.

Isoelastic demand curve is

Slope –b = Price elasticity of demand

Constant c = Income elasticity




• Using the data on raspberries

– Price elasticity = -0.34 (inelastic)

– Income elasticity = 1.32

log( ) 0.23 0.34log( ) 1.32log( )Q P I




• Substitutes: b2 is positive.

• Complements: b2 is negative.

Estimation with substitutes and complements

)log(log)log()log( 22 IcPbPbaQ


Concluding Remarks

• The demand curves of individual consumers for a product

can be derived from information available about their

preferences for goods and services as well as their budget

constraints.

• Engel curves describe the relationship between the

consumed quantity of a good and the income.


Concluding Remarks

• Two goods are substitute goods (complements) when an increase in the price of one good leads to an increase (decrease) in the quantity demanded of the other good.

• The effects of a price change on the demanded quantity can be divided into a substitution effect and an income effect.


Concluding Remarks

• The market demand curve is the horizontal addition of

individual demand curves for all consumers.

• The percentage change in the demanded quantity resulting

from a one percent change in the price determines the

elasticity of demand.

• A number of methods can be used to determine information

about consumer demand.

4. individual and market demand...income and substitution effects •a fall in the price of a good...

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