2646140886Bahan Kuliah Teori Ekonomi Mikro

(1)

TEORI EKONOMI MIKRO

DOSEN:

(2)

1

RANCANGAN PEMBELAJARAN SEMESTER ( RPS)

Program Studi /Jurusan : EKONOMI PEMBANGUNAN/ILMU EKONOMI

Matakuliah / Kode : TEORI EKONOMI MIKRO /

SKS / Semester : 3 (tiga x 50 menit)/ II (dua)

Mata Kuliah Prasyarat : Ekonomi Mikro Pengantar

Dosen : Dr. H. Ardito Bhinadi, M.Si

I.Deskripsi Mata Kuliah:

Matakuliah ini membahas sejumlah teori ekonomi mikro dari teori konsumen, teori produsen, berbagai bentuk pasar dan eksternalitas.

II.Kompetensi Umum :

Pada akhir perkuliahan mahasiswa diharapkan mampu memahami dan menjelaskan model-model ekonomi, pilihan dan permintaan, produksi dan penawaran, pasar kompetitif, kekuatan pasar, penetapan harga di pasar input, dan kegagalan pasar.

III. Analisis Instruksional

Terlampir

IV. Strategi Pembelajaran :

Pembelajaran menggunakan metoda ceramah dan diskusi dengan harapan muncul sensitifitas mahasiswa terhadap masalah mikro ekonomi. Materi perkuliahan didasarkan pada beberapa buku dan studi kasus yang harus difahami oleh mahasiswa. Dosen menyampaikan materi dalam bentuk dalam power point. Media yang digunakan adalah papan tulis, LCD, dan Laptop.

V. Rencana Pembelajaran Mingguan

Pertemuan Ke

Kompetensi Pokok/Sub-pokok

Bahasan Metoda Pembelajaran Media Pembelajaran Metoda Evaluasi Referensi 1 (Satu) Mahasiswa mampu memahami berbagai model ekonomi. Model-Model Ekonomi Ceramah dan diskusi Papan tulis, LCD, Laptop, Pertanyaan kuis/umpan balik Ch1 2 (Dua) Mahasiswa mampu memahami preferensi dan utilitas konsumen. Preferensi dan Utilitas Mahasiswa Presentasi, Ceramah dan diskusi Papan tulis, LCD, Laptop, Pertanyaan kuis/umpan balik Ch 3 3 (Tiga) Mahasiswa mampu efek substitusi dan pendapatan.

(3)

5 (Lima) Mahasiswa mampu memahami fungsi-fungsi produksi Fungsi-Fungsi Produksi Mahasiswa Presentasi, Ceramah dan diskusi Papan tulis, LCD, Laptop, Pertanyaan kuis/umpan balik Ch 9 6 (Enam) Mahasiswa mampu memahami fungsi-fungsi biaya. Fungsi-Fungsi Biaya. Mahasiswa Presentasi, Ceramah dan diskusi Papan tulis, LCD, Laptop, Pertanyaan kuis/umpan balik Ch 10 7 (Tujuh) Mahasiwa mampu menghitung maksimisasi laba.

Maksimisasi Laba Mahasiswa Presentasi, Ceramah dan Diskusi

Papan tulis, LCD, Laptop

Pertanyaan umpan balik

Ch 11

Ujian Tengah Semester Pertemuan

Ke

Kompetensi Pokok/Sub-pokok Bahasan Metoda Pembelajaran Media Pembelajaran Metoda Evaluasi Referensi 8 (Delapan) Mahasiwa mampu memahami model persaingan keseimbangan parsial.

Model Persaingan Keseimbangan Parsial

Diskusi dan Kuis

Papan tulis, LCD, Laptop Pertanyaan umpan balik Ch 12 9 (Sembilan) Mahasiwa mampu memahami keseimbangan umum dan kesejahteraan. Keseimbangan Umum dan Kesejahteraan Diskusi dan Kuis Papan tulis, LCD, Laptop Pertanyaan umpan balik Ch 13 10 (Sepuluh) Mahasiwa mampu memahami monopoli.

Monopoli Diskusi dan Kuis Papan tulis, LCD, Laptop Pertanyaan umpan balik Ch 14 11 (Sebelas) Mahasiwa mampu memahami persaingan tidak sempurna. Persaingan Tidak Sempurna Diskusi dan Kuis Papan tulis, LCD, Laptop Pertanyaan umpan balik Ch 15 12 (Dua Belas) Mahasiwa mampu memahami pasar tenaga kerja

Pasar Tenaga Kerja Diskusi dan Kuis Papan tulis, LCD, Laptop Pertanyaan umpan balik Ch 16 13 (Tiga Belas) Mahasiwa mampu memahami informasi asimetris.

(4)

3 14

(Empat Belas)

Mahasiwa mampu memahami eksternalitas dan barang publik.

Eksternalitas dan Barang Publik

Diskusi dan Kuis

Papan tulis, LCD, Laptop

Pertanyaan umpan balik

Ch 19

Ujian Akhir Semester

1. Sumber Referensi

Nicholson, Walter and Christopher Snyder, 2008. Microeconomic Theory, Basic Principles and Extensions, Tenth Edition, Thomson South-Western, United Stated of America.

2. Komponen Penilaian

1.Ujian Tengah Semester = 30%

2.Ujian Akhir Semester = 30%

3.Partisipasi Kelas = 20%

(5)

1

Microeconomic Theory

Basic Principles and Extensions, 9e

By

WALTER NICHOLSON

Slides prepared by

Linda Ghent

Eastern Illinois University

2

Chapter 1

ECONOMIC MODELS

Theoretical Models

• Economists use models to describe

economic activities

• While most economic models are

abstractions from reality, they provide aid in understanding economic behavior

Verification of Economic Models

• There are two general methods used to

verify economic models:

–direct approach

• establishes the validity of the model’s

assumptions

–indirect approach

(6)

real-5

Verification of Economic Models

• We can use the profit-maximization model

to examine these approaches

–is the basic assumption valid? do firms really

seek to maximize profits?

–can the model predict the behavior of real-world

firms?

6

Features of Economic Models

• Ceteris Paribus assumption

• Optimization assumption

• Distinction between positive and

normative analysis

7

Ceteris Paribus

Assumption

• Ceteris Paribusmeans “other things the

same”

• Economic models attempt to explain

simple relationships

–focus on the effects of only a few forces at a

time

–other variables are assumed to be unchanged

during the period of study

8

Optimization Assumptions

• Many economic models begin with the

assumption that economic actors are rationally pursuing some goal

–consumers seek to maximize their utility

–firms seek to maximize profits (or minimize

costs)

–government regulators seek to maximize

(7)

9

Optimization Assumptions

• Optimization assumptions generate

precise, solvable models

• Optimization models appear to be

perform fairly well in explaining reality

10

Positive-Normative Distinction

• Positive economic theories seek to

explain the economic phenomena that is observed

• Normative economic theories focus on

what “should” be done

The Economic Theory of Value

• Early Economic Thought

– “value” was considered to be synonymous with “importance”

–since prices were determined by humans,

it was possible for the price of an item to differ from its value

– prices > value were judged to be “unjust”

The Economic Theory of Value

• The Founding of Modern Economics

– the publication of Adam Smith’s The Wealth of

Nations is considered the beginning of modern

economics

– distinguishing between “value” and “price”

continued (illustrated by the diamond-water paradox)

(8)

13

The Economic Theory of Value

• Labor Theory of Exchange Value

–the exchange values of goods are determined by

what it costs to produce them

•these costs of production were primarily affected by labor costs

•therefore, the exchange values of goods were determined by the quantities of labor used to produce them

–producing diamonds requires more labor than

producing water

14

The Economic Theory of Value

• The Marginalist Revolution

–the exchange value of an item is not determined

by the total usefulness of the item, but rather

the usefulness of the last unit consumed

•because water is plentiful, consuming an additional unit has a relatively low value to individuals

15

The Economic Theory of Value

• Marshallian Supply-Demand Synthesis

–Alfred Marshall showed that supply and demand

simultaneously operate to determine price

–prices reflect both the marginal evaluation that

consumers place on goods and the marginal costs of producing the goods

•water has a low marginal value and a low marginal cost of production  Low price

•diamonds have a high marginal value and a high marginal cost of production  High price

16

Supply-Demand Equilibrium

Quantity per period Price

P*

Q*

D

The demand curve has a negative slope because the marginal value falls as quantity increases

S

The supply curve has a positive slope because marginal cost rises as quantity increases Equilibrium

(9)

17

Supply-Demand Equilibrium

q_D = 1000 - 100p q_S = -125 + 125p

Equilibrium q_D = q_S

1000 - 100p = -125 + 125p

225p = 1125

p* = 5

q* = 500

18

Supply-Demand Equilibrium

• A more general model is

q_D = a + bp q_S = c + dp

Equilibrium q_D = q_S

a + bp = c + dp

b d

c a p

  

*

A shift in demand will lead to a new equilibrium:

Q’_D = 1450 - 100P

Q’D = 1450 - 100P = QS = -125 + 125P

225P = 1575

P* = 7

Q* = 750

S

D Price

5 7

D’

An increase in demand...

(10)

21

• General Equilibrium Models

–the Marshallian model is a partial

equilibrium model

•focuses only on one market at a time

–to answer more general questions, we

need a model of the entire economy •need to include the interrelationships between

markets and economic agents

The Economic Theory of Value

22

• The production possibilities frontier can

be used as a basic building block for general equilibrium models

• A production possibilities frontier shows

the combinations of two outputs that can be produced with an economy’s resources

The Economic Theory of Value

23

Quantity of clothing (weekly) Quantity of food

(weekly)

10 9.5

4 2

Opportunity cost of clothing = 1/2 pound of food

Opportunity cost of clothing = 2 pounds of food

3 4 12 13

A Production Possibility Frontier

24

• The production possibility frontier

reminds us that resources are scarce

• Scarcity means that we must make

choices

–each choice has opportunity costs

–the opportunity costs depend on how much

of each good is produced

(11)

25

A Production Possibility Frontier

• Suppose that the production possibility

frontier can be represented by

225 2 2_ 2 _

y x

• To find the slope, we can solve for Y

2

225 x

y  

• If we differentiate

y x y

x x x

dx

dy 2

2 4 ) 4 ( ) 2 225 ( 2

1 _ 2 1/2_ _ _ _

 

26

A Production Possibility Frontier

• when x=5, y=13.2, the slope= -2(5)/13.2= -0.76

• when x=10, y=5, the slope= -2(10)/5= -4

• the slope rises as y rises

y x y

x x x

dx

dy 2

2 4 ) 4 ( ) 2 225 ( 2

1 _ 2 1/2_ _ _ _

 

• Welfare Economics

–tools used in general equilibrium analysis have

been used for normative analysis concerning the desirability of various economic outcomes

•economists Francis Edgeworth and Vilfredo Pareto helped to provide a precise definition of economic efficiency and demonstrated the conditions under

The Economic Theory of Value

Modern Tools

• Clarification of the basic behavioral

assumptions about individual and firm behavior

• Creation of new tools to study markets

• Incorporation of uncertainty and imperfect

information into economic models

(12)

29

Important Points to Note:

• Economics is the study of how scarce

resources are allocated among alternative uses

–economists use simple models to

understand the process

30

Important Points to Note:

• The most commonly used economic

model is the supply-demand model

–shows how prices serve to balance

production costs and the willingness of buyers to pay for these costs

31

• The supply-demand model is only a

partial-equilibrium model

–a general equilibrium model is needed to

look at many markets together

32

Important Points to Note:

• Testing the validity of a model is a

difficult task

– are the model’s assumptions

reasonable?

–does the model explain real-world

(13)

1

Chapter 3

PREFERENCES AND UTILITY

Axioms of Rational Choice

• Completeness

–if A and B are any two situations, an

individual can always specify exactly one of these possibilities:

•A is preferred to B

•B is preferred to A

•A and B are equally attractive

Axioms of Rational Choice

• Transitivity

–if A is preferred to B, and B is preferred to C, then A is preferred to C

– assumes that the individual’s choices are

internally consistent

Axioms of Rational Choice

• Continuity

–if A is preferred to B, then situations suitably

“close to” A must also be preferred to B – used to analyze individuals’ responses to

(14)

5

Utility

• Given these assumptions, it is possible to

show that people are able to rank in order all possible situations from least desirable to most

• Economists call this ranking utility

–if A is preferred to B, then the utility assigned to A exceeds the utility assigned to B

U(A) > U(B)

6

Utility

• Utility rankings are ordinal in nature

–they record the relative desirability of commodity bundles

• Because utility measures are not unique,

it makes no sense to consider how much more utility is gained from A than from B

• It is also impossible to compare utilities

between people

7

Utility

• Utility is affected by the consumption of

physical commodities, psychological attitudes, peer group pressures, personal experiences, and the general cultural environment

• Economists generally devote attention to

quantifiable options while holding

constant the other things that affect utility

–ceteris paribus assumption

8

Utility

• Assume that an individual must choose

among consumption goods x₁, x₂,…, x_n

• The individual’s rankings can be shown by a utility function of the form:

utility = U(x1, x2,…, xn; other things)

–this function is unique up to an

(15)

9

Economic Goods

• In the utility function, the x’s are assumed

to be “goods”

–more is preferred to less

Quantity of x Quantity of y

x* y*

Preferred to x*, y*

?

Worse than

x*, y* 10

Indifference Curves

• An indifference curve shows a set of

consumption bundles among which the individual is indifferent

x1 y1

y2

x2

U1

Combinations (x1, y1) and (x2, y2)

provide the same level of utility

Marginal Rate of Substitution

• The negative of the slope of the

indifference curve at any point is called

the marginal rate of substitution (MRS)

Quantity of y

y1

1

U U

dx

dy

MRS







Marginal Rate of Substitution

• MRS changes as x and y change

– reflects the individual’s willingness to trade y for x

Quantity of y

y1

At (x1, y1), the indifference curve is steeper.

The person would be willing to give up more

y to gain additional units of x

At (x2, y2), the indifference curve

(16)

13

Indifference Curve Map

• Each point must have an indifference

curve through it

U₁ < U₂ < U₃

U1

U2

U3 Increasing utility

14

Transitivity

• Can any two of an individual’s indifference curves intersect?

U1 U2

A B C

The individual is indifferent between A and C. The individual is indifferent between B and C. Transitivity suggests that the individual should be indifferent between A and B

But B is preferred to A because B contains more

x and y than A

15

Convexity

• A set of points is convex if any two points

can be joined by a straight line that is contained completely within the set

U1

The assumption of a diminishing MRS is equivalent to the assumption that all

combinations of x and y which are

preferred to x* and y* form a convex set

x* y*

16

Convexity

• If the indifference curve is convex, then

the combination (x₁ + x₂)/2, (y₁ + y₂)/2 will be preferred to either (x₁,y₁) or (x₂,y₂)

U1

x2 y1

y2

x1

This implies that “well-balanced” bundles are preferred to bundles that are heavily weighted toward one commodity

(17)

17

Utility and the MRS

• Suppose an individual’s preferences for

hamburgers (y) and soft drinks (x) can

be represented by

y x



10

utility

• Solving for y, we get

y = 100/x

• Solving for MRS = -dy/dx:

MRS = -dy/dx = 100/x2

18

Utility and the MRS

MRS = -dy/dx = 100/x2

• Note that as x rises, MRS falls

–when x = 5, MRS = 4

–when x = 20, MRS = 0.25

Marginal Utility

• Suppose that an individual has a utility

function of the form utility = U(x,y)

• The total differential of U is

dy y U dx x U dU

     

• Along any indifference curve, utility is

Deriving the

MRS

• Therefore, we get:

y U

x U

dx dy MRS

    



constant U

• MRS is the ratio of the marginal utility of

(18)

21

Diminishing Marginal Utility

and the

MRS

• Intuitively, it seems that the assumption

of decreasing marginal utility is related to

the concept of a diminishing MRS

–diminishing MRS requires that the utility function be quasi-concave

•this is independent of how utility is measured

–diminishing marginal utility depends on how

utility is measured

• Thus, these two concepts are different

22

Convexity of Indifference

Curves

• Suppose that the utility function is

y x



utility

• We can simplify the algebra by taking the

logarithm of this function

U*(x,y) = ln[U(x,y)] = 0.5 ln x + 0.5 ln y

23

Convexity of Indifference

Curves

x y

y x

y U

x U

MRS  





 

5 . 0

* *

• Thus,

24

Curves

• If the utility function is

U(x,y) = x + xy + y

• There is no advantage to transforming

this utility function, so

x y

y U x U

MRS

  





 

(19)

25

Convexity of Indifference

Curves

• Suppose that the utility function is

2 2 utility  x y

• For this example, it is easier to use the

transformation

U*(x,y) = [U(x,y)]2₌_x2₊_y2

26

Curves

y x y x

y U x U

MRS  

   

2 2 * *

• Thus,

Examples of Utility Functions

• Cobb-Douglas Utility

utility = U(x,y) = x_y

where  and  are positive constants

–The relative sizes of  and  indicate the

relative importance of the goods

Examples of Utility Functions

• Perfect Substitutes

utility = U(x,y) = x + y

Quantity of y

(20)

29

• Perfect Complements

utility = U(x,y) = min (x, y)

The indifference curves will be

L-shaped. Only by choosing more of the two goods together can utility be increased.

U1 U2 U3

30

• CES Utility (Constant elasticity of

substitution)

utility = U(x,y) = x_/_₊_y_/_

when  0 and

utility = U(x,y) = ln x + ln y

when  = 0

–Perfect substitutes   = 1

–Cobb-Douglas   = 0

–Perfect complements   = -

31

Examples of Utility Functions

• CES Utility (Constant elasticity of

substitution)

–The elasticity of substitution () is equal to 1/(1 - )

•Perfect substitutes  = 

•Fixed proportions  = 0

32

Homothetic Preferences

• If the MRS depends only on the ratio of

the amounts of the two goods, not on the quantities of the goods, the utility function is homothetic

–Perfect substitutes  MRS is the same at

every point

(21)

33

Homothetic Preferences

• For the general Cobb-Douglas function,

the MRS can be found as

x y y x y x y U x U MRS          

 _1__₁

34

Nonhomothetic Preferences

• Some utility functions do not exhibit

homothetic preferences utility = U(x,y) = x + ln y

y y y U x U

MRS  

    1 1

The Many-Good Case

• Suppose utility is a function of n goods

given by

utility = U(x₁, x₂,…, x_n)

• The total differential of U is

n n dx x U dx x U dx x U dU         

 ₂ ...

2 1 1

The Many-Good Case

• We can find the MRS between any two

goods by setting dU = 0

x U dx   j j i i dx x U dx x U dU       0

(22)

37

Multigood Indifference

Surfaces

• We will define an indifference surface

as being the set of points in n

dimensions that satisfy the equation

U(x1,x2,…xn) = k

where k is any preassigned constant

38

Multigood Indifference

Surfaces

• If the utility function is quasi-concave,

the set of points for which Uk will be

convex

–all of the points on a line joining any two points on the U = k indifference surface will also have U  k

39

• If individuals obey certain behavioral

postulates, they will be able to rank all commodity bundles

–the ranking can be represented by a utility

function

–in making choices, individuals will act as if they were maximizing this function

• Utility functions for two goods can be

illustrated by an indifference curve map

40

Important Points to Note:

• The negative of the slope of the

indifference curve measures the marginal

rate of substitution (MRS)

–the rate at which an individual would trade

an amount of one good (y) for one more unit

of another good (x)

• MRS decreases as x is substituted for y

–individuals prefer some balance in their

(23)

41

Important Points to Note:

• A few simple functional forms can capture

important differences in individuals’ preferences for two (or more) goods

–Cobb-Douglas function

–linear function (perfect substitutes)

–fixed proportions function (perfect

complements)

–CES function

•includes the other three as special cases

42

Important Points to Note:

• It is a simple matter to generalize from

two-good examples to many goods

– studying peoples’ choices among many

goods can yield many insights

–the mathematics of many goods is not

(24)

1

Chapter 5

INCOME AND SUBSTITUTION EFFECTS

Demand Functions

• The optimal levels of x₁,x₂,…,x_n can be expressed as functions of all prices and income

• These can be expressed as n demand

functions of the form:

x1* = d1(p1,p2,…,pn,I)

x2* = d2(p1,p2,…,pn,I)

• • •

xn* = dn(p1,p2,…,pn,I)

3

Demand Functions

• If there are only two goods (x and y), we

can simplify the notation

x* = x(p_x,p_y,I)

y* = y(px,py,I)

• Prices and income are exogenous

–the individual has no control over these

parameters

4

Homogeneity

• If we were to double all prices and

income, the optimal quantities demanded will not change

–the budget constraint is unchanged

x_i* = d_i(p1,p2,…,pn,I) = di(tp1,tp2,…,tpn,tI)

• Individual demand functions are

(25)

5

Homogeneity

• With a Cobb-Douglas utility function

utility = U(x,y) = x0.3_y0.7

the demand functions are

• Note that a doubling of both prices and

income would leave x* and y*

unaffected

x

p x*0.3I

y

p y*0.7I

6

Homogeneity

• With a CES utility function

utility = U(x,y) = x0.5₊_y0.5

the demand functions are

• Note that a doubling of both prices and

income would leave x* and y*

unaffected x y

x p p

p

x  I

 

/ 1

1 *

y x

y p p

p

y  I

 

/ 1

1 *

Changes in Income

• An increase in income will cause the

budget constraint out in a parallel fashion

• Since px/py does not change, the MRS

will stay constant as the worker moves to higher levels of satisfaction

Increase in Income

• If both x and y increase as income rises,

x and y are normal goods

Quantity of y

C B

As income rises, the individual chooses

(26)

9

Increase in Income

• If x decreases as income rises, x is an

inferior good

Quantity of x

Quantity of y

C

U3

As income rises, the individual chooses

to consume less x and more y

Note that the indifference curves do not have to be “oddly” shaped. The assumption of a diminishing

MRS is obeyed.

B

U2

A

U1

10

Normal and Inferior Goods

• A good x_i for which x_i/_I  0 over some range of income is a normal good in that range

• A good x_i for which x_i/I < 0 over some range of income is an inferior good in that range

11

Changes in a Good’s Price

• A change in the price of a good alters

the slope of the budget constraint

–it also changes the MRSat the consumer’s

utility-maximizing choices

• When the price changes, two effects

come into play

–substitution effect

–income effect

12

Changes in a Good’s Price

• Even if the individual remained on the same

indifference curve when the price changes, his optimal choice will change because the

MRS must equal the new price ratio

–the substitution effect

• The price change alters the individual’s “real” income and therefore he must move to a new indifference curve

(27)

13

Changes in a Good’s Price

Quantity of x

Quantity of y

U1 A

Suppose the consumer is maximizing utility at point A.

U2 B

If the price of good x falls, the consumer will maximize utility at point B.

Total increase in x

14

Changes in a Good’s Price

U1

Quantity of x

Quantity of y

A

To isolate the substitution effect, we hold

“real” income constant but allow the

relative price of good x to change

Substitution effect C

The substitution effect is the movement from point A to point C

The individual substitutes good x for good y because it is now relatively cheaper

Changes in a Good’s Price

U1

U2

Quantity of y

A

The income effect occurs because the

individual’s “real” income changes when

the price of good x changes

C B

The income effect is the movement from point C to point B

If x is a normal good, the individual will buy

more because “real”

income increased

Changes in a Good’s Price

U2

U1

Quantity of y

B A

An increase in the price of good x means that the budget constraint gets steeper

(28)

17

Price Changes for

Normal Goods

• If a good is normal, substitution and

income effects reinforce one another

–when price falls, both effects lead to a rise in quantity demanded

–when price rises, both effects lead to a drop

in quantity demanded

18

Price Changes for

Inferior Goods

• If a good is inferior, substitution and

income effects move in opposite directions

• The combined effect is indeterminate

–when price rises, the substitution effect leads

to a drop in quantity demanded, but the income effect is opposite

–when price falls, the substitution effect leads

to a rise in quantity demanded, but the income effect is opposite

19

Giffen’s Paradox

• If the income effect of a price change is

strong enough, there could be a positive relationship between price and quantity demanded

–an increase in price leads to a drop in real

income

–since the good is inferior, a drop in income

causes quantity demanded to rise

20

A Summary

• Utility maximization implies that (for normal

goods) a fall in price leads to an increase in quantity demanded

–the substitution effect causes more to be

purchased as the individual moves along an indifference curve

–the income effect causes more to be purchased

(29)

21

A Summary

• Utility maximization implies that (for normal

goods) a rise in price leads to a decline in quantity demanded

–the substitution effect causes less to be

purchased as the individual moves along an indifference curve

–the income effect causes less to be purchased

because the resulting drop in purchasing power moves the individual to a lower

indifference curve ₂₂

A Summary

• Utility maximization implies that (for inferior

goods) no definite prediction can be made for changes in price

–the substitution effect and income effect move

in opposite directions

–if the income effect outweighs the substitution

effect, we have a case of Giffen’s paradox

The Individual’s Demand Curve

• An individual’s demand for x depends

on preferences, all prices, and income:

x* = x(p_x,p_y,I)

• It may be convenient to graph the

individual’s demand for x assuming that

income and the price of y (p_y) are held

constant

x

…quantity of x demanded rises.

The Individual’s Demand Curve

Quantity of y _p

x

px’’

U2

px’

U1

px’’’

(30)

25

The Individual’s Demand Curve

• An individual demand curve shows the

relationship between the price of a good and the quantity of that good purchased by an individual assuming that all other

determinants of demand are held constant

26

Shifts in the Demand Curve

• Three factors are held constant when a

demand curve is derived

–income

–prices of other goods (p_y)

– the individual’s preferences

• If any of these factors change, the

demand curve will shift to a new position

27

Shifts in the Demand Curve

• A movement along a given demand

curve is caused by a change in the price of the good

–a change in quantity demanded

• A shift in the demand curve is caused by

changes in income, prices of other goods, or preferences

–a change in demand

28

Demand Functions and Curves

• If the individual’s income is $100, these

functions become x

p x*0.3I

y

p y*0.7I

• We discovered earlier that

x

p x* 30

y

(31)

29

Demand Functions and Curves

• Any change in income will shift these

demand curves

30

Compensated Demand Curves

• The actual level of utility varies along

the demand curve

• As the price of x falls, the individual

moves to higher indifference curves

–it is assumed that nominal income is held

constant as the demand curve is derived

– this means that “real” income rises as the

price of x falls

Compensated Demand Curves

• An alternative approach holds real income

(or utility) constant while examining

reactions to changes in p_x

–the effects of the price change are

“compensated” so as to constrain the

individual to remain on the same indifference curve

–reactions to price changes include only

Compensated Demand Curves

• A compensated (Hicksian) demand curve

shows the relationship between the price of a good and the quantity purchased assuming that other prices and utility are held constant

• The compensated demand curve is a

(32)

33

xc …quantity demanded

rises.

Compensated Demand Curves

Quantity of y

Quantity of x Quantity of x

px

U2

x’’

px’’

x’’

y x p p slope ''

x’

px’

y x p p slope '

x’ x’’’

px’’’

y x p p slope '''

x’’’

Holding utility constant, as price falls...

34

Compensated &

Uncompensated Demand

Quantity of x px

x

xc

x’’

px’’

At px’’, the curves intersect because the individual’s income is just sufficient

to attain utility level U2

35

Compensated &

Quantity of x px

x

xc

px’’

x*

x’

px’

At prices above px2, income

compensation is positive because the individual needs some help to remain on U2

36

Compensated &

Quantity of x px

x

xc

px’’

x*** x’’’

px’’’

At prices below px2, income

(33)

37

Compensated &

• For a normal good, the compensated

demand curve is less responsive to price changes than is the uncompensated demand curve

–the uncompensated demand curve reflects

both income and substitution effects

–the compensated demand curve reflects only

substitution effects

38

Compensated Demand

Functions

• Suppose that utility is given by

utility = U(x,y) = x0.5_y0.5

• The Marshallian demand functions are

x = I/2px y = I/2py

• The indirect utility function is

5 . 0 5 . 0

2 ) , , ( utility

y x y x

p p p p

V I  I



Compensated Demand

Functions

• To obtain the compensated demand

functions, we can solve the indirect

utility function for I and then substitute

into the Marshallian demand functions

5 . 0 5 . 0

y

p Vp

x 0.5

5 . 0

y x

p Vp y

Compensated Demand

Functions

• Demand now depends on utility (V)

rather than income

• Increases in p_x reduce the amount of x

demanded

5 . 0 5 . 0

x y

p Vp

x 0.5

5 . 0

y x

p Vp

(34)

41

A Mathematical Examination

of a Change in Price

• Our goal is to examine how purchases of

good x change when p_x changes

x/p_x

• Differentiation of the first-order conditions

from utility maximization can be performed to solve for this derivative

• However, this approach is cumbersome

and provides little economic insight

42

A Mathematical Examination

• Instead, we will use an indirect approach

• Remember the expenditure function

minimum expenditure = E(px,py,U)

• Then, by definition

xc₍_p

x,py,U) = x[px,py,E(px,py,U)]

–quantity demanded is equal for both demand

functions when income is exactly what is needed to attain the required utility level

43

A Mathematical Examination

• We can differentiate the compensated

demand function and get

xc₍_p

x,py,U) = x[px,py,E(px,py,U)]

x x x c p E E x p x p x            x x c x p E E x p x p x            44

• The first term is the slope of the

compensated demand curve

–the mathematical representation of the

(35)

45

• The second term measures the way in

which changes in p_x affect the demand

for x through changes in purchasing

power

–the mathematical representation of the

income effect x x c x p E E x p x p x            46

The Slutsky Equation

• The substitution effect can be written as

constant effect on substituti        U x x c p x p x

• The income effect can be written as

x x p E x p E E x               I effect income

The Slutsky Equation

• Note that E/p_x = x

–a $1 increase in px raises necessary

expenditures by x dollars

–$1 extra must be paid for each unit of x

purchased

The Slutsky Equation

• The utility-maximization hypothesis

(36)

49

• The first term is the substitution effect

–always negative as long as MRS is

diminishing

–the slope of the compensated demand curve

must be negative

I          x x p x p x U x x constant 50

• The second term is the income effect

–if x is a normal good, then x/I > 0 •the entire income effect is negative

–if x is an inferior good, then x/I < 0 •the entire income effect is positive

I          x x p x p x U x x constant 51

A Slutsky Decomposition

• We can demonstrate the decomposition

of a price effect using the Cobb-Douglas example studied earlier

• The Marshallian demand function for

good x was

x y x p p p

x( , ,I)0.5I

52

A Slutsky Decomposition

• The Hicksian (compensated) demand

function for good x was

5 . 0 5 . 0 ) , , ( x y y x c p Vp V p p x 

• The overall effect of a price change on

the demand for x is

2 5 . 0 x x p p

x _  I

(37)

53

A Slutsky Decomposition

• This total effect is the sum of the two

effects that Slutsky identified

• The substitution effect is found by

differentiating the compensated demand function 5 . 1 5 . 0 5 . 0 effect on substituti x y x c p Vp p

x _

  

54

A Slutsky Decomposition

• We can substitute in for the indirect utility

function (V)

2 5 . 1 5 . 0 5 . 0 5 . 0 25 . 0 ) 5 . 0 ( 5 . 0 effect on substituti x x y y x p p p p p _I

I _ 

 

 

A Slutsky Decomposition

• Calculation of the income effect is easier

2 25 . 0 5 . 0 5 . 0 effect income x x

x p p

p x

x I I

I            

• Interestingly, the substitution and income

effects are exactly the same size

Marshallian Demand

Elasticities

• Most of the commonly used demand

elasticities are derived from the

Marshallian demand function x(p_x,p_y,I)

• Price elasticity of demand (e_x_,_px)

x p p x p p x x e x p

x x  

(38)

57

Marshallian Demand

Elasticities

• Income elasticity of demand (e_x_,_I)

x x x x

e_x I

I I I

I _ 

     / / ,

• Cross-price elasticity of demand (e_x_,_py)

x p p x p p x x e y y y y p

x y  

     / / , 58

Price Elasticity of Demand

• The own price elasticity of demand is

always negative

– the only exception is Giffen’s paradox

• The size of the elasticity is important

–if e_x,px < -1, demand is elastic

–if e_x,px > -1, demand is inelastic

–if e_x,px = -1, demand is unit elastic

59

Price Elasticity and Total

Spending

• Total spending on x is equal to

total spending =pxx

• Using elasticity, we can determine how

total spending changes when the price of

x changes

] 1 [ ) ( ,          x p x x x x

x _x _x_e

p x p p x p 60

Price Elasticity and Total

Spending

• The sign of this derivative depends on

whether e_x,px is greater or less than -1

–if e_x,px > -1, demand is inelastic and price and total spending move in the same direction

–if e_x,px < -1, demand is elastic and price and total spending move in opposite directions

] 1 [ ) ( ,          x p x x x x

x _x _x_e

(39)

61

Compensated Price Elasticities

• It is also useful to define elasticities

based on the compensated demand function

62

Compensated Price Elasticities

• If the compensated demand function is

xc₌_xc₍_p x,py,U)

we can calculate

–compensated own price elasticity of

demand (e_xc ,px)

–compensated cross-price elasticity of

demand (exc,py)

• The compensated own price elasticity of

demand (e_xc

,px) is

c x x c x x c c c p x x p p x p p x x e

x  

     / / ,

• The compensated cross-price elasticity

of demand (e_xc

,py) is

Compensated Price Elasticities

• The relationship between Marshallian

and compensated price elasticities can be shown using the Slutsky equation

I            

 x x

x p p x x p e p x x p _x x c c x p x x x x ,

(40)

65

• The Slutsky equation shows that the

compensated and uncompensated price elasticities will be similar if

–the share of income devoted to x is small

–the income elasticity of x is small

66

Homogeneity

• Demand functions are homogeneous of

degree zero in all prices and income • Euler’s theorem for homogenous

functions shows that

I I_

 

   

 

 x

p x p p

x p

y y x x 0

67

Homogeneity

• Dividing by x, we get

I , , ,

0expx expy ex

• Any proportional change in all prices

and income will leave the quantity of x

demanded unchanged

68

Engel Aggregation

• Engel’s law suggests that the income elasticity of demand for food items is less than one

(41)

69

Engel Aggregation

• We can see this by differentiating the

budget constraint with respect to income (treating prices as constant)

I I       

px x py y

1 I I I I I I I

I , ,

1 _x _y s_xe_x s_ye_y

y y y p x x x

p   

         70

Cournot Aggregation

• The size of the cross-price effect of a

change in the price of x on the quantity

of y consumed is restricted because of

the budget constraint

• We can demonstrate this by

differentiating the budget constraint with

respect to p_x

Cournot Aggregation

x y x x x p y p x p x p p             0 I y y p p y p p x x x p p x p x x y x x x

x _  

           I I I 0 x

x x y yp

p x

xe s s e

s , ,

0  

Demand Elasticities

• The Cobb-Douglas utility function is

U(x,y) = xy (+=1)

• The demand functions for x and y are

x

p

xI

y

(42)

73

Demand Elasticities

• Calculating the elasticities, we get

1 2 ,                 x x x x x p x p p p x p p x e x I I 0 0 , _       x p x p p x

e y y

y p x y 1 ,                x x x p p x x e I I I I I 74

Demand Elasticities

• We can also show

–homogeneity 0 1 0 1 , ,

,p  xp  xI    

x e e

e

y x

–Engel aggregation

1 1

1

,

,I  y yI   

x

xe s e

s

–Cournot aggregation

x p y y p x

xe s e s

s

x

x  , (1)0

,

75

Demand Elasticities

• We can also use the Slutsky equation to

derive the compensated price elasticity

          

 , , 1 (1) 1

, xp x xI

c p

x e se

e

x x

• The compensated price elasticity

depends on how important other goods (y) are in the utility function

76

Demand Elasticities

• The CES utility function (with  = 2,

 = 5) is

U(x,y) = x0.5 ₊_y0.5

• The demand functions for x and y are

) 1

( _ 1



y x

x p p

p x I ) 1 ( 1 y x

y p p

p

y _



(43)

77

Demand Elasticities

• We will use the “share elasticity” to derive the own price elasticity

x x

x xp

x x x x p s e s p p s

e , _  1 ,

 

• In this case,

1 1 1     y x x x p p x p s I 78

Demand Elasticities

• Thus, the share elasticity is given by

1 1 1 1 2 1 1 , 1 ) 1 ( ) 1 (                   y x y x y x x y x y x x x x p s p p p p p p p p p p s p p s e x x

• Therefore, if we let p_x = p_y

5 . 1 1 1 1 1 1 , , _     

 _x _x

x s p

p

x e

e

Demand Elasticities

• The CES utility function (with  = 0.5,

 = -1) is

U(x,y) = -x -1 _-_y -1

• The share of good x is

5 . 0 5 . 0 1 1     x y x x p p x p s I

Demand Elasticities

• Thus, the share elasticity is given by

5 . 0 5 . 0 5 . 0 5 . 0 1 5 . 0 5 . 0 2 5 . 0 5 . 0 5 . 1 5 . 0 , 1 5 . 0 ) 1 ( ) 1 ( 5 . 0                 x y x y x y x x y x y x x x x p s p p p p p p p p p p p s p p s e x x

(44)

81

Consumer Surplus

• An important problem in welfare

economics is to devise a monetary measure of the gains and losses that individuals experience when prices change

82

Consumer Welfare

• One way to evaluate the welfare cost of a

price increase (from p_x0_to_p

x1) would be

to compare the expenditures required to

achieve U₀under these two situations

expenditure at p_x0₌_E

0 = E(px0,py,U0)

expenditure at p_x1₌_E

1 = E(px1,py,U0)

83

Consumer Welfare

• In order to compensate for the price rise,

this person would require a

compensating variation (CV) of

CV = E(px1,py,U0) - E(px0,py,U0)

84

Consumer Welfare

Quantity of x

Quantity of y

U1 A

Suppose the consumer is maximizing utility at point A.

U2 B

If the price of good x rises, the consumer will maximize utility at point B.

The consumer’s utility

(45)

85

Consumer Welfare

Quantity of x

Quantity of y

U1 A

U2 B

CV is the amount that the individual would need to be compensated

The consumer could be compensated so that he can afford to remain on U1

C

86

Consumer Welfare

• The derivative of the expenditure function

with respect to p_x is the compensated

demand function

) , , ( ) , , (

0 0

U p p x p

U p p E

y x c

x y

x _

 

Consumer Welfare

• The amount of CV required can be found

by integrating across a sequence of

small increments to price from p_x0_to_p

x1









1

0 1

0

) , ,

( 0

x

x x

x p

p p

p

x y

x

c _p _p _U _dp

x dE CV

–this integral is the area to the left of the

welfare loss

Consumer Welfare

px

xc_(p x…U0)

px1

px0

When the price rises from px0 to px1,

(46)

89

Consumer Welfare

• Because a price change generally

involves both income and substitution effects, it is unclear which compensated demand curve should be used

• Do we use the compensated demand

curve for the original target utility (U₀) or

the new level of utility after the price

change (U₁)?

90

The Consumer Surplus

Concept

• Another way to look at this issue is to

ask how much the person would be willing to pay for the right to consume all of this good that he wanted at the

market price of p_x0

91

The Consumer Surplus

Concept

• The area below the compensated

demand curve and above the market price is called consumer surplus

–the extra benefit the person receives by

being able to make market transactions at the prevailing market price

92

Consumer Welfare

Quantity of x px

xc_(..._U 0)

px1

x1

When the price rises from px0 to px1, the actual

market reaction will be to move from A to C

xc_(..._U 1)

x(px…)

A C

px0

x0

(47)

93

Consumer Welfare

Quantity of x px

xc_(..._U 0)

px1

x1

Is the consumer’s loss in welfare

best described by area px1BApx0

[using xc_(...U

0)] or by area px1CDpx0

[using xc_(...U

1)]?

xc_(..._U 1) A

B C

D

px0

x0

Is U0 or U1 the

appropriate utility target?

94

Consumer Welfare

Quantity of x px

xc_(..._U 0)

px1

x1

We can use the Marshallian demand curve as a compromise

xc_(..._U 1)

x(px…)

A B C

D

px0

x0

The area px1CApx0

falls between the sizes of the welfare losses defined by xc_(...U

0) and

xc_(...U

1)

Consumer Surplus

• We will define consumer surplus as the

area below the Marshallian demand curve and above price

–shows what an individual would pay for the

right to make voluntary transactions at this price

–changes in consumer surplus measure the

Welfare Loss from a Price

Increase

• Suppose that the compensated demand

function for x is given by

5 . 0 5 . 0

) , , (

x y y

x c

p Vp V p p

x 

• The welfare cost of a price increase

(48)

97

Welfare Loss from a Price

Increase

• If we assume that V = 2 and p_y = 2,

CV = 222(4)0.5–₂₂₂₍₁₎0.5_{= 8}

• If we assume that the utility level (V)

falls to 1 after the price increase (and used this level to calculate welfare loss),

CV = 122(4)0.5–₁₂₂₍₁₎0.5_{= 4}

98

Welfare Loss from Price

Increase

• Suppose that we use the Marshallian

demand function instead

1

5 . 0 ) , ,

(

-x y

x p p

p

x _I  _I

• The welfare loss from a price increase

from p_x = 1 to p_x = 4 is given by

4

1 1

4

1

ln 5 . 0 5

.

0 

 





x

x p

p x x

-xdp p

p

Loss I I

99

Welfare Loss from a Price

Increase

• If income (I) is equal to 8,

loss=4ln(4)-4ln(1)=4ln(4)=4(1.39)=5.55

–this computed loss from the Marshallian

demand function is a compromise between the two amounts computed using the compensated demand functions

100

Revealed Preference and

the Substitution Effect

• The theory of revealed preference was

proposed by Paul Samuelson in the late 1940s

• The theory defines a principle of

(49)

101

Revealed Preference and

• Consider two bundles of goods: A and B

• If the individual can afford to purchase

either bundle but chooses A, we say that

A had been revealed preferred to B

• Under any other price-income

arrangement, B can never be revealed

preferred to A

102

Revealed Preference and

Quantity of x

Quantity of y

A

I1

Suppose that, when the budget constraint is given by I1, A is chosen

B

I3

A must still be preferred to B when income is I3 (because both A and B are available)

I2

If B is chosen, the budget constraint must be similar to that given by I2 where A is not

available

Negativity of the

Substitution Effect

• Suppose that an individual is indifferent

between two bundles: C and D

• Let p_xC_,_p

yC be the prices at which

bundle C is chosen

• Let p_xD_,_p

yD be the prices at which

Negativity of the

Substitution Effect

• Since the individual is indifferent between

C and D

–When C is chosen, D must cost at least as

much as C

p_xC_x

C + pyCyC≤ pxCxD + pyCyD

–When D is chosen, C must cost at least as

(50)

105

Negativity of the

Substitution Effect

• Rearranging, we get

p_xC_(x

C - xD) + pyC(yC -yD) ≤ 0

p_xD_(x

D - xC) + pyD(yD -yC) ≤ 0

• Adding these together, we get

(p_xC–_p

xD)(xC - xD) + (pyC–pyD)(yC - yD) ≤ 0

106

Negativity of the

Substitution Effect

• Suppose that only the price of x changes

(p_yC₌_p

yD)

(p_xC–_p

xD)(xC - xD) ≤ 0

• This implies that price and quantity move

in opposite direction when utility is held constant

–the substitution effect is negative

107

Mathematical Generalization

• If, at prices p_i0_bundle_x

i0 is chosen

instead of bundle x_i1_{(and bundle}_x

i1 is

affordable), then



 



n

i

n

i i i i

ix p x

p

1 1

1 0 0

0

• Bundle 0has been “revealed preferred”

to bundle 1

108

Mathematical Generalization

• Consequently, at prices that prevail

when bundle 1 is chosen (p_i1_{), then}



 



n

i

n

i i i i

ix p x

p

1 1

1 1 0

1

• Bundle 0 must be more expensive than

(51)

109

Strong Axiom of Revealed

Preference

• If commodity bundle 0 is revealed

preferred to bundle 1, and if bundle 1 is

revealed preferred to bundle 2, and if

bundle 2 is revealed preferred to bundle

3,…,and if bundle K-1 is revealed

preferred to bundle K, then bundle K

cannot be revealed preferred to bundle 0

110

• Proportional changes in all prices and

income do not shift the individual’s budget constraint and therefore do not alter the quantities of goods chosen

–demand functions are homogeneous of

degree zero in all prices and income

Important Points to Note:

• When purchasing power changes

(income changes but prices remain the same), budget constraints shift

–for normal goods, an increase in income

means that more is purchased

–for inferior goods, an increase in income

means that less is purchased

Important Points to Note:

• A fall in the price of a good causes

substitution and income effects

–for a normal good, both effects cause more

of the good to be purchased

–for inferior goods, substitution and income

(52)

113

• A rise in the price of a good also

causes income and substitution effects

–for normal goods, less will be demanded

–for inferior goods, the net result is ambiguous

114

Important Points to Note:

• The Marshallian demand curve

summarizes the total quantity of a good demanded at each possible price

–changes in price prompt movements

along the curve

–changes in income, prices of other goods,

or preferences may cause the demand curve to shift

115

Important Points to Note:

• Compensated demand curves illustrate

movements along a given indifference curve for alternative prices

–they are constructed by holding utility

constant and exhibit only the substitution effects from a price change

–their slope is unambiguously negative (or

zero)

116

Important Points to Note:

• Demand elasticities are often used in

empirical work to summarize how individuals react to changes in prices and income

–the most important is the price elasticity of

demand

(53)