2646140886Bahan Kuliah Teori Ekonomi Mikro

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TEORI EKONOMI MIKRO

DOSEN:

DR. ARDITO BHINADI, SE., M.SI

JURUSAN ILMU EKONOMI, FAKULTAS EKONOMI,

UPN VETERAN YOGYAKARTA

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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.

Efek Substitusi dan Pendapatan Mahasiswa Presentasi, Ceramah dan diskusi Papan tulis, LCD, Laptop, Pertanyaan kuis/umpan balik Ch 5 4 (Empat) Mahasiswa mampu memahami hubungan permintaan antar barang. Hubungan Permintaan Antar Barang Mahasiswa Presentasi, Ceramah dan diskusi Papan tulis, LCD, Laptop, Pertanyaan kuis/umpan balik Ch 6

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2 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

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.

Asimetris Informasi Diskusi dan Kuis Papan tulis, LCD, Laptop Pertanyaan umpan balik Ch 18

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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%

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Microeconomic Theory

Basic Principles and Extensions, 9e

WALTER NICHOLSON

Slides prepared by

Linda Ghent

Eastern Illinois University

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

•shows that the model correctly predicts real-world events

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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?

Features of Economic Models

• Ceteris Paribus assumption

• Optimization assumption

• Distinction between positive and normative analysis

Ceteris Paribus

Assumption

• Ceteris Paribus means “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

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

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Optimization Assumptions

• Optimization assumptions generate precise, solvable models

• Optimization models appear to be perform fairly well in explaining reality

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)

•the value of an item meant its “value in use” •the price of an item meant its “value in exchange”

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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

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

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

Supply-Demand Equilibrium

Quantity per period Price

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 QD = Qs

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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

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

  

Supply-Demand Equilibrium

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

Supply-Demand Equilibrium

Quantity per period

Price

500 7

750

D’

An increase in demand...

…leads to a rise in the

equilibrium price and quantity.

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• 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

• 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

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

• 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

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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 2 225 x

y  

• If we differentiate

y x y

x x x

dy 2

2 4 ) 4 ( ) 2 225 ( 2

1 _ 2 1/2_ _ _ _

 

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

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 which markets can attain that goal

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

• Increasing use of computers to analyze data

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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

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

Important Points to Note:

• The supply-demand model is only a partial-equilibrium model

–a general equilibrium model is needed to

look at many markets together

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

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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

relatively small changes in income and prices

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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)

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

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

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

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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

Quantity of x Quantity of y

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 x Quantity of y

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 x Quantity of y

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 is flatter. The person would be willing to give up less y to gain additional units of x

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Indifference Curve Map

• Each point must have an indifference curve through it

Quantity of x Quantity of y

U₁ < U₂ < U₃ U1

U2 U3

Increasing utility

Transitivity

• Can any two of an individual’s indifference

curves intersect?

Quantity of x Quantity of y

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

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

Quantity of x Quantity of y

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*

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)

Quantity of x Quantity of y

This implies that “well-balanced” bundles are preferred

to bundles that are heavily weighted toward one commodity

(x1 + x2)/2

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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

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 constant (dU = 0)

Deriving the

MRS

• Therefore, we get:

y U

x U dx

dy MRS

    



constant U

• MRS is the ratio of the marginal utility of x to the marginal utility of y

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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

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

Convexity of Indifference

Curves

x y y x y U

x U

MRS  

   

5 . 0

5 . 0 * *

• Thus,

Convexity of Indifference

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

      

1 1

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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

Convexity of Indifference

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 x Quantity of y

The indifference curves will be linear. The MRS will be constant along the indifference curve.

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Examples of Utility Functions

• Perfect Complements

utility = U(x,y) = min (x, y)

Quantity of x Quantity of y

The indifference curves will be

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

Examples of Utility Functions

• 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   = -

Examples of Utility Functions

• CES Utility (Constant elasticity of substitution)

–The elasticity of substitution () is equal to

1/(1 - )

•Perfect substitutes  =  •Fixed proportions  = 0

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

–Perfect complements  MRS =  if y/x >

/, undefined if y/x = /, and MRS = 0 if y/x < /

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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

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 35

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

j i i j j i x U x U dx dx x x MRS        ) for ( j j i i dx x U dx x U dU       0

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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

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

Important Points to Note:

• 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

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

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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

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

especially intuitive, so we will rely on two-good cases to build intuition

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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)

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

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

homogeneous of degree zero in all prices and income

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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

p x*0.3I

y p y*0.7I

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

x  I

 

/ 1

1 *

y x

y 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 x

Quantity of y

As income rises, the individual chooses to consume more x and y

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Increase in Income

• If x decreases as income rises, x is an inferior good

Quantity of x

Quantity of y

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.

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

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

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

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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

Changes in a Good’s Price

Quantity of x

Quantity of y

To isolate the substitution effect, we hold “real” income constant but allow the relative price of good x to change

Substitution effect

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 x

Quantity of y

The income effect occurs because the individual’s “real” income changes when the price of good x changes

Income effect

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 x

Quantity of y

B A

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

C The substitution effect is the _{movement from point A to point C}

Substitution effect

Income effect

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

(28)

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

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

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

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

because the resulting rise in purchasing power allows the individual to move to a higher indifference curve

(29)

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

…quantity of x demanded rises.

The Individual’s Demand Curve

Quantity of y

Quantity of x Quantity of x

x’’

px’’

I = px’’ + py

x’

px’

I = px’ + py

x’’’

px’’’

I = px’’’ + py As the price of x falls...

(30)

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

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

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

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

p x* 30

p y*70

(31)

Demand Functions and Curves

• Any change in income will shift these demand curves

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

substitution effects

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 two-dimensional representation of the

compensated demand function x* = xc₍_p

(32)

xc …quantity demanded rises.

Compensated Demand Curves

Quantity of y

Quantity of x Quantity of x

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...

Compensated &

Uncompensated Demand

Quantity of x px

x’’

px’’

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

to attain utility level U2

Compensated &

Uncompensated Demand

Quantity of x px

px’’

x* x’

px’

At prices above px2, income compensation is positive because the individual needs some help to remain on U2

Compensated &

Uncompensated Demand

Quantity of x px

px’’

x*** x’’’

px’’’

At prices below px2, income

compensation is negative to prevent an increase in utility from a lower price

(33)

Compensated &

Uncompensated Demand

• 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

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

x 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

–only a substitution effect

5 . 0 5 . 0

x y p Vp

x 0.5

5 . 0

y x p Vp y 

(34)

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

A Mathematical Examination

of a Change in Price

• 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

A Mathematical Examination

of a Change in Price

• 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

A Mathematical Examination

of a Change in Price

• The first term is the slope of the compensated demand curve

–the mathematical representation of the

substitution effect x x c x p E E x p x p x           

(35)

A Mathematical Examination

of a Change in Price

• 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 47

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 shows that the substitution and income effects arising from a price change can be represented by I              x x p x p x p x U x x x constant effect income effect on substituti

(36)

The Slutsky Equation

• 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

   

  





x x p

x p

U x

x constant

The Slutsky Equation

• 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

   

  





x x p

x p

U x

x constant

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

p p

x( , ,I)0.5I

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

5 . 0

x p

x _  I

 

(37)

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 _   

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 x x x p

x x  

     / / ,

(38)

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

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

p x p p x p

(39)

Compensated Price Elasticities

• It is also useful to define elasticities based on the compensated demand function

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)

Compensated Price Elasticities

• 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

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

y  

     / / , 64

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 , I , ,

, x x

c p x p

x e s e

e _x  _x 

(40)

Compensated Price Elasticities

• 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

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

Homogeneity

• Dividing by x, we get

, , ,

0expx expy ex

• Any proportional change in all prices and income will leave the quantity of x demanded unchanged

Engel Aggregation

• Engel’s law suggests that the income

elasticity of demand for food items is less than one

–this implies that the income elasticity of

demand for all nonfood items must be greater than one

(41)

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  

x p y y p x

xe s e s

x  , 

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 p yI

(42)

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

y x

–Engel aggregation

1 1

,I  y yI    x

xe s e

–Cournot aggregation

x p y y p x

xe s e s

x  , (1)0

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

x x

• The compensated price elasticity depends on how important other goods (y) are in the utility function

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

y _



(43)

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

x 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 80

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

• Again, if we let p_x = p_y

75 . 0 1 2 5 . 0 1 ,

,px  sxpx   

x e

(44)

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

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)

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)

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 falls from U₁ to U₂

(45)

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

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

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}









0 1

) , ,

( 0

x x

p p

x y

c _p _p _U _dp

x dE CV

–this integral is the area to the left of the

compensated demand curve between p_x0

and p_x1

welfare loss

Consumer Welfare

Quantity of x px

xc_(p x…U0) px1

px0

When the price rises from px0 to px1, the consumer suffers a loss in welfare

(46)

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)?

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

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

Consumer Welfare

Quantity of x px

xc_(..._U 0) px1

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

(47)

Consumer Welfare

Quantity of x px

xc_(..._U 0) px1

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

Is U0 or U1 the

appropriate utility target?

Consumer Welfare

Quantity of x px

xc_(..._U 0) px1

We can use the Marshallian demand curve as a compromise

xc_(..._U 1) x(px…) A B C D px0

The area px1CApx0 falls between the sizes of the welfare losses defined by xc_(...U

0) and

xc_(...U

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 effects of price changes

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 from px = 1 to px = 4 is given by

4 1 5 . 0 5 . 0 4 1 5 . 0 5 .

0 ₂ 



 _



_

X p p x y x

y p Vp p

Vp CV

(48)

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}

Welfare Loss from Price

Increase

• Suppose that we use the Marshallian demand function instead

5 . 0 ) , ,

(

-x y

x 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

ln 5 . 0 5

0 





p p x x

-xdp p

Loss I I

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

rationality based on observed behavior and then uses it to approximate an

(49)

101

Revealed Preference and

the Substitution Effect

• 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

the Substitution Effect

Quantity of x

Quantity of y

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

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

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

available

103

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

bundle D is chosen

104

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

much as D

(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



 



i i i i

ix p x

1 1

1 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}



 



i i i i

ix p x

1 1

1 1 0

• Bundle 0 must be more expensive than bundle 1

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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

Important Points to Note:

• 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

111

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

112

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

effects work in opposite directions •no unambiguous prediction is possible

(52)

113

Important Points to Note:

• 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

•measures the proportionate change in quantity in response to a 1 percent change in price

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117

Important Points to Note:

• There are many relationships among demand elasticities

–own-price elasticities determine how a

price change affects total spending on a good

–substitution and income effects can be

summarized by the Slutsky equation

–various aggregation results hold among

elasticities

118

Important Points to Note:

• Welfare effects of price changes can be measured by changing areas below either compensated or ordinary

demand curves

–such changes affect the size of the

consumer surplus that individuals receive by being able to make market transactions

119

Important Points to Note:

• The negativity of the substitution effect is one of the most basic findings of demand theory

–this result can be shown using revealed

preference theory and does not necessarily require assuming the existence of a utility function

(54)

Chapter 6

DEMAND RELATIONSHIPS AMONG GOODS

The Two-Good Case

• The types of relationships that can occur when there are only two goods are limited

• But this case can be illustrated with two-dimensional graphs

Gross Complements

Quantity of x

Quantity of y

U1 U0

When the price of y falls, the substitution effect may be so small that the consumer purchases more x and more y

In this case, we call x and y gross complements

x/py < 0

Gross Substitutes

Quantity of x

Quantity of y

In this case, we call x and y gross substitutes

x1 x0

When the price of y falls, the substitution effect may be so large that the consumer purchases less x and more y

(1)

Public Goods and

Resource Allocation

• The first-order conditions for a maximum are

L/y_sA_{= U}

1Af’ - U2A + U1Bf’ = 0

L/y_sB_{= U}

1Af’ - U2B + U1Bf’ = 0

• Comparing the two equations, we find

U2B = U2A

Public Goods and

Resource Allocation

• We can now derive the optimality condition for the production of x

• From the initial first-order condition we know that

U1A/U2A + U1B/U2B = 1/f’

MRSA_{+ MRS}B₌_1/f’

• The MRS must reflect all consumers because all will get the same benefits

Failure of a

Competitive Market

• Production of x and y in competitive markets will fail to achieve this allocation

–with perfectly competitive prices p_x and p_y, each individual will equate his MRS to p_x/p_y

–the producer will also set 1/f’ equal to p_x/p_y

to maximize profits

–the price ratio p_x/p_y will be too low

•it would provide too little incentive to produce x

Failure of a

Competitive Market

• For public goods, the value of producing one more unit is the sum of each

consumer’s valuation of that output –individual demand curves should be added

vertically rather than horizontally

• Thus, the usual market demand curve will not reflect the full marginal valuation

(2)

Inefficiency of a

Nash Equilibrium

• Suppose that individual A is thinking about contributing s_A of his initial y endowment to the production of x

• The utility maximization problem for A is then

choose s_A to maximize UA_[_f₍_s

A + sB),yA - sA]

Inefficiency of a

Nash Equilibrium

• The first-order condition for a maximum is

U₁Af’ _{- U} 2A = 0

U₁A_/_U

2A = MRSA = 1/f’

• Because a similar argument can be applied to B, the efficiency condition will fail to be achieved

–each person considers only his own benefit

The Roommates’ Dilemma

• Suppose two roommates with identical

preferences derive utility from the number of paintings hung on their walls (x) and the number of granola bars they eat (y) with a utility function of

U_i(x,y_i) = x1/3_y

i2/3 (for i=1,2)

• Assume each roommate has $300 to spend and that p_x = $100 and p_y = $0.20

The Roommates’ Dilemma

• We know from our earlier analysis of

Cobb-Douglas utility functions that if each individual lived alone, he would spend 1/3 of his income on paintings (x = 1) and 2/3 on granola bars (y = 1,000)

• When the roommates live together, each must consider what the other will do

–if each assumed the other would buy paintings, x = 0 and utility = 0

(3)

The Roommates’ Dilemma

• If person 1 believes that person 2 will

not buy any paintings, he could choose to purchase one and receive utility of

U1(x,y1) = 11/3(1,000)2/3 = 100

while person 2’s utility will be

U2(x,y2) = 11/3(1,500)2/3 = 131

• Person 2 has gained from his free-riding position

The Roommates’ Dilemma

• We can show that this solution is

inefficient by calculating each person’s

MRS x y y U x U MRS i i i i i 2 / / _     

• At the allocations described,

MRS1 = 1,000/2 = 500

MRS2 = 1,500/2 = 750

The Roommates’ Dilemma

• Since MRS₁ + MRS₂ = 1,250, the

roommates would be willing to sacrifice 1,250 granola bars to have one additional painting

–an additional painting would only cost them 500 granola bars

–too few paintings are bought

The Roommates’ Dilemma

• To calculate the efficient level of x, we must set the sum of each person’s MRS equal to the price ratio

20 . 0 100 2 2 2 2 1 2 1 2

1  

     y x p p x y y x y x y MRS MRS

• This means that

(4)

The Roommates’ Dilemma

• Substituting into the budget constraint,

we get

0.20(y1 + y2) + 100x = 600

x = 2

y1 + y2 = 2,000

• The allocation of the cost of the paintings depends on how each

roommate plays the strategic financing

game 62

Lindahl Pricing of

Public Goods

• Swedish economist E. Lindahl suggested that individuals might be willing to be taxed for public goods if they knew that others were being taxed

–Lindahl assumed that each individual would be presented by the government with the proportion of a public good’s cost he was expected to pay and then reply with the level of public good he would prefer

Lindahl Pricing of

Public Goods

• Suppose that individual A would be quoted a specific percentage (A_{) and} asked the level of a public good (x) he would want given the knowledge that this fraction of total cost would have to be paid

• The person would choose the level of x which maximizes

Lindahl Pricing of

Public Goods

• The first-order condition is given by

U1A - AU2B(1/f’)=0

MRSA₌A_/f’

• Faced by the same choice, individual B would opt for the level of x which satisfies

(5)

Lindahl Pricing of

Public Goods

• An equilibrium would occur when A₊B_{= 1}

–the level of public goods expenditure favored by the two individuals precisely generates enough tax contributions to pay for it

MRSA_{+ MRS}B₌₍A₊B_)/f’_{= 1/}f’

Shortcomings of the

Lindahl Solution

• The incentive to be a free rider is very strong

–this makes it difficult to envision how the information necessary to compute equilibrium Lindahl shares might be computed

•individuals have a clear incentive to understate their true preferences

Important Points to Note:

• Externalities may cause a

misallocation of resources because of a divergence between private and social marginal cost

–traditional solutions to this divergence includes mergers among the affected parties and adoption of suitable Pigouvian taxes or subsidies

Important Points to Note:

• If transactions costs are small, private bargaining among the parties

affected by an externality may bring social and private costs into line

–the proof that resources will be efficiently allocated under such

circumstances is sometimes called the Coase theorem

(6)

Important Points to Note:

• Public goods provide benefits to individuals on a nonexclusive basis - no one can be prevented from consuming such goods

–such goods are usually nonrival in that the marginal cost of serving another user is zero

Important Points to Note:

• Private markets will tend to underallocate resources to public goods because no single buyer can appropriate all of the benefits that such goods provide

Important Points to Note:

• A Lindahl optimal tax-sharing scheme can result in an efficient allocation of resources to the production of public goods

–computation of these tax shares requires substantial information that individuals have incentives to hide