MICROECONOMICS Classroom Lecture Notes (3 credits, as of 2004)

MICROECONOMICS

Classroom Lecture Notes

(3 credits, as of 2004)

based on Hal R. Varian’s Intermediate Microeconomics,

Sixth Edition, referring to Pindyck and Rubinfeld’s

Microeconomics,

Fourth Edition.

Chapter 0Chapter 0

The source of all economic problems is scarcity.

Problem of trade-off, and choice.

Economics, as a way of thinking, as a dismal science.

Problems - solutions - hidden consequences.

Main Main decision-making agentsdecision-making agents: :

1 individuals (household), 2 firms, and 3 governments.

Objects of economic choice are

commoditiescommodities,,including

goods and services.

Main economic activities:Main economic activities:

Consumption, Production, and Exchange.

MicroMicroeconomics and economics and macromacroeconomicseconomics::

to show the market mechanism (the invisible hand),

to supplement it.

The circular flow of economic The circular flow of economic activities. activities.

product market factor market

The The product marketproduct market and and the the factor marketfactor market. .

The market relation is mutual and voluntary.

Positive issues and normative issues.

Marginal analysisMarginal analysisRelations between Total magnitudes, Average magnitudes, and Marginal magnitudes.

1, MM is the slope of the TM curve;2, AM is the slope of the ray from the

origin to the point at the TM curve; TM

MM(x*)

AM(x*)

x* x

3, TM increasing (decreasing)

if and only if

MM > 0 ( MM < 0 );

4, If TM is at maximum or minimum,

then MM = 0;

5, AM increasing (decreasing) if and only if MM > AM ( MM < AM );

6, If AM is at maximum or minimum, then MM = AM, or MM cuts AM at the latter’s maximum or minimum.

Chapter 1Chapter 1

Economics proceeds by developing Models of social phenomena.

By a model we mean a simplified representation of reality.

Exogenous variables: taken as determined by factors

not discussed in a model.

Endogenous variables: determined by forces described

in the model.

The The optimizationoptimization principle: principle:

People try to choose what’s best for them.

The The equilibriumequilibrium principle: principle:

Prices adjust until demand and supply are equal.

The The demanddemand curve: curve:

A curve that relates the quantity demanded to price.

The The reservationreservation price: price: One’s maximum willingness to pay for something.

From people's reservation prices to the demand curve.

Similarly, the supply curve.

Fig.

Pareto efficiencyPareto efficiency::

A concept to evaluate different ways of allocating resources.

A Pareto improvement is a change to make some people better off without hurting anybody else.

An economic situation is Pareto efficient or Pareto optimal if there is already no way to make any

more Pareto improvement.

Short run and long runShort run and long run

Equilibria in the short run (some factors are unchanged)

and in the long run.

Chapter 2Chapter 2

* Vector variables and vector functions. * The inner product of two vectors. * With the price vector p = ( p1, …, pn ),

the value of

the commodity bundle x = ( x1, …, xn )

is pTx = Σi pixi.

However, two goods are often enough to discuss.

The budget constraint:

p1 x1 + p2 x2 ≤ m.

The budget line and the budget set (the market opportunity set).

The slope of the budget line: d x2 /d x1 = – p1 / p2 .

How the budget line moves when the income changes, or

when a price changes.

x2

x1

Budget set

Budget lineSlope = -p1/p2

m/p2

m/p1

Budget lineBudget line and and budget setbudget set

x2

x1

Budget line

Slope = - p1/p2

m’/p2

m/p2

m/p1 m’/p1

Increasing incomeIncreasing income

Slope

= - p’1/p2

m/p2 Budget line

Slope = - p1/p2

m/p’1 m/p1

Increasing priceIncreasing price

A subsidy

is the opposite of a quantity tax.  

Taxes, quantity taxes, value taxes (ad valorem taxes), and lump-sum taxes.

Rationing.

Their effects on the budget set.

Chapter 3Chapter 3

* Prerequisite: A binary relation R on X is said to be

Complete if xRy or yRx for any pair of x and y in X;

Reflexive if xRx for any x in X;

Transitive if xRy and yRz imply xRz.

Rational agents and stable Rational agents and stable preferences preferences

Bundle x is strictly preferred (s.p.), or weakly preferred (w.p.), or indifferent (ind.), to Bundle y.

(If x is w.p. to y and y is w.p. to x, we say x is indifferent to y.)

Assumptions about PreferencesAssumptions about Preferences

Completeness: x is w.p. to y or y is w.p. to x for any pair of x and y.

Reflexivity: x is w.p. to x for any bundle x.

Transitivity: If x is w.p. to y and y is w.p. to z, then x is w.p. to z.

The indifference sets, the indifference curves.

They cannot cross each other.

Fig.

indifference curvesindifference curvesx2

x1

Perfect substitutes and perfect complements. Goods, bads, and neutrals. Satiation. Figs

Blue pencils

Red pencils

Indifference curves

Perfect Perfect substitutessubstitutes

Perfect Perfect complementscomplements

Indifference curves

Left shoes

Right shoes

Well-behaved preferences are monotonic (meaning more is better) and

convex (meaning average are preferred to extremes).

Figs

x2

x1

Betterbundles(x1, x2)

MonotonicityMonotonicity

Betterbundles

The marginal rate of substitution (MRS) measures the slope of the indifference curve.

MRS = d x2 / d x1, the marginal willingness to pay ( how much to give up of x2 to acquire one more of x1 ).

Usually negative. Fig

Convex indifference curves exhibit a diminishing marginal rate of substitution.

Fig.

x2

x1

ConvexityConvexity

Averagedbundle

(y1,y2)

(x1,x2)

Chapter 4Chapter 4

(as a way to describe preferences)

UtilitiesUtilities

Essential ordinal utilities,versus

convenient cardinal utility functions.

Cardinal utility functions: u ( x ) ≥ u ( y ) if and only if bundle x is w.p. to bundle y.

The indifference curves are the projections of contours of

u = u ( x1, x2 ).

Fig.

Utility functions are indifferent up to any strictly increasing transformation.

Constructing a utility function in the two-commodity case of well-behaved preferences:

Draw a diagonal line and label each indifference curve with how far it is from the origin.

Examples of utility functionsExamples of utility functions u (x1, x2) = x1 x2 ;

u (x1, x2) = x12 x2

2 ;

u (x1, x2) = ax1 + bx2

(perfect substitutes); u (x1, x2) = min{ax1, bx2}

(perfect complements).

Quasilinear preferences: All indifference curves are vertically (or

horizontally) shifted copies of a single one, for example u (x1, x2) = v (x1) + x2 .

Cobb-Douglas preferences:

u (x1, x2) = x1c x2

d , or

u (x1, x2) = x1ax2

1-a ;

and their log equivalents:

u (x1, x2) = c ln x + d ln x2 , or

u (x1, x2) = a ln x + (1– a) ln x2

Cobb-DouglasCobb-Douglas

MRS along an indifference curve.Derive MRS = – MU1 / MU2

by taking total differential along any indifference curve.

Marginal utilities

MU1 and MU2.

MarginalMarginal analysis analysis

MM is the slope of the TM curve

AM is the slope of the ray from the origin to the point at the TM curve.

500490

480 The demand curve

ReservationReservation priceprice

Number of apartment

From peoples’ reservation prices to the market demand curve.

supply

Demand

PP

Q

EquilibriumEquilibrium

P*P*

Q*

E (P*,Q*)

supply

Demand

pp

q

E

EquilibriumEquilibrium

x2

x1

Budget lineBudget set

RationingRationing

R*

Marketopportunity

MRSMRS

Indifferencecurve

Slope = dx2/dx1

x2

x1

dx2dx1

Chapter 5Chapter 5

Choice of consumption

Optimal choice is at the point in the budget line with highest utility.

The tangency solution of an indifferent curve and the budget line:

MRS = – p1 / p2.

Fig.

Basic equations:MU1 / p1 = MU2 / p2 and p1 x1 + p2 x2 = m.

Figs.

( How if negative solutions.)

Interior solutions, and Boundary (Corner) solutions. Kinky tastes.

Figs.

Three approaches to

the basic equations: Graphically;As-one-variable;*Lagrangian.

The optimal choice is the consumer’s demanded bundle.

The demand function.

Examples:perfect substitutes,perfect complements,neutrals and bads,concave preferences.

Figs.

Cobb-Douglas demand functions.

* Choosing taxes.

(By *Slutsky decomposition.)

Figs.

Chapter 6Chapter 6

Demand

Demand functions:x1 = x1 (p1, p2, m),x2 = x2 (p1, p2, m).

Normal and inferior goods (by income); Fig.

Luxury and necessary goods (by income). Fig.

Ordinary and Giffen goods (by price). Fig.

The income expansion path

or the income offer curves,

and the Engel curve.

Figs.

The price offer curve

and the Demand curve.

Figs.

Substitutes and complements. Cobb-Douglas preferences. Quasilinear preferences.

* Homothetic preferences:

if (x1, x2) is preferred to (y1, y2),

then (tx1, tx2) is preferred to

(ty1, ty2) for any t > 0. Thus both the income offer

curves and the Engel curves are all rays through the origin.

Example:Quasilinear preferences

lead to

vertical (horizontal) income offer curves and

vertical (horizontal) Engel curves.

Chapter 8Chapter 8

Slutsky Equation

How the optimum moves when the price of a good changes?

Decomposition: the total effect =

the substitution effect + the income effect.

p139

The pivot gives the substitution effect,

the shift gives the income effect.

P103andp137

Slutsky identity, pivoting the budget line around the original choice.

Fig.Hicks decomposition,

pivoting the budget line around the indifference curve.

Fig.

Chapter 9 Chapter 9

Buying and Selling

for a consumer with an endowment ω

ω

x1 x1

x2 p1

ω1 ω1

Net and gross demands, net supply.

Offer curve and demand curve.p164

Labor supply p174

$

Leisure R Labor

W

Leisure

E

Chapter 10Chapter 10

Intertemporal Choice

Suppose for example in a 3-period model,

the consumption is ck and

the interest rate is rk in period k,

then the present value of the consumptions is

c1 + c2 / (1+r1) + c3 / (1+r1) (1+r2).p190

Chapter 12Chapter 12

Uncertainty

Utilities and probabilities. Utilities and probabilities. Expected utility functions, or von Neumann-Morgenstern utility functions. They are indifferent up to any positive affine transformation.(affine transformation: y = a + bx).

Risk aversion and risk loving.

Concave vs convex utility.

The second derivatives.

$ $

U U

Chapter 14Chapter 14

Consumer’s Consumer’s surplussurplus

Net Surplus

1 2 3 4 5 6

p

r1

r2

r3

r4

r5r6

Consumers’ Surplus p250

消费者得益

总收益

Producer’s surplus p259Producer’s surplus p259

Producer’s surplus

Supply curve

Q

P*

Q*

P

Q

Supply curve

Change in producer’s surplus

R T

Q’ Q’’

P

P’’

P’

The water-diamond paradoxThe water-diamond paradox

Pd

Pw

Q

Calculating gains and lossesCalculating gains and losses

Change in consumers’ surplus

B T

Chapter 15Chapter 15

Market Market DemandDemand

One can think of the One can think of the market demandmarket demand as the as the

demand of some demand of some ““representative consumerrepresentative consumer”.”.

Adding up demand curves: Adding up demand curves:

The horizontal The horizontal summation principle.summation principle.

+ =

Horizontal Horizontal summationsummation

PRICE

DEMAND CURVE

D(p)

QUANTITY

It is the sum of the individual demand curve

The market demand curve

The The price elasticity of demandprice elasticity of demand::

εε= (Δq / q ) / (Δp / p)= (Δq / q ) / (Δp / p) = ( p / q ) / (Δp /Δq), or = ( p / q ) / (Δp /Δq), or

εε= ( d q / q ) / ( d p / p)= ( d q / q ) / ( d p / p) = ( p / q ) / ( d p / d q) = ( p / q ) / ( d p / d q) = = slope of rayslope of ray / / slope of curve .slope of curve .

A good has anA good has an

elasticelastic ( ( inelasticinelastic, , unitaryunitary) ) demanddemand

if if

|ε| > 1 ( |ε| < 1 , |ε| = 1 ).|ε| > 1 ( |ε| < 1 , |ε| = 1 ).

Elasticity and revenue.Elasticity and revenue.

R = pq, ΔR = qΔp + pΔq R = pq, ΔR = qΔp + pΔq , and , and then then

ΔR/ Δp = q [ 1 +ε(p) ]ΔR/ Δp = q [ 1 +ε(p) ] where where

ε( p ) = ( pΔq ) / (qΔp)ε( p ) = ( pΔq ) / (qΔp). .

QUANTITY

PRICE

a /2

a / 2b

︱ ε ︱ =∞

︱ ε ︱ >1

︱ ε ︱ =1

︱ ε ︱ <1

︱ ε ︱ =0

The elasticity of a linear demand curveThe elasticity of a linear demand curvep = a – b q

p267

Strikes and profits.Strikes and profits. The Laffer curve.The Laffer curve.

Similarly, Similarly, MR = ΔR / Δq MR = ΔR / Δq = p (q) [ 1 + 1 /ε(q) ] = p (q) [ 1 + 1 /ε(q) ] where where ε( q ) = ( pΔq ) / (qΔp). ε( q ) = ( pΔq ) / (qΔp).

The income elasticity of demand.

The arc elasticityand

the point elasticity.

PRICE

QUANTITY

a

a/2Slope=-2b

Slope=-b

a/2b a/b

MR

Demand, AR

Marginal revenue p275

Marginal revenue for a linear demand curve.

MR = p(q)[1-1/e]

D, AR

QUANTITY

PRICE

Marginal revenue

MR for a constant elasticity demand curve

Chapter 16Chapter 16

EquilibriumEquilibrium

The market supply curve.

The competitive equilibrium.

Pareto efficiency.

Supply

Demand

QUANTITY

PRICE

P’d

Pd=Ps=P*

P’s

Willing to

buy at this price

Willing to sell at this price Q’

Pareto efficiency p301

Q*

Market supply and market shortage

P*

P’

Q* QdQs

Market shortage

equilibrium

price

quantity

supplydemand

Shortage is not scarcity.Shortage is not scarcity.

QUANTITY

PRICE

p*

q*

Demand curve

Supply curvePRICE

QUANTITYq*

p*Supply curve

Demand curve

A B

Special cases of equilibrium p291Special cases of equilibrium p291

Algebra of the equilibrium. Comparative statics. Shifting both curves. p294

Taxes. Distinguish

Pp , the price paid by consumers,

Pr , the price received by

producers, and

Po , the original price.

Supply

Demand

QUANTITY

PRICE

A

C

Pp

Pr

Q*

Amount of tax revenue:

A+C

The deadweight loss of a tax p301

The deadweight loss of the tax: B+D

B

D

Chapter 17Chapter 17

TechnologyTechnology

Inputs and outputs.Inputs and outputs.

Factors of production:Factors of production:

land, labor, capital, land, labor, capital, raw materials, raw materials, and so on.and so on.

Y = f (X ) = production function

Y = Output

X = Input

Production set

A production set p307

Examples ofExamples of technology technology

((isoquants analysisisoquants analysis): ):

Fixed proportions, Perfect substitutes, Cobb-Douglas. Figs. p308

Isoquants

x1

x2

Fixed proportion

Isoquants

x1

x2

Perfect subsitutes

Assumptions of technology: Assumptions of technology: monotonic (free disposal),monotonic (free disposal),

and convex. p310

(a1/2 + b1/2 , a2/2 + b2/2)

isoquant

x1

x2

a2

b2

a1 b1

The The marginal productmarginal product, ,

MPMPii = d y / d x = d y / d x

i i . Y is output. Y is output

The The technical rate of technical rate of substitution (substitution (TRSTRS):):

With d y = 0 along any isoquant,

TRS (x1, x2 ) = d x2 / d x1

= – MP1 (x1, x2) / MP2 (x1, x2 ).

TheThe long runlong run (LR) (LR) andand

the the short run short run (SR)(SR)

Returns to scale:Returns to scale: Increasing, decreasing, and Increasing, decreasing, and

constantconstant: : >>

f ( t x ) < t f ( x )f ( t x ) < t f ( x )==

Chapter 18Chapter 18

Profit Profit MaximizationMaximization

The organization of The organization of firms:firms:

Proprietorships, partnerships, corporations.

SR profit maximizationSR profit maximization

π= py - w1x1 - w2x2

y = π/ p + w2x2 / p + w1x1 / p

describes isoprofit lines, max x1π gives pMP1 = w1.

Fig. p323

Isoprofit lines slope = w1/p

y = f (x1, x2)

Production function

x1x1*

Output

y*

π/p+w2x2/p

Profit maximization

OptimumOptimum lies on the lies on the

tangencytangency of an isoprofit line of an isoprofit line and the production function. and the production function.

P324 Comparative P324 Comparative statics:statics:

Increasing p increases x1 and then y.

Increasing w1 reduces x1,

and thus the factor demand curve follows.

LR: both x1 and x2 are variable.

Figs.

A x1

f(x1)

High w1 Low w1

B x1

f(x1)

Comparative statics

Low pHigh p

要素价格 产品价格

Chapter 19Chapter 19Cost

Minimization

Basic modelBasic model: :

min x1, x2 w1 x1 + w2 x2 subject to f (x1 , x2 ) = ygives c ( w1 , w2 , y )

Isocost lines: p337

x2 = C/w2 – w1x1/w2.

Tangency of an isocost line and an isoquant.

– MP1 (x1, x2) / MP2 (x1, x2 )= TRS(x1, x2 ) = – w 1 / w 2

Isocost lines slope= – w 1 / w 2

Isoquant f (x1 , x2 ) = y

Optimal choice

x2*

x2

x1* x1

.

Minimizing costs for

y = min{ax1 , bx2}; 完全互补 y = ax1 + bx2; 完全替代 and y = x1

a x2b. Cobb-

Fixed and variable costs.

(FC and VC)

Total, average, marginal, and average variable costs. (TC, AC, MC and AVC)

MC > (<) AC if and only if AC is increasing (decreasing)

MC cuts AC (AVC) at AC’s (AVC’s) extreme.

MC

AVC

AC

y

ACAVCMC

..

Chapter 20Chapter 20

Cost

Curves

The area under MC

gives VC:

∫MC = VC

MC

Variable costs

MC

y

Division of output Division of output among plants of a firm.among plants of a firm.

MC1

MC2

Typical cost Typical cost curves. curves.

c (y) = y 2 + 1.

Example:

AC MCAVC

y

MC

AVC

AC

The cost curves for c (y) = y 2 + 1

. 2

1

LR and SR cost curves.

y

AC SAC=C(y1, k* )/y

LAC=C(y)/y

. y*

Short-run and long-run average costs

y

AC Short-run average cost curves

Long-run average

cost curves y*

Short-run and long-run average costs

are costs that are not recoverable.

A special kink of fixed costs.

Sunk costs

Chapter 21Chapter 21

Firm Supply

Pure Pure competitioncompetition. .

Price Taker..

The demand curve facing a competitive firm. p368

Q

P

P*

Market price

Demand curve facing firm

Market demand

The supply decision:The supply decision:

FOC: MC ( y* ) = p.

SOC: MC ’ ( y* ) ≥ 0.

The The firm’s supply curvefirm’s supply curve is is the upward-sloping part of MCthe upward-sloping part of MC that lies above the AVC curve. that lies above the AVC curve.

The part of MC is also seen as the inverse supply function.

MC

AVC

AC

y

ACAVCMC

P

y2 y1

firm’s supply curve

Three Three equivalent waysequivalent ways to to measure the producer’s surplus measure the producer’s surplus

( = R – VC =π + FC ).( = R – VC =π + FC ). p375p375

P377 Example:

c ( y ) = y 2 + 1.

LR: p = MC ( y, k ( y ) )LR: p = MC ( y, k ( y ) )

vs

SR: p = MC ( y, k )

Chapter 22Chapter 22

Industry Supply

Horizontal summation Horizontal summation gives gives

the industry supply.

Y

P S1 S2 S1 + S2

Entry and Entry and exit. exit.

The The “zero profit” “zero profit” theorem theorem..

Free entryFree entry vs vs

barriers to entry. barriers to entry.

Economists Economists versus versus lobbyistslobbyists

Rent seeking.Rent seeking.

Chapter 23Chapter 23

The coincidence of the inverse demand curve D and the average revenue curve AR.

Fig.

With

MR = d R / d y = p (y ) [ 1 + 1 /ε(y) ],

p ( y ) = MC ( y ) / [1 – 1 / |ε( y ) | ].

Two equivalent ways to determine the equilibrium:

MC = MR, or AR = MC / ( 1– |ε| ). Figs. FOC: MC = MR. SOC: MC ’ ≥ MR ’.

The impact of taxes on a monopoly. p411

Inefficiency of monopoly. Fig. p412

Deadweight loss of monopoly. Fig,

Inefficiency of monopolyInefficiency of monopoly

Mc

MRDemand, AR

Price

pm

pc

ym yc output

Deadweight lost

Deadweight lossDeadweight loss of of monopolymonopoly

AB

C

PRICE

MonopolyPrice P*

Competitiveprice

MC

Demand, AR

MR

Y*

output

垄断收益

Natural monopoly.

Figs. p417

What causes monopolies: by nature or by permission.

The minimum efficient scale factor.

Regulation of monopoly: AC = AR.

Chapter 24Chapter 24

Price discriminations of first-degree (perfect), of second-degree (bulk discounts), andPrice discrimination of third-degree (market segmentation): Figs.

MC(y1+y2) = MR1(y1) = MR2 (y2)

gives p1 [ 1 – 1 / |ε1 ( y1 )| ]

= p2 [ 1 – 1 / |ε2 ( y2 )| ].

Fig!Fig!

Chapter 26Chapter 26

Oligopoly,

mainly Duopoly

Quantity or price competitions.

Sequential games.

Backward solution.

Identical products:

p = p (Y ), Y = y1 + y2 .

Quantity leadership:

– Stackelberg model.

gives the follower’s reaction function

y2 = f 2 (y1) ;then

max y1 p (y1+ f2 (y1 )) y1 – c1 ( y1 )

determines y1.

dp / dy2 = MC2 MR2 = p (y1+y2) + y2

Example:p ( y1 + y2) = a – b ( y1 + y2) ,

c = 0.

The leader is supposed to set p first, then max

Price leadership:

y2 py2 – c2 (y2)

S2(p).gives

R(p) = D(p) - S2(p).

Now, the leader goes as a monopolist facing the residual demand

Example:

D(p) = a – bp,

c2 ( y2 ) = y22 / 2,

c1 ( y1 ) = c y1.

Simultaneous games. Bertrand price competition

leads to p = MC even only two firms.

Thus only quantity setting consideration.

Cournot model of quantity competition:

max yi p( yi + yje) yi – ci ( yi ),

where yje is the output of Firm j

expected by Firm i,

gives yi = fi (yje),

then the consistence determines the equilibrium.

Adjustment to an equilibrium.

where si = yi / Y.

p (Y) [1 – si / |ε(Y)| ] = MCi(yi)

Y = y1 + … + yn ,

Several firms in Cournot equilibrium:

Chapter 27Chapter 27Game Theory

Three fundamental elements to describe a game:

Players, (pure) strategies or actions, payoffs.

B b r

bA r

1, -1 -1, 1

-1, 1 1, -1

Color MatchingColor Matching

Payoff matrices for Two-person games.

Simultaneous(-move) games.

Finite games: Both the numbers of players and of alternative pure strategies are finite

B Confess Deny

Confess

A Deny

-3*, -3* 0, -5

-5, 0 -1, -1

The Prisoner’s DilemmaThe Prisoner’s Dilemma

Dominant strategies, and dominated strategies.

Method of iterated elimination of strictly dominated strategies.

The Prisoner’s Dilemma

shows also that a Nash equilibrium does not necessarily lead to a Pareto efficient outcome.

Two-win games.

A pair of strategies is a

Nash equilibrium if A’s choice

is optimal given B’s choice,

and vice versa. Nash is a situation,

or a strategy combination of

no incentive to deviate unilaterally.

Girl Soccer Ballet

Soccer

Boy Ballet

2*, 1* 0, 0

-1, -1 1*, 2*

Battle of SexesBattle of Sexes

Method of underlining relatively advantageous strategies.

Double underlining gives Nash.

There can be no, one, and

multiple (pure) Nash equilibria.

Pepsi L H

L

Coke H

3*, 3* 6, 1

1, 6 5, 5

Price StrugglePrice Struggle

How if there is no Nash of pure strategies?

Mixed strategies (by probability).

Method of response functions.

B b r q 1-q

b pA r 1-p

1, -1 -1, 1

-1, 1 1, -1

Color Matching againColor Matching again

With

EUA = 1 pq + (-1)p (1-q) + (-1) (1-p) q + 1 (1-p) (1-q) = pq - p + pq - q + pq + 1 - p - q + pq = 4 pq - 2 p - 2 q + 1 = 2 p (2 q - 1) + (1 - 2 q ) , we have 1 if q > 1/2 ,p = [0, 1] if q = 1/2 , 0 if q < 1/2 .

Similarly, 0 if p > 1/2 ,q = [0, 1] if p = 1/2 , 1 if p < 1/2 .

q1

1 p

N

0

Method of response functions: The intersections of response functions give Nash equilibria

((p*, q*) = (1/2, 1/2) in example)Nash Theorem:

There is always a ( maybe “mixed”) Nash equilibrium for any finite game

Sequential games.

Games in extensive form

versus

in normal form.

Battle of Sexes again

Boy

Girl

Ballet

Ballet

Ballet

Soccer

Soccer

Soccer

( 1, 2)

( -1, -1)

( 0, 0)

( 2, 1)

Strategies as Plans of Actions.

Boy’s strategies: Ballet, and Soccer.Girl’s Strategies: Ballet strategy; Soccer strategy; Strategy to follow; and Strategy to oppose.

Chapter 28Chapter 28ExchangeExchange

Partial equilibrium Partial equilibrium and and

general equilibriumgeneral equilibrium

Edgeworth box p497Edgeworth box p497

A pure exchange model of two goods, two consumers with fixed endowments w.

Region of mutual advantages. Pareto set and the contract curve. Bargaining for relative prices. Gross demand x (p) , Net or excess demand

z (p) = x (p) - w (p).

Person B

Person A xA1 wA

1

Endowment

wA2

xA2

GOOD 2

GOOD 1

xB1 wB

1

xB2

wB2

M

Endowment

Person B’s indifference curve

A Pareto efficient allocation

Person A’s indifference curve

Contract curve

Person A GOOD 1

GOOD 2 Person B

From disequilibrium to the competitive equilibrium.

Which good is too cheap?

Offer curve approach. The existence problem of

equilibrium.

A’s ind, curves

B’s ind. curves

A’s offer curve

B’s offer curve

Good 1 is Too cheap

Equilibrium price

W

E

Chapter 29Chapter 29ProductionProduction

The Robinson Crusoe economyThe Robinson Crusoe economy

Production function

Indifference curves

LaborL*

C*

Coconuts

Production possibilities set

F*

C*

COCNUTS

FISH

PRODUCTION POSSIBILITIES SET

SLOPE=MARGINAL RATE OF TRANSFORMATION

(Two outputs case)(Two outputs case)

Trade leads toTrade leads toSeparation of prod. and coms. (P/C),Separation of prod. and coms. (P/C),Production specialization(A P), andProduction specialization(A P), and

Wealth improvement( A C)Wealth improvement( A C)..

AP C

Heckscher-Ohlin theoryHeckscher-Ohlin theory on on international trade,international trade,

under many idealization assumptions.under many idealization assumptions.

* Costs of exchange. * Price difference between

selling and buying.

Fig.

* GATT and WTO.

Chapter 30Chapter 30WelfareWelfare

The social preference. The social preference.

Two kinds of voting: Two kinds of voting: majority, majority,

andand rank-order. rank-order.

The social welfare The social welfare function.function.

Benthamite:

W (u1, … ,u n ) = a 1u 1 + … + a n u n .

Rawlsian:

W (u1, … ,u n ) = min {u1 , … , u n }.

Three requirements on a social Three requirements on a social decision mechanism:decision mechanism:

1, It should be complete, reflexive, and transitive;

2, If everyone prefers X to Y, then the society should prefer X to Y;

3, The preferences between X and Y should depend only on how people rank X versus Y, and not on how they rank other alternatives.

Arrow's Impossibility TheoremArrow's Impossibility Theorem

If a social decision mechanism satisfies properties 1, 2, and 3,

then it must be a dictatorship:

all social rankings are the rankings of one individual.

Chapter 31Chapter 31

Externalities

The lack of markets for externalities

causes problems.

With externalities,the market will not

necessarily result in a Pareto efficient provision of

resources.

However, some other social institutions can

"mimic"

the market mechanism.

The model of

smokers and nonsmokers

(showing excellent analysis

techniques).

Person A

Person BSMOKE

MONEY

A’s indifference curves

Possible equilibrium X

Possible

endowment E

Possible

endowment E’

Possible equilibrium

X’

Bad

Good

The practical problems with externalities generally arise because of poorly defined

property rights.

Caose Theorem

ChapterChapter 35 35 Asymmetric Information

Common knowledge and

private information.

The latter leads to

Asymmetric information, or

Asymmetry of information.

Quality

Density

Akerlof model: the market for lemons.

Adverse selection as a hidden information problem.

Moral hazard

as a hidden action problem.

Signaling

Two roles of education:To raise and to distinguish

Productivities

Spence model

$ C(Y) for L

wage system

C(Y) for H

Y* Y

Best Choice of L, and of H

Graph to show separating equilibria

and pooling equilibria.

ENDand

Thanks