microeconomics classroom lecture notes (3 credits, as of 2005)
TRANSCRIPT
MICROECONOMICS
Classroom Lecture Notes
(3 credits, as of 2005)
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 p246
消费者得益
总收益
Producer’s surplus p255Producer’s surplus p255
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 p286Special cases of equilibrium p286
Algebra of the equilibrium. Comparative statics. Shifting both curves. p289
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 p296
The deadweight loss of the tax: B+D
B
D
Chapter 18Chapter 18
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 p321
Examples ofExamples of technology technology
((isoquants analysisisoquants analysis): ):
Fixed proportions, Perfect substitutes, Cobb-Douglas. Figs. p322
Isoquants
x1
x2
Fixed proportion
Isoquants
x1
x2
Perfect subsitutes
Assumptions of technology: Assumptions of technology: monotonic (free disposal),monotonic (free disposal),
and convex. p324
(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 19Chapter 19
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. p337
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 20Chapter 20Cost
Minimization
Basic modelBasic model: :
min x1, x2 w1 x1 + w2 x2 subject to f (x1 , x2 ) = ygives c ( w1 , w2 , y )
Isocost lines: p351
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-
Douglas
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 21Chapter 21
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 kind of fixed costs.
Sunk costs
Chapter 22Chapter 22
Firm Supply
Pure Pure competitioncompetition. .
Price Taker..
The demand curve facing a competitive firm. p380
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 ). p389p389
P389 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 23Chapter 23
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 24Chapter 24
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. p425
Inefficiency of monopoly. Fig. p426
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 25Chapter 25
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 28Chapter 28
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 28Chapter 28Game 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 29Chapter 29ExchangeExchange
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