microeconomics classroom lecture notes (3 credits, as of 2005)
TRANSCRIPT
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MICROECONOMICS
Classroom Lecture Notes
(3 credits, as of 2005)
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based on Hal R. Varian’s Intermediate Microeconomics,
Sixth Edition, referring to Pindyck and Rubinfeld’s
Microeconomics,
Fourth Edition.
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Chapter 0Chapter 0
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The source of all economic problems is scarcity.
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Problem of trade-off, and choice.
Economics, as a way of thinking, as a dismal science.
Problems - solutions - hidden consequences.
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Main Main decision-making agentsdecision-making agents: :
1 individuals (household), 2 firms, and 3 governments.
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Objects of economic choice are
commoditiescommodities,,including
goods and services.
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Main economic activities:Main economic activities:
Consumption, Production, and Exchange.
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MicroMicroeconomics and economics and macromacroeconomicseconomics::
to show the market mechanism (the invisible hand),
to supplement it.
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The circular flow of economic The circular flow of economic activities. activities.
product market factor market
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The The product marketproduct market and and the the factor marketfactor market. .
The market relation is mutual and voluntary.
Positive issues and normative issues.
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Marginal analysisMarginal analysisRelations between Total magnitudes, Average magnitudes, and Marginal magnitudes.
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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
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3, TM increasing (decreasing)
if and only if
MM > 0 ( MM < 0 );
4, If TM is at maximum or minimum,
then MM = 0;
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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.
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Chapter 1Chapter 1
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Economics proceeds by developing Models of social phenomena.
By a model we mean a simplified representation of reality.
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Exogenous variables: taken as determined by factors
not discussed in a model.
Endogenous variables: determined by forces described
in the model.
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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.
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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.
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From people's reservation prices to the demand curve.
Similarly, the supply curve.
Fig.
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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.
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An economic situation is Pareto efficient or Pareto optimal if there is already no way to make any
more Pareto improvement.
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Short run and long runShort run and long run
Equilibria in the short run (some factors are unchanged)
and in the long run.
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Chapter 2Chapter 2
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* 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.
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The budget constraint:
p1 x1 + p2 x2 ≤ m.
The budget line and the budget set (the market opportunity set).
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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.
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x2
x1
Budget set
Budget lineSlope = -p1/p2
m/p2
m/p1
Budget lineBudget line and and budget setbudget set
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x2
x1
Budget line
Slope = - p1/p2
m’/p2
m/p2
m/p1 m’/p1
Increasing incomeIncreasing income
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Slope
= - p’1/p2
m/p2 Budget line
Slope = - p1/p2
m/p’1 m/p1
Increasing priceIncreasing price
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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.
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Chapter 3Chapter 3
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* 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.
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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.)
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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.
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The indifference sets, the indifference curves.
They cannot cross each other.
Fig.
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indifference curvesindifference curvesx2
x1
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Perfect substitutes and perfect complements. Goods, bads, and neutrals. Satiation. Figs
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Blue pencils
Red pencils
Indifference curves
Perfect Perfect substitutessubstitutes
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Perfect Perfect complementscomplements
Indifference curves
Left shoes
Right shoes
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Well-behaved preferences are monotonic (meaning more is better) and
convex (meaning average are preferred to extremes).
Figs
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x2
x1
Betterbundles(x1, x2)
MonotonicityMonotonicity
Betterbundles
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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
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Convex indifference curves exhibit a diminishing marginal rate of substitution.
Fig.
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x2
x1
ConvexityConvexity
Averagedbundle
(y1,y2)
(x1,x2)
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Chapter 4Chapter 4
(as a way to describe preferences)
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UtilitiesUtilities
Essential ordinal utilities,versus
convenient cardinal utility functions.
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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.
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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.
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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).
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Quasilinear preferences: All indifference curves are vertically (or
horizontally) shifted copies of a single one, for example u (x1, x2) = v (x1) + x2 .
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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
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Cobb-DouglasCobb-Douglas
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MRS along an indifference curve.Derive MRS = – MU1 / MU2
by taking total differential along any indifference curve.
Marginal utilities
MU1 and MU2.
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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.
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500490
480 The demand curve
ReservationReservation priceprice
Number of apartment
From peoples’ reservation prices to the market demand curve.
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supply
Demand
PP
Q
EquilibriumEquilibrium
P*P*
Q*
E (P*,Q*)
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supply
Demand
pp
q
E
EquilibriumEquilibrium
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x2
x1
Budget lineBudget set
RationingRationing
R*
Marketopportunity
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MRSMRS
Indifferencecurve
Slope = dx2/dx1
x2
x1
dx2dx1
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Chapter 5Chapter 5
Choice of consumption
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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.
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Basic equations:MU1 / p1 = MU2 / p2 and p1 x1 + p2 x2 = m.
Figs.
( How if negative solutions.)
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Interior solutions, and Boundary (Corner) solutions. Kinky tastes.
Figs.
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Three approaches to
the basic equations: Graphically;As-one-variable;*Lagrangian.
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The optimal choice is the consumer’s demanded bundle.
The demand function.
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Examples:perfect substitutes,perfect complements,neutrals and bads,concave preferences.
Figs.
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Cobb-Douglas demand functions.
* Choosing taxes.
(By *Slutsky decomposition.)
Figs.
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Chapter 6Chapter 6
Demand
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Demand functions:x1 = x1 (p1, p2, m),x2 = x2 (p1, p2, m).
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Normal and inferior goods (by income); Fig.
Luxury and necessary goods (by income). Fig.
Ordinary and Giffen goods (by price). Fig.
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The income expansion path
or the income offer curves,
and the Engel curve.
Figs.
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The price offer curve
and the Demand curve.
Figs.
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Substitutes and complements. Cobb-Douglas preferences. Quasilinear preferences.
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* 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.
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Example:Quasilinear preferences
lead to
vertical (horizontal) income offer curves and
vertical (horizontal) Engel curves.
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Chapter 8Chapter 8
Slutsky Equation
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How the optimum moves when the price of a good changes?
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Decomposition: the total effect =
the substitution effect + the income effect.
p139
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The pivot gives the substitution effect,
the shift gives the income effect.
P103andp137
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Slutsky identity, pivoting the budget line around the original choice.
Fig.Hicks decomposition,
pivoting the budget line around the indifference curve.
Fig.
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Chapter 9 Chapter 9
Buying and Selling
for a consumer with an endowment ω
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ω
x1 x1
x2 p1
ω1 ω1
Net and gross demands, net supply.
Offer curve and demand curve.p164
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Labor supply p174
$
Leisure R Labor
W
Leisure
E
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Chapter 10Chapter 10
Intertemporal Choice
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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
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Chapter 12Chapter 12
Uncertainty
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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).
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Risk aversion and risk loving.
Concave vs convex utility.
The second derivatives.
$ $
U U
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Chapter 14Chapter 14
Consumer’s Consumer’s surplussurplus
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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
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Producer’s surplus p255Producer’s surplus p255
Producer’s surplus
Supply curve
Q
P*
Q*
P
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Q
Supply curve
Change in producer’s surplus
R T
Q’ Q’’
P
P’’
P’
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The water-diamond paradoxThe water-diamond paradox
Pd
Pw
Q
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Calculating gains and lossesCalculating gains and losses
Change in consumers’ surplus
B T
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Chapter 15Chapter 15
Market Market DemandDemand
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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”.”.
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Adding up demand curves: Adding up demand curves:
The horizontal The horizontal summation principle.summation principle.
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+ =
Horizontal Horizontal summationsummation
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PRICE
DEMAND CURVE
D(p)
QUANTITY
It is the sum of the individual demand curve
The market demand curve
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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 .
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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 ).
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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). .
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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
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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).
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The income elasticity of demand.
The arc elasticityand
the point elasticity.
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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.
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MR = p(q)[1-1/e]
D, AR
QUANTITY
PRICE
Marginal revenue
MR for a constant elasticity demand curve
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Chapter 16Chapter 16
EquilibriumEquilibrium
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The market supply curve.
The competitive equilibrium.
Pareto efficiency.
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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*
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Market supply and market shortage
P*
P’
Q* QdQs
Market shortage
equilibrium
price
quantity
supplydemand
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Shortage is not scarcity.Shortage is not scarcity.
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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
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Algebra of the equilibrium. Comparative statics. Shifting both curves. p289
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Taxes. Distinguish
Pp , the price paid by consumers,
Pr , the price received by
producers, and
Po , the original price.
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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
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Chapter 18Chapter 18
TechnologyTechnology
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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.
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Y = f (X ) = production function
Y = Output
X = Input
Production set
A production set p321
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Examples ofExamples of technology technology
((isoquants analysisisoquants analysis): ):
Fixed proportions, Perfect substitutes, Cobb-Douglas. Figs. p322
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Isoquants
x1
x2
Fixed proportion
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Isoquants
x1
x2
Perfect subsitutes
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Assumptions of technology: Assumptions of technology: monotonic (free disposal),monotonic (free disposal),
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and convex. p324
(a1/2 + b1/2 , a2/2 + b2/2)
isoquant
x1
x2
a2
b2
a1 b1
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The The marginal productmarginal product, ,
MPMPii = d y / d x = d y / d x
i i . Y is output. Y is output
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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 ).
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TheThe long runlong run (LR) (LR) andand
the the short run short run (SR)(SR)
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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 )==
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Chapter 19Chapter 19
Profit Profit MaximizationMaximization
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The organization of The organization of firms:firms:
Proprietorships, partnerships, corporations.
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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
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Isoprofit lines slope = w1/p
y = f (x1, x2)
Production function
x1x1*
Output
y*
π/p+w2x2/p
Profit maximization
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OptimumOptimum lies on the lies on the
tangencytangency of an isoprofit line of an isoprofit line and the production function. and the production function.
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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.
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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
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Chapter 20Chapter 20Cost
Minimization
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Basic modelBasic model: :
min x1, x2 w1 x1 + w2 x2 subject to f (x1 , x2 ) = ygives c ( w1 , w2 , y )
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Isocost lines: p351
x2 = C/w2 – w1x1/w2.
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Tangency of an isocost line and an isoquant.
– MP1 (x1, x2) / MP2 (x1, x2 )= TRS(x1, x2 ) = – w 1 / w 2
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Isocost lines slope= – w 1 / w 2
Isoquant f (x1 , x2 ) = y
Optimal choice
x2*
x2
x1* x1
.
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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
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Fixed and variable costs.
(FC and VC)
Total, average, marginal, and average variable costs. (TC, AC, MC and AVC)
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MC > (<) AC if and only if AC is increasing (decreasing)
MC cuts AC (AVC) at AC’s (AVC’s) extreme.
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MC
AVC
AC
y
ACAVCMC
..
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Chapter 21Chapter 21
Cost
Curves
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The area under MC
gives VC:
∫MC = VC
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MC
Variable costs
MC
y
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Division of output Division of output among plants of a firm.among plants of a firm.
MC1
MC2
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Typical cost Typical cost curves. curves.
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c (y) = y 2 + 1.
Example:
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AC MCAVC
y
MC
AVC
AC
The cost curves for c (y) = y 2 + 1
. 2
1
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LR and SR cost curves.
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y
AC SAC=C(y1, k* )/y
LAC=C(y)/y
. y*
Short-run and long-run average costs
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y
AC Short-run average cost curves
Long-run average
cost curves y*
Short-run and long-run average costs
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are costs that are not recoverable.
A special kind of fixed costs.
Sunk costs
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Chapter 22Chapter 22
Firm Supply
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Pure Pure competitioncompetition. .
Price Taker..
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The demand curve facing a competitive firm. p380
Q
P
P*
Market price
Demand curve facing firm
Market demand
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The supply decision:The supply decision:
FOC: MC ( y* ) = p.
SOC: MC ’ ( y* ) ≥ 0.
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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.
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MC
AVC
AC
y
ACAVCMC
P
y2 y1
firm’s supply curve
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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
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P389 Example:
c ( y ) = y 2 + 1.
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LR: p = MC ( y, k ( y ) )LR: p = MC ( y, k ( y ) )
vs
SR: p = MC ( y, k )
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Chapter 23Chapter 23
Industry Supply
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Horizontal summation Horizontal summation gives gives
the industry supply.
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Y
P S1 S2 S1 + S2
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Entry and Entry and exit. exit.
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The The “zero profit” “zero profit” theorem theorem..
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Free entryFree entry vs vs
barriers to entry. barriers to entry.
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Economists Economists versus versus lobbyistslobbyists
Rent seeking.Rent seeking.
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Chapter 24Chapter 24
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The coincidence of the inverse demand curve D and the average revenue curve AR.
Fig.
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With
MR = d R / d y = p (y ) [ 1 + 1 /ε(y) ],
p ( y ) = MC ( y ) / [1 – 1 / |ε( y ) | ].
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Two equivalent ways to determine the equilibrium:
MC = MR, or AR = MC / ( 1– |ε| ). Figs. FOC: MC = MR. SOC: MC ’ ≥ MR ’.
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The impact of taxes on a monopoly. p425
Inefficiency of monopoly. Fig. p426
Deadweight loss of monopoly. Fig,
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Inefficiency of monopolyInefficiency of monopoly
Mc
MRDemand, AR
Price
pm
pc
ym yc output
Deadweight lost
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Deadweight lossDeadweight loss of of monopolymonopoly
AB
C
PRICE
MonopolyPrice P*
Competitiveprice
MC
Demand, AR
MR
Y*
output
垄断收益
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Natural monopoly.
Figs. p417
What causes monopolies: by nature or by permission.
The minimum efficient scale factor.
Regulation of monopoly: AC = AR.
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Chapter 25Chapter 25
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Price discriminations of first-degree (perfect), of second-degree (bulk discounts), andPrice discrimination of third-degree (market segmentation): Figs.
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MC(y1+y2) = MR1(y1) = MR2 (y2)
gives p1 [ 1 – 1 / |ε1 ( y1 )| ]
= p2 [ 1 – 1 / |ε2 ( y2 )| ].
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Fig!Fig!
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Chapter 28Chapter 28
Oligopoly,
mainly Duopoly
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Quantity or price competitions.
Sequential games.
Backward solution.
Identical products:
p = p (Y ), Y = y1 + y2 .
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Quantity leadership:
– Stackelberg model.
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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
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Example:p ( y1 + y2) = a – b ( y1 + y2) ,
c = 0.
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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
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Example:
D(p) = a – bp,
c2 ( y2 ) = y22 / 2,
c1 ( y1 ) = c y1.
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Simultaneous games. Bertrand price competition
leads to p = MC even only two firms.
Thus only quantity setting consideration.
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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.
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Adjustment to an equilibrium.
where si = yi / Y.
p (Y) [1 – si / |ε(Y)| ] = MCi(yi)
Y = y1 + … + yn ,
Several firms in Cournot equilibrium:
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Chapter 28Chapter 28Game Theory
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Three fundamental elements to describe a game:
Players, (pure) strategies or actions, payoffs.
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B b r
bA r
1, -1 -1, 1
-1, 1 1, -1
Color MatchingColor Matching
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Payoff matrices for Two-person games.
Simultaneous(-move) games.
Finite games: Both the numbers of players and of alternative pure strategies are finite
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B Confess Deny
Confess
A Deny
-3*, -3* 0, -5
-5, 0 -1, -1
The Prisoner’s DilemmaThe Prisoner’s Dilemma
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Dominant strategies, and dominated strategies.
Method of iterated elimination of strictly dominated strategies.
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The Prisoner’s Dilemma
shows also that a Nash equilibrium does not necessarily lead to a Pareto efficient outcome.
Two-win games.
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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.
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Girl Soccer Ballet
Soccer
Boy Ballet
2*, 1* 0, 0
-1, -1 1*, 2*
Battle of SexesBattle of Sexes
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Method of underlining relatively advantageous strategies.
Double underlining gives Nash.
There can be no, one, and
multiple (pure) Nash equilibria.
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Pepsi L H
L
Coke H
3*, 3* 6, 1
1, 6 5, 5
Price StrugglePrice Struggle
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How if there is no Nash of pure strategies?
Mixed strategies (by probability).
Method of response functions.
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B b r q 1-q
b pA r 1-p
1, -1 -1, 1
-1, 1 1, -1
Color Matching againColor Matching again
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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 .
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Similarly, 0 if p > 1/2 ,q = [0, 1] if p = 1/2 , 1 if p < 1/2 .
q1
1 p
N
0
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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
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Sequential games.
Games in extensive form
versus
in normal form.
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Battle of Sexes again
Boy
Girl
Ballet
Ballet
Ballet
Soccer
Soccer
Soccer
( 1, 2)
( -1, -1)
( 0, 0)
( 2, 1)
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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.
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Chapter 29Chapter 29ExchangeExchange
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Partial equilibrium Partial equilibrium and and
general equilibriumgeneral equilibrium
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Edgeworth box p497Edgeworth box p497
A pure exchange model of two goods, two consumers with fixed endowments w.
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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).
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Person B
Person A xA1 wA
1
Endowment
wA2
xA2
GOOD 2
GOOD 1
xB1 wB
1
xB2
wB2
M
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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
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From disequilibrium to the competitive equilibrium.
Which good is too cheap?
Offer curve approach. The existence problem of
equilibrium.
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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
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Chapter 29Chapter 29ProductionProduction
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The Robinson Crusoe economyThe Robinson Crusoe economy
Production function
Indifference curves
LaborL*
C*
Coconuts
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Production possibilities set
F*
C*
COCNUTS
FISH
PRODUCTION POSSIBILITIES SET
SLOPE=MARGINAL RATE OF TRANSFORMATION
(Two outputs case)(Two outputs case)
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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
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Heckscher-Ohlin theoryHeckscher-Ohlin theory on on international trade,international trade,
under many idealization assumptions.under many idealization assumptions.
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* Costs of exchange. * Price difference between
selling and buying.
Fig.
* GATT and WTO.
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Chapter 30Chapter 30WelfareWelfare
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The social preference. The social preference.
Two kinds of voting: Two kinds of voting: majority, majority,
andand rank-order. rank-order.
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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 }.
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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.
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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.
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Chapter 31Chapter 31
Externalities
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The lack of markets for externalities
causes problems.
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With externalities,the market will not
necessarily result in a Pareto efficient provision of
resources.
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However, some other social institutions can
"mimic"
the market mechanism.
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The model of
smokers and nonsmokers
(showing excellent analysis
techniques).
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Person A
Person BSMOKE
MONEY
A’s indifference curves
Possible equilibrium X
Possible
endowment E
Possible
endowment E’
Possible equilibrium
X’
Bad
Good
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The practical problems with externalities generally arise because of poorly defined
property rights.
Caose Theorem
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ChapterChapter 35 35 Asymmetric Information
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Common knowledge and
private information.
The latter leads to
Asymmetric information, or
Asymmetry of information.
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Quality
Density
Akerlof model: the market for lemons.
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Adverse selection as a hidden information problem.
Moral hazard
as a hidden action problem.
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Signaling
Two roles of education:To raise and to distinguish
Productivities
Spence model
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$ C(Y) for L
wage system
C(Y) for H
Y* Y
Best Choice of L, and of H
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Graph to show separating equilibria
and pooling equilibria.
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ENDand
Thanks