General Equilibrium (Welfare Economics) ( )

General EquilibriumGeneral Equilibrium(Welfare Economics)( )

General EquilibriumGeneral Equilibrium

Partial Equilibrium: Neglects the way in which changes in one marketin which changes in one market affect other (product/factor) markets.G l E ilib i A l h General Equilibrium: Analyses the way in which the choices of yeconomic agents are co-ordinated across all product and factoracross all product and factor markets.

AgendaAgenda Exchange Economy Exchange Economy

– 2 individuals/consumers (A and B)2 products (X and Y)– 2 products (X and Y)

Production Economy2 products (X and Y)– 2 products (X and Y)

– 2 factors (L and K) General Equilibrium General Equilibrium

– 2 individuals/consumers (A and B)2 products (X and Y)– 2 products (X and Y)

– 2 factors (L and K)

Exchange EconomyExchange Economy

2 Individuals: A and B

2 Products:A i i

YX and Assume a world with no production and with fixed endowments of X and Y (hence h li f X d Y)the line on top of X and Y).

Edgeworth BoxEdgeworth Box

1. Look at the world from Individual A’s perspectiveA s perspective

2. Look at the world from Individual B’ iB’s perspective

3. Combine A and B’s worlds to form3. Combine A and B s worlds to form an Edgeworth box

Edgeworth Box

Total

Yamount of

YAU

A1U

2U

XTotal

Individual A

Xamount of

Edgeworth BoxXTotal

amount ofI di id l

B1UBU

Individual B

Total amount of

B2U

Y

Individual A

Edgeworth BoxXTotal

amount ofI di id lIndividual

B

Total amount of

Y

Individual A Each point within the box represents a particular p p p

allocation of the two products between the two individuals

Pareto Efficient AllocationPareto Efficient Allocation

Pareto Efficient Allocation: Each individual is on the highest possibleindividual is on the highest possible indifference curve, given the indifference curve of the otherindifference curve of the other individual.


I di id l

Total

Individual B

Yamount of

YYBYB

Individual A

X Total XA X amount ofA

Pareto Inefficient AllocationPareto Inefficient Allocation

and are Pareto inefficient allocationsallocations.

Why? Because there exists changes i ll i i fin allocations, starting from or that would make at least one individual better off without making the other individual worse off.the other individual worse off.


I di id l

Total

Individual B

Yamount of is a

pareto Y pefficient point p

Individual A

X Total X amount of

Pareto Efficient AllocationPareto Efficient Allocation

• At point/allocation • Individual A is on the higher possible• Individual A is on the higher possible

indifference curve given B’s indifference curve andcu e a d

• Individual B is on the highest possible indifference curve given A’s indifferenceindifference curve given A s indifference curve.Th f i t ffi i t ll ti• Therefore, is a pareto efficient allocation

• Note: The two indifference curves are tangential to each other

Pareto Efficient AllocationsPareto Efficient Allocations

I di id l

Total

Individual B

Yamount of

and are also

Y also Pareto efficient efficient allocations

Individual A

X Total X amount of

Contract CurveContract Curve

I di id l

Total

Individual B

Yamount of Joining

up these

Y p

Pareto efficient

points yields the

Individual A

X Total

ycontract curveX amount of

Contract CurveContract Curve

The curve connecting all Pareto efficient allocations is known as theefficient allocations is known as the contract curve.A h i h At each point on the contract curve, the MRS’s for A and B are equal, i.e.

MRSAxy = MRSB

xy

Market PlaceMarket Place

A “ ti ” dj t thAn “auctioneer” adjusts the product prices (Px and Py) until ythe following three conditions hold:

XA

PPMRS XB

PPMRS

o d

(1) (2)YP YP

(3) Xfor XDemand(3)YX

Yfor Demand for XDemand

Market Place: Exchange E E ilib iEconomy Equilibrium

I di id l

Total

Individual BUA

Yamount of

Y UBXP

YP

Individual A

X Total X amount of

Exchange Edgeworth Box: SSummary

I di id lXB

Total

Individual B

XB

Yamount of

YY YBYA

YB

XPIndividual

AX Total XA

YP

X amount ofA

Production EconomyProduction Economy

Two firms produce two products (X and Y)and Y)

The firms use two factors of d i i l (K) d l b (L)production, capital (K) and labour (L)

Assume fixed endowments of K and Assume fixed endowments of K and L.

(Production) Edgeworth Box( ) g

Firm

Total

Firm Producing

Good YY0

Kamount of

Y1X1 At the K Y1

tangency points:

X0

pMRTSX

LK=MRTSY

LKFirm

Producing G d X L Total

LK

Good X L amount of

(Production) Edgeworth Box( ) g

Firm

Total

Firm Producing

Good YY0

Kamount of

Y1X1 You can

j iKY*

Y1 join up all these (P t )Y* X0(Pareto) efficient

i t tFirm Producing

G d X L Total

points to form the

t tGood X L amount of contract curve.

Market Place: Production Economy Equilibrium

A “ ti ” dj t thAn “auctioneer” adjusts the factor prices (Pl = w and Pk = r) until the following three conditions hold:

wMRTS X wMRTSY

co d t o s o d

(1) (2)r r

(3) LLforDemand(3)K

Kfor Demand

L Lfor Demand

Production Possibility CurveProduction Possibility Curve

y Each point on the production

possibility curve is (Pareto)

efficient

x


y MRTSXLK = MRTSY

LKMRTS LK MRTS LK

x


y Points lie inside the s de t ecurve are

(Pareto) ( )inefficient

x


y Where on the PPC? C

How much X d hand how

much Y h ld bshould be

produced?

x


y Slope of the PPC = y/x

How manyHow many units of Y that have to givenhave to given up in order to produce oneproduce one

more unit of X

Marginal rate of product transformation (MRPTMarginal rate of product transformation (MRPT or MRT)


Claim: In equilibrium, firms will produce at the point on the production possibility p p p ycurve at which MRPT = Px/Py

If MRPT < P /P produce more X and If MRPT < Px/Py produce more X and less Y

If MRPT > P /P produce less X and If MRPT > Px/Py produce less X and more Y[A id MRS P /P MRPT MRS ] [Aside: MRSxy = Px/Py MRPTxy = MRSxy]


y The slope of the PPF = P /PPPF = Px/Py

Px/Py

x


y At this point we can draw in thecan draw in the amount of x and y producedproduced

Px/Py

x


y This is the amount of xamount of x produced

Px/Py

xXX


y This is the amount of yamount of y produced

YPx/Py

x


yRecall the EdgeworthRecall the Edgeworth

box

YPx/Py

xXX


y

Individual BY Individual B

Px/Py

xXIndividual A

X


y

Individual BY Individual B

Px/Py

xXIndividual A

X


yRecall that

MRS = P /P

Individual B

MRSxy Px/Py

Y Individual B

Px/Py

xXIndividual A

X


y MRS = MRPT = Px/Py

YPx/PyPx/Py UB

UA

xXX

General EquilibriumGeneral EquilibriumThree Conditions for GeneralThree Conditions for General Equilibrium:

XBXY

AXY P

PMRSMRS (1)YP

wPMRTSMRTS LYLK

XLK (2)

rPKLKLK( )

X MRSPMRPT(3) XYY

XXY MRS

PPMRPT (3)

Welfare EconomicsWelfare Economics1st Fundamental Theorem of Welfare Economics:If all markets are perfectly competitive, the yallocation of resources will be Pareto efficient.2nd Fundamental Theorem of Welfare Economics:Any Pareto efficient allocation can be obtained as the outcome of competitive

k t id d th t thmarket processes, provided that the economy's initial endowment of resources can be redistributed via lump sum taxescan be redistributed, via lump sum taxes and subsidies, among agents.

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General Equilibrium (Welfare Economics) ( )