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General Equilibrium (Welfare Economics). General Equilibrium . Partial Equilibrium: Neglects the way in which changes in one market affect other (product/factor) markets.

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general equilibrium
General Equilibrium
  • Partial Equilibrium: Neglects the way in which changes in one market affect other (product/factor) markets.
  • General Equilibrium: Analyses the way in which the choices of economic agents are co-ordinated across all product and factor markets.
agenda
Exchange Economy

2 individuals/consumers (A and B)

2 products (X and Y)

Production Economy

2 products (X and Y)

2 factors (L and K)

General Equilibrium

2 individuals/consumers (A and B)

2 products (X and Y)

2 factors (L and K)

Agenda
exchange economy
Exchange Economy

2 Individuals: A and B

2 Products:

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

edgeworth box
Edgeworth Box
  • Look at the world from Individual A’s perspective
  • Look at the world from Individual B’s perspective
  • Combine A and B’s worlds to form an Edgeworth box
edgeworth box6
Edgeworth Box

Total amount of

Individual A

Total amount of

edgeworth box7
Edgeworth Box

Total amount of

Individual B

Total amount of

Individual A

edgeworth box8
Edgeworth Box

Total amount of

Individual B

Total amount of

Individual A

Each point within the box represents a particular allocation of the two products between the two individuals

pareto efficient allocation
Pareto Efficient Allocation
  • Pareto Efficient Allocation: Each individual is on the highest possible indifference curve, given the indifference curve of the other individual.
edgeworth box10
Edgeworth Box

Individual B

a

Total amount of

YB

b

Individual A

XA

Total amount of

pareto inefficient allocation
Pareto Inefficient Allocation
  • a and b are Pareto inefficient allocations.
  • Why? Because there exists changes in allocations, starting from a or b, that would make at least one individual better off without making the other individual worse off.
edgeworth box12
Edgeworth Box

Individual B

Total amount of

g is a pareto efficient point

g

Individual A

Total amount of

pareto efficient allocation13
Pareto Efficient Allocation
  • At point/allocation g:
  • Individual A is on the higher possible indifference curve given B’s indifference curve and
  • Individual B is on the highest possible indifference curve given A’s indifference curve.
  • Therefore, g is a pareto efficient allocation
  • Note: The two indifference curves are tangential to each other
pareto efficient allocations
Pareto Efficient Allocations

Individual B

Total amount of

e

e and d are also Pareto efficient allocations

g

d

Individual A

Total amount of

contract curve
Contract Curve

Individual B

Total amount of

e

Joining up these Pareto efficient points yields the contract curve

g

d

Individual A

Total amount of

contract curve16
Contract Curve
  • The curve connecting all Pareto efficient allocations is known as the contract curve.
  • At each point on the contract curve, the MRS’s for A and B are equal, i.e.

MRSAxy = MRSBxy

market place
Market Place

An “auctioneer” adjusts the product prices (Px and Py) until the following three conditions hold:

(1)

(2)

(3)

market place exchange economy equilibrium
Market Place: Exchange Economy Equilibrium

Individual B

UA

Total amount of

UB

Individual A

Total amount of

exchange edgeworth box summary
Exchange Edgeworth Box: Summary

XB

Individual B

Total amount of

YB

YA

Individual A

XA

Total amount of

production economy
Production Economy
  • Two firms produce two products (X and Y)
  • The firms use two factors of production, capital (K) and labour (L)
  • Assume fixed endowments of K and L.
production edgeworth box
(Production) Edgeworth Box

Firm Producing Good Y

Y0

Total amount of

X1

At the tangency points: MRTSXLK=MRTSYLK

Y1

X0

Firm Producing Good X

Total amount of

production edgeworth box22
(Production) Edgeworth Box

Firm Producing Good Y

Y0

Total amount of

X1

You can join up all these (Pareto) efficient points to form the contract curve.

Y1

Y*

X0

Firm Producing Good X

Total amount of

market place production economy equilibrium
Market Place: Production Economy Equilibrium

An “auctioneer” adjusts the factor prices (Pl = w and Pk = r) until the following three conditions hold:

(1)

(2)

(3)

production possibility curve
Production Possibility Curve

Each point on the production possibility curve is (Pareto) efficient

y

x

production possibility curve25
Production Possibility Curve

y

MRTSXLK = MRTSYLK

x

production possibility curve26
Production Possibility Curve

Points lie inside the curve are (Pareto) inefficient

y

x

production possibility curve27
Production Possibility Curve

Where on the PPC?

How much X and how much Y should be produced?

y

x

production possibility curve28
Production Possibility Curve

Slope of the PPC = Dy/Dx

y

How many units of Y that have to given up in order to produce one more unit of X

Marginal rate of product transformation (MRPT or MRT)

general equilibrium29
General Equilibrium
  • Claim: In equilibrium, firms will produce at the point on the production possibility curve at which MRPT = Px/Py
  • If MRPT < Px/Py produce more X and less Y
  • If MRPT > Px/Py produce less X and more Y
  • [Aside: MRSxy = Px/Py MRPTxy = MRSxy]
general equilibrium30
General Equilibrium

The slope of the PPF = Px/Py

y

Px/Py

x

general equilibrium31
General Equilibrium

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

y

Px/Py

x

general equilibrium32
General Equilibrium

This is the amount of x produced

y

Px/Py

x

general equilibrium33
General Equilibrium

This is the amount of y produced

y

Px/Py

x

general equilibrium34
General Equilibrium

Recall the Edgeworth box

y

Px/Py

x

general equilibrium35
General Equilibrium

y

Individual B

Px/Py

Individual A

x

general equilibrium36
General Equilibrium

y

Individual B

Px/Py

Individual A

x

general equilibrium37
General Equilibrium

Recall that

MRSxy= Px/Py

y

Individual B

Px/Py

Individual A

x

general equilibrium38
General Equilibrium

y

MRS = MRPT = Px/Py

UA

Px/Py

Px/Py

UB

x

general equilibrium39
General Equilibrium

Three Conditions for General Equilibrium:

welfare economics
Welfare Economics

1st Fundamental Theorem of Welfare Economics:

If all markets are perfectly competitive, the allocation of resources will be Pareto efficient.

2nd Fundamental Theorem of Welfare Economics:

Any Pareto efficient allocation can be obtained as the outcome of competitive market processes, provided that the economy's initial endowment of resources can be redistributed, via lump sum taxes and subsidies, among agents.