GWLecture3
Transcript of GWLecture3
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Part IIa: Paper 1General Equilibrium and Welfare
Economics
Dr Snje Reiche
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Outline
Summarising competitive equilibrium
Cowell 6.4
Varian 32.9-32.13
Questions remaining
Excess demand functions and defining
equilibrium
Properties of excess demand functions
Cowell 7.4-7.4.2
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Competitive Equilibrium in a
Closed Economy
x
y
y
x
p
p
Agg I.C.
PPF
MRTp
pMRS
y
x !!
sd
xx !
sdyy !
Contract
Curve
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Competitive Equilibrium in an
Open Economy
x
y
y
x
p
p
y
x
ppMRS
d
x
d
y
y
x
p
pMRT
sy
s
x Import
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Questions to Address
Existence: Under what circumstances can we be
sure that an equilibrium exists?
Uniqueness:Will an economy have only oneequilibrium?
Stability: Will the economy somehow tend to or
revert to this equilibrium?
Price Determination: And will this determine the
price system for us?
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Excess Demand Function
d sx xE p x p x p R|
Aggregate
demand forxgiven prices
Aggregate
supply forxgiven prices
Economys
natural resourceofx
This function gives excess demand for good x as a
function of the price vectorp. xE p
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Aggregation of Consumer Demand
,d d
i ii x p x p m
!
Partial equilibrium approach
General equilibrium approach
d dii
x p x p!
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x
px px
x
Individual 1 Individual 2
x
px MarketDemand
Convenientlydownward
sloping!
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Aggregation of Supply s sf
f
x p x p!
x
px px
x
Firm 1 Firm 2
x
px MarketSupply
Conveniently
upward sloping!
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xR
px
Resource Stock
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d sx xp x p x p R|
Putting these three elements together ...
xp
xE p
Excesssupply
Excessdemand
0x p !
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Competitive EquilibriumEquilibrium given by price vectorp*which
satisfies 3 conditions
* 0
* 0
* * 0
E p
p
E p p
e
u
!g
foreach good
So, if stronglymonotone preferences,
and
equilibrium given by
* 0E p !
No excess demand
Prices non-negative
If excess supply,
price must be zero
* 0p "
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Properties of Excess Demand
Functions(these properties hold in and out of equilibrium)
(1) Homogenous of degree zero
0x xE t p E p t ! "g
so, we can normalise prices aribitrarily:
E.g. divide by labourp
or, divide by so that prices sum to 1.h
hp
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(2) Walrass Law (local non-satiation)
0h hh
p p !
Once we know excess demand in H-1 markets, we
know excess demand in the Hth market
xp
xE p
Excesssupply
Excessdemand
Diagram for two goods and normalised prices
1
Individuals spend all their income because of non satiation.
Income is determined by resources and profits.
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ExistenceIs there a set of prices such that ? 0
x
E p !
Well-behaved economy
xp
x
E p
Excesssupply
Excessdemand
1
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Existence requires each excessdemand
function tobe continuous
production function concave
indifference curves continuous and strictly convex
Problems
Discontinuous excess demand
xp
x p
xcesssupply
xcessdemand
1
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Problem of non-concavity of production
labour
sx
more generally, non-concave if
increasing returns to scale
s
x
One firm
Many firms
labour
BUT:
if increasing returns to
scale, then only a
small number of
firms, so non-
concavity remains
p
w
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Non-Convexity of indifference curves
x
y
x
px
Discontinuousdemandfunction
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Summary
Defined excess demand functions and showed
requirements for competitive equilibrium using these
functions
Properties of excess demand functions
Homogenous of degree 0
Walrass Law
Using excess demand functions to consider
existence