General Equilibrium and International Trade

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Part IIa Paper 1General Equilibrium and Welfare
EconomicsDr Hamish Low

• Lecture 2

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Outline

• Summarising competitive equilibrium
• Questions remaining
• Excess demand functions and defining equilibrium
• Properties of excess demand functions

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Competitive Equilibrium in a Closed Economy
y
Agg I.C.
Contract Curve
PPF
x
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Competitive Equilibrium in an Open Economy
y
Export
x
Import
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Points to Note

• Spending power determined by position of PPF
• Well-behaved functions
• concave production function
• indifference curves are convex

only one point of tangency
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Questions to Address

• Existence Under what circumstances can we be
  sure that an equilibrium exists?
• UniquenessWill an economy have only one
  equilibrium?
• 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
Aggregate demand for x given prices
Aggregate supply for x given prices
Economys natural resource of x
This function gives excess demand
for a particular price vector.
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Aggregation of Consumer Demand
Partial equilibrium approach
General equilibrium approach
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Individual 2
p
Individual 1
p
Conveniently downward sloping! Limited wealth
effects.
x
x
p
Market Demand
x
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Aggregation of Supply
Firm 2
p
Firm 1
p
Conveniently upward sloping!
x
x
p
Market Supply
x
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Resource Stock
px
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Putting these three elements together ...
Excess demand
Excess supply
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Competitive Equilibrium
No excess demand
Equilibrium given by price vector p which
satisfies 3 conditions
So, if no satiation, then equilibrium given by
Prices non-negative
for each good
If excess supply, price must be zero (i.e.
satiation)
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Properties of Excess Demand Functions
(these properties hold in and out of equilibrium)
(1) Homogenous of degree zero
so, can normalise prices aribitrarily E.g.
divide by
or, divide by so that prices sum to
1.
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Individuals spend all their income. Income is
determined by resources and profits.
(2) Walrass Law
Once know excess demand in H-1 markets, know
excess demand in the Hth market
Diagram for two goods and normalised prices
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Excess demand
Excess supply
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Existence
Is there a set of prices such that
?
Well-behaved economy
1
Excess demand
Excess supply
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Problems

• Discontinuous excess demand

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Excess demand
Excess supply
Existence requires each excess demand function to
be continuous

• production function concave
• indifference curves continuous and strictly
  convex

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Problem of non-concavity of production
One firm
BUT if increasing returns to scale, then only a
small number of firms, so non-concavity remains
labour
more generally, non-concave if increasing
returns to scale
Many firms
labour
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Non-Convexity of indifference curves
y
x
px
Discontinuous demand function
x
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Summary

• Defined excess demand function 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

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Outline

• UniquenessWill an economy have only one
  equilibrium?
• Stability Will the economy somehow tend to or
  revert to this equilibrium?
• Price Determination And will this determine the
  price system for us?
• Gross substitutes

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Excess Demand Function
Individuals must satisfy their budget constraints
(1) Walrass Law
Prices lie between 0 and 1
(2) Only relative prices matter, so
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Assume each good is desirable, then equilibrium
means
Diagram for two goods and normalised prices
Good y is free
Know excess demand for y through Walrass Law
Equilibrium
1
Excess demand
Excess supply
Good x is free
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Uniqueness
Given non-satiation, equilibrium requires that
Well-behaved economy
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Excess demand
Excess supply
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As price falls from A to B, demand decreases and
supply rises.
Problems
1
A
B
Unique if excess demand downward
sloping Uniqueness requires aggregate demand to
be downward sloping and aggregate supply upward
sloping.
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Gross substitutes
Individual consumer with 2 goods raising price
of one good, increases compensated demand for the
other good. (Net of wealth effects) With wealth
effects raising price of one good may reduce the
uncompensated demand for the other Gross
substitutes raising price of y increases
uncompensated demand for x
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y
y
B
B
C
A
A
C
x
x
Gross complements
Gross substitutes
Condition of gross substitutes says that wealth
effects are less important than direct price
effects (for aggregate demand)
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1
This possibility is ruled out
A
B
Assume,
downward sloping Ex
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Fragility of uniqueness.
increase in resource of good x
1
unique even if gross substitutes not satisfied
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Stability

• Once an economy is in an equilibrium, it is
  stable
• if small movements in prices do not dislodge it
  from that equilibrium, or
• if it reverts to that equilibrium.

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Need to define what happens to prices out of
equilibrium
Auctioneer
BUT trade only occurs once
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1
if trade at non-market clearing prices, then
actual wealth changes
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Stable
Unstable
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Stable
Equilibrium are stable if goods are gross
substitutes

• an increase in price always reduces excess
  demand
• a reduction in price always increases excess
  demand

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Gross substitutes
Increases in py change the value of wealth. This
changes demands. Condition of gross substitutes
says that wealth effects are less important than
direct price effects.
stability
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Summary

• Use excess demand functions to determine
  properties of equilibrium
• Existence requires continuous aggregate demand
  and supply curves convex indifference curves and
  concave production functions
• Uniqueness requires downward sloping demand and
  upward sloping supply
• Stability requires a price mechanism such that
  price increases if excess demand and falls if
  excess supply. But, no trades out of equilibrium
• Need gross substitutes
• Trade distorts relative prices and effects
  equilibrium

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Consumers and International Trade
Scotland puts a tarriff on Wine, France puts one
on Haggis.
France
Wine
Excess Supply
e
Haggis
Scotland
Excess Supply