General Equilibrium and International Trade

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Part IIa Paper 1General Equilibrium and
International TradeDr Hamish Low

• Lecture 3

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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
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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
• Next time using excess demand functions to
  consider existence, uniqueness and stability