Part IIa: Paper 1 General Equilibrium and International Trade Dr Hamish Low

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Part IIa Paper 1General Equilibrium and
International TradeDr Hamish Low

• Lecture 2

2
Questions

• Will wages in different countries equalise?
• What happens if there is spare capacity in a
  country?
• What happens if there is more than one factor of
  production?
• Does comparative advantage lead to complete
  specialisation by countries?

3
Outline

• Robinson Crusoe Model
• Social optimal outcome
• Competitive equilibrium
• Model of Exchange Edgeworth Box Analysis

4
Idea of Competitive Equilibrium

• General Equilibrium when all individuals and
  firms are price-takers
• Two conditions must be satisfied
• (1) Optimality consumers are maximising utility
  and producers maximising profits given prices
• (2) Feasibility demand must equal supply in all
  markets, markets clear
• A Competitive Equilibrium is a set of prices and
  a set of choices which satisfy these conditions

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Robinson Crusoe Model
One individual on an island who both consumes
and produces. Simplest model because only one
consumer and one producer.
As a consumer consumes leisure and eats
coconuts As a producer uses labour to produce
coconuts with some given technology
Recognises interdependence between consumption
and production choices, and maximises social
welfare.
Choices made separately subject to prices for
leisure and coconuts
Distinguish Social Optimum from Competitive
Equilibrium
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Social Optimum (recognising that both consumer
and producer)
Marginal Product of Labour Marginal Rate of
transformation of leisure into coconuts
First-order conditions
Marginal Rate of Substitution
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Social Indifference Curve
C
MRS MRT
f(H-z)
H
This is the optimal choice
Labour H - z
but this tells us nothing about the behaviour
of markets
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Competitive Equilibrium
because R.C. owns the firm
As a consumer
Income from working
Key assumption is price taking behaviour. So,
choice of c and z will not change p and w
Real wage financial rate of transformation
Marginal Rate of Substitution
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As a producer
Consumer MRS w/p Producer MRT w/p
L H-z
Again, price taking behaviour. So, choice of L
does not change p and w
Real wage financial rate of transformation
Marginal Rate of Transformation
Also, firms hire labour until the marginal
product of labour is equal to the real wage.
Note also that only relative price is important
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Have satisfied optimality, but is this a
competitive equilibrium?
NO, because not necessarily feasible.
C
f(H-z)
Excess Supply
H
Excess demand
wage too low
Labour H - z
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Higher wage, lower price
C
f(H-z)
c
H
L
Labour H - z
Competitive equilibrium is defined by price ratio
which clears markets, given that agents optimise
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Optimality
(1) c and z are chosen to maximise u(c,z)
subject to (2) L is chosen to maximise
Feasibility
If an inequality, then satiation and price must
be zero, so assume non-satiation.
Assumptions
(1) Price-taking behaviour (2) No
externalities (3) No uncertainty
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Exchange and Edgeworth Box
Optimality Utility maximisation
Feasibility
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Optimisation by A
First order conditions
similarly for B
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So, optimality
But not necessarily feasible
Use Edgewoth Box
Trade can lead to increased utility for both
individuals
OB
y
IB
e
IA
OA
x
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What happens in the market?
OB
y
Note change in px will have a wealth effect
changes the value of endowments
IB
B
Excess supply
A
IA
e
OA
x
Excess demand
price of x is too low
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Competitive Equilibrium
OB
y
AB
e
OA
x
Price Adjustment
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Core set of possible equilibrium which improve
utility relative to endowment, e2
Contract Curve and the Core
OB
y
OA
x
Need price vector that passes through endowment
and is tangential to indifference curves on the
contract curve.
Contract Curve Locus of points of tangency
between MRS
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Summary

• Competitive equilibrium a price vector and
  allocation which is optimal and feasible.
• Individuals and firms are price-taking, so
  possible to optimise, but the market does not
  clear, so no equilibrium.
• Shown in R.C. model and model of exchange.
• Core set of possible equilibrium for given
  endowment. As number of people increase, core
  shrinks.