Part IIa: Paper 1 General Equilibrium and Welfare Economics Dr Hamish Low

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Part IIa Paper 1General Equilibrium and
Welfare EconomicsDr Hamish Low

• Lecture 3

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Outline Trade and Production

• Solving GE Models
• Competitive equilibrium in production deriving
  PPF
• What happens to factor prices when the price of
  a final good changes? Stolper-Samuelson Theory
• What happens to production when factor
  endowments change? Rybczynski Theorem
• Explaining the pattern of trade Heckscher-Ohlin

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Solving General Equilibrium Models
Robinson Crusoe Model
Consumer
Producer
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Solution Steps
(1) Solve consumers problem taking prices and
wages as given (2) Solve producers problem
taking prices and wages as given (3) Find excess
demand functions for c and for z (4) Verify that
Walras Law holds (5) Set excess demand equal to
zero and solve for equilibrium price (6) Check
for uniqueness and stability
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(1) Solving consumers problem
First-order conditions
Into budget constraint
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(2) Solving producers problem
First-order condition
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Marshallian Demand
(3) Find excess demand functions for c and for z
Excess demand function for c
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Supply of leisure
Excess demand function for z
Demand for leisure
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(4) Verify Walras Law
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(5) Set excess demand equal to zero and solve for
equilibrium price
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(6) Check for uniqueness and stability
Gross substitutes ?
Unique and stable equilibrium
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Production and Edgeworth Box
Optimality Profit maximisation
Feasibility
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Profit Maximisation
Firm x
First-order conditions
Marginal Rate of Technical Substitution
MRTS (Slope of isoquant)
Say, MRTS gt w/r,
then increase L and decrease K
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Edgeworth Box
-w/r
Isoquant for Firm y
Oy
K
XS
Ox
L
XD
so wage rate has to rise, but, w/r will clear
market at some point if different factor
intensities.
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Points on the contract curve give the maximum
output of x given the output of y.
Oy
K
B
A
Ox
L
Each point on the contract curve represents a
different combination of x and y. If x and y
have different factor intensities, then each
point will have different w/r solutions. For
example, if x is labour intensive relative to y,
then w/r will be greater at B than at A.
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Contract curve translates into a production
possibility frontier
MRT Px/Py
Introduce Prices of Final Goods
y
A
This is the effect just seen in the MRTS diagram
B
x
Increase in Px
shift towards x.
x is labour intensive, so increase in demand for
labour
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So, given relative prices, we can tell the split
between x and y in production using
Gives a relationship between the final goods
price and factor prices.
This ties down the point on the contract curve,
and so determines the ratio, w/r.
So, given the technology and output prices, we
have a unique value of w/r
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What does it mean to say x is more labour
intensive than y?
for a given
Assume that firms x and y are equally flexible,
then no factor intensity reversal.
As w/r changes, relative factor intensities may
change, depending on flexibility of the two
firms.
e.g. if y is very flexible, then as w falls, firm
y increases labour faster than x
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No factor intensity reversal
This relationship is determined by technology and
the assumption that factor markets are
competitive.
y
x
y
Factor intensity reversal y is more flexible
than x
x
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What happens to factor prices when the price of a
final good changes?
(x is labour intensive)
Price must equal cost of production. Increase in
Px must lead to increase in w
Stolper-Samuelson if the price of a good rises,
the price of the input used intensively in that
industry will rise.
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Summary

• Can show competitive equilibrium in production
  (MRTS Condition). This translates into a
  production possibility frontier.
• For any given price vector, can determine the
  optimal split between goods and hence the
  necessary ratio of factor prices to clear the
  market.
• An increase in the price of the final good leads
  to an increase in the price of the factor used
  intensively in the production of that good.

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Outline

• Rybczinski
• Heckscher-Ohlin Model of trade
• What goods would we expect a country to export?
• Assuming labour is immobile, how would we
  expect wages to differ between countries?
• What assumptions are crucial?

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What happens to production when factor endowments
change?
Oy
Oy
K
B
A
Ox
L
Prices of final goods given, these determine w/r
which determines the labour to capital ratio. So,
any change in production must keep ratios of
factors used constant.
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Rybczinski if the endowment of a factor
increases, the output of the good using that
factor intensively increases, and production of
the other good decreases.
Want to expand production of capital, but have to
keep capital - labour ratio constant. So need
more labour and this requires production of the
other good to fall.
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Expanded production possibility frontier
y
fall in production of x
x
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An economy will tend to produce more of a good
which uses intensively factors with which the
economy is well endowed. If labour is abundant,
then produce more labour intensive goods.
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Hecksher-Ohlin Model
A is labour abundant B is capital abundant
Assumptions

• no mobility of factors
• identical technology in the 2 countries
• cosntant returns to scale
• identical preferences of consumers

x is labour intensive y is capital intensive

• countries differ in factor endowments
• industries differ in factor intensities

Key points
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Under Autarky
B
A
Abundant in labour. So, using Rybczynski,
production of x will be high and production of y
low. Similarly, wage will be low and price of x
will be low.
Abundant in capital. So, using Rybczynski,
production of y will be high and production of x
low. Similarly, wage will be high and price of y
will be low.
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Allowing trade
Prices of tradable goods must equalise.
A
can sell x in B for a higher price, so A
increases production of x and exports it.
demand for labour rises in A and the wage rate
rises.
Similarly, p MC, if price of x rises, so must
wage.
B
can sell y in A for a higher price, so B
increases production of y and exports it.
demand for capital rises in B and the rental rate
rises.
Similarly, p MC, if price of y rises, so must
rental rate.
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equalises in both countries (increasing in A and
decreasing in B)
LabourCapital ratio in x has fallen.
Oy
K
A
A
Ox
L
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What goods would we expect a country to export?
Hecksher-Ohlin Theory Countries export goods
whose production intensively uses factors which
are abundant in that country.
Equalisation of final goods prices.
equalisation of wages by Stolper-Samuelson
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How would we expect wages to differ across
countries?
Factor Price Equalisation The return to factors
equalises across countries trade in final goods
is a substitute for the mobility of factors
Imagine , then increase
production of labour intensive good in A and
undercut B.
Pre-trade
Post-trade
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Implications

• factor which is used intensively in the
  exporting industry has increased return and gains
  from trade.
• factor which is used intensively in the
  importing industry loses from trade.

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Key Assumptions

• No factor intensity reversal
• No complete specialisation cone of
  diversification
• Common technology
• Common preferences

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Summary

• Hecksher-Ohlin Comparative advantage
  determined by relative factor endowments
• Export good which uses intensively the factor
  which is abundant in that country.
• Factor prices will equalise across countries
  trade is a substitute for mobility