EMEA4: General Equilibrium Models

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EMEA4 General Equilibrium Models

• A small exchange economy
• A large exchange economy
• A production economy
• Theory and practice
• Applications
• Climate change and agriculture
• Sea level rise
• Biodiversity conservation
• Markets, efficiency, optimality, utilitarianism
• Top-down versus bottom-up models

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Bilateral Exchange

• Consider an economy with two commodities and two
  consumers. Each consumer has an initial endowment
  of both commodities.
• Assume non-satiation, rationality, strict
  convexity, no cost of exchange, perfect
  information
• The exchange rate of commodity 1 for commodity 2
  is the inverse of the exchange rate of 2 for 1

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Bilateral Exchange -2

• Consumption cannot exceed the initial endowment
  plus whats acquired through exchange. For good
  1, consumer 1
• The same holds for good 2
• The last bit follows from the symmetry of prices

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Bilateral Exchange -3

• Add the two constraints
• Divide by two and add
• Or, total consumption (measured in commodity 1)
  should not exceed total endowments
• Because of satiation, equality

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Bilateral Exchange -4

• Now introducte utility maximisation, subject to
  the two constaints just derived this gives the
  demand functions
• The economy has two constraints
• So, there are 6 equations and 5 variables
• This is no problem because the equations are not
  independent (Walras Law)

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Bilateral Exchange -5

• Add the total budget constraints of the two
  agents
• Subtract the market equilibrium for good 1
• Divide by the price, and you have the market
  equilibrium for good 2
• So, five equations, five variables

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General Exchange

• Now consider an economy with m consumers and n
  goods. Each consumer has a conventional utility
  function. Each consumer has a non-negative bundle
  of commodities as an initial endowments.
• The exchange rates between the goods can be
  written as a matrix

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General Exchange -2

• The exchange rate matrix satisfies all sorts of
  constraints. The diagonal elements are unity, and
  it is inverse-symmetric
• But also
• This allows for normalisation

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General Exchange -3

• A feasible exchange of good i for j meets
• That is, the exchange does not change the value
  of the consumers holdings
• This holds for all goods, so

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General Exchange -4

• Each consumer maximises under constraint
• Of course, the markets are in equilibrium

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General Exchange -5

• Define market demand
• Define market supply
• Market equilibrium follows from
• Note that there is again a redundant equation!

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Production Economy

• Consider an economy with m consumers, l producers
  and n commodities
• Assume that producers maximise profits, and that
  the production process can be represented by a
  regular production function Profits are handed
  to consumers
• Consumers are rational etcetera
• There is no cost of exchange there is perfect
  information Therefore, exchange ratios are
  equated by arbitrage normalise all prices with
  good 1

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Production Economy -2

• Consumer behaviour follows from
• From which we can derive
• Producer behaviour follows from
• From which we can derive

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Production Economy -3

• Market equilibrium
• There are nm demand functions (and demands), nl
  net supply functions (and supplies), l profit
  functions (and profits), and n equilibrium
  conditions (and only n-1 prices)
• Walras Law again ensures identification

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Computable General Equilibrium Models

• We have now seen 3 general equilibrium models
  tomorrow, well introduce time
• We could analyse under what conditions an
  equilibrium exists, is unique, and equals a
  social optimum
• Instead, we will look at two empirical examples
• Empirical studies use computable general
  equilibrium models, because full-fledged general
  equilibrium involves more

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CGEs

• CGEs will deliver quantities and prices
• CGEs need a number of inputs
• Typically, there is a representative consumer
• Typically, there is a representative producer for
  each good
• Consumption, intermediates and prices (for
  calibration) are easy to get
• The hard bit is the elasticities
• Programming and solving is easy nowadays

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Applied CGEs

• Ill show three examples
• FARM is an 8-region, 11-sector, 13 commodity
  static CGE
• It uses nested CES production functions
• It distinguished between domestic and foreign
  product with Armington elasticities
• It is coupled to a GIS of land quantity and
  quality
• GTAP is another static CGE, adjusted to look at
  impacts of climate change

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Production Functions

• Constant Elasticity of Substitution

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Prices and Production in the EC, 10 Land
Retirement
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Sea level rise

• Impact of sea level rise from Hoozemans et al.
  (1993) dryland loss and costs of protection
• Dryland lost is a loss of the endowment land
• Coastal protection is a defensive investment,
  financed by a forced increase in savings note
  that we are using a static CGE

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Virtual Water

• How much water is needed for a cup of coffee?
• 125 ml water and 7 g coffee
• In Brasil, you need about 3000 m3 water per tonne
  of coffee cherries
• After washing, drying, roasting etc., this makes
  22500 m3 water per tonne of coffee
• That makes 140 l water for 7 g coffee
• 14 buckets, 1100 cups
• This water is not from the environs of Hamburg,
  however

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Netherlands Virtual import of water for coffee
Besides for coffee, one could do this for
tee, cotton, wheat and all other products.
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Import and Export of virtual water (absolute)
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Import and Export of virtual water (relative)
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No more fossil water
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Trade liberalisation
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Markets, Efficiency, Optimality, Utilitarianism

• Economic efficiency is also known as Pareto
  optimality
• A situation is Pareto superior to another
  situation if no one is worse off and someone is
  better off
• It is hard to disagree with Pareto superiority as
  a decision criterion
• If there are no Pareto improvements possible, the
  economy is an Pareto optimum
• Under certain regularity conditions, this optimum
  is unique

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Markets, Efficiency, Optimality, Utilitarianism

• A market transaction is voluntary, and therefore
  mutually beneficial, that is Pareto improving
• The market would thus work to exhaust Pareto
  improvements until it is in equilibrium this
  implies that the market leads to a Pareto optimum
  under certain conditions, the Pareto optimum
• That is, through individual, selfish action, the
  social optimum is established

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Markets, Efficiency, Optimality, Utilitarianism

• Pareto improvements increase the welfare of some,
  decrease the welfare of none hence, a Pareto
  improvement increases the sum of individual
  welfare
• In the Pareto optimum, the sum of individual
  welfare is maximum
• The sum of individual welfare is known as
  (strictly) utilitarian welfare
• Hence, the market establishes the Pareto optimum,
  the utilitarian optimum, and economic efficiency

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Markets, Efficiency, Optimality, Utilitarianism

• Note that Pareto optimality etc is defined
  conditional on the starting point, that is, the
  initial distribution of income and goods
• We take the current situation as given, and seek
  to improve on that without harming anyone, that
  is, without questioning the current situation
• Besides Pareto improvements, there are potential
  Pareto improvements that is, someone gains and
  someone loses, but the gains are sufficient to
  compensate the losses this does not necessarily
  happen

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Markets, Efficiency, Optimality, Utilitarianism

• As the outcome of decentralised behaviour in the
  market, that is, millions of producers and
  consumers acting in their own self-interest,
  corresponds to the outcome of a central planner
  we may rewrite the market equilibrium as a social
  planning problem
• The difference is that in the former
  representation, you would need to find the
  maximum of a million problems or a zero- or
  fixed-point in a high-dimensional space

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Top-down and bottom-up

• CGEs are sometimes referred to as top-down
  models, as opposed to engineering models that are
  known as bottom-up models
• Top-down models work under the assumption that
  actors are rational and markets are perfect
• That implies that every polity that constrains a
  resource is necessarily costly the economy is at
  its summit, and the only way is down

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Top-down and bottom-up -2

• Bottom-up models include elaborate technologies
  as well as their costs
• These models typically find that one can save
  money while reducing emissions
• The rivalry between top-down and bottom has been
  bitter
• Bottom-up models only include investment and
  maintenance costs and tend to use discount rates
  that are too low
• Bottom-up models optimise a system from an
  environmental perspective, not from a welfare
  perspective

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Top-down and bottom-up -3

• So, part of the cost savings of bottom-up models
  are simply wrong
• However, there may be some left
• Particularly, if markets are distorted (e.g.,
  coal subsidies) or there are principal agent
  problems (e.g., Hamburg U), then money can be
  made
• CGEs would almost never pick this up
• However, reducing market distortions require very
  smart policy interventions, perhaps beyond our
  dear leaders