Chapter 7 General Equilibrium and Market Efficiency

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Chapter 7General Equilibrium and Market
Efficiency
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Outline.

• A simple exchange economy
• Efficiency in production
• Efficiency in product mix
• Sources of inefficiency

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A simple exchange economy

• Consider a simple economy in which there are only
  two consumers A (Ann) and B (Bill) and two goods
  food and clothing.
• Available quantities of goods are exogenous
• Food 100
• Clothing 200
• An allocation is an assignment of these
  quantities between A and B.
• The amounts of goods with which A and B start
  each period are called their initial endowments.

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Personal bargaining

• What do A and B do with their initial endowments?
  
• They may either consume what they already have or
  to engage in exchange one with the other.
• Exchange is purely voluntary so it only takes
  place if it is beneficial to both parties
• Exchange makes someone better off if it places
  him on a higher indifference curve

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The Edgeworth Box
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Improving utility through exchange
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Further improving utility through exchange
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Reaching a Pareto-optimal allocation
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The Contract Curve
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From initial endowments to the contract curve
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Market economies

• In our very simple example, exchange took place
  through personal bargaining. In market economies,
  most exchanges have a more impersonal character.
• People have given endowments and they face given
  prices. They then decide how many goods and
  services they want to buy and sell.
• We can introduce market-type exchanges by
  assuming that there exists a third (fictive)
  person playing the role of an auctioneer.

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Exchanges in a market economy
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General equilibrium in a market economy
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The first theorem of welfare economics

• It is also called the theorem of the Invisible
  Hand.
• It can be stated as follows an equilibrium
  produced by competitive markets will exhaust all
  possible gains from exchange.
• Another way to put it is that equilibrium in
  competitive markets is Pareto optimal
  competitive equilibrium is efficient

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The second theorem of welfare economics

• It states that any allocation on the contract
  curve can be sustained as a competitive
  equilibrium.
• The basic condition that assures this result is
  that consumer indifference curves be convex when
  viewed from the origin.
• Why not redistribute initial endowments in order
  to achieve the desired outcome directly?
• Lack of information on consumers' indifference
  curves
• Consequence of the theorem the issue of equity
  in distribution is logically separable from the
  issue of efficiency in allocation

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Decentralisation of the optimum
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Outline.

• Efficiency in production
• Efficiency in product mix
• Sources of inefficiency

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Efficiency in production

• The product mix in an economy is the result of
  the allocation of productive inputs
• Suppose we add a productive sector to our
  exchange economy.
• It consists of 2 firms, each of them using
  capital K and labour L.
• Firm C produces clothing and firm F produces
  food.
• Suppose the total quantities of the 2 inputs are
  fixed with K 50 and L 100.
• The production processes used by the 2 firms
  give rise to conventional convex-shaped
  isoquants.

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The Edgeworth production box
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The efficiency of general equilibrium

• If firms maximise their profits, the resulting
  general equilibrium will satisfy the requirements
  of efficiency in production
• Suppose that food and clothing prices are PF and
  PC.
• Suppose that firms hire labour and capital on
  perfectly competitive markets at hourly rates w
  and r.
• If both firms minimise costs we have
• Given that the price of inputs is the same for
  both firms, this yields

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Outline.

• Efficiency in product mix
• Sources of inefficiency

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Efficiency in production mix

• An economy may be efficient in production and, at
  the same time do a very poor job in satisfying
  the wants of its members
• So, there is one more efficiency criterion of
  concern which is whether the economy has an
  efficient mix of the two products
• To define the efficient product mix, it is
  useful to translate the contract curve from the
  Edgeworth production box into a production
  possibilities frontier
• Definition this is the set of all possible
  output combinations that can be produced with
  given quantities of capital and labour.

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The marginal rate of transformation

• The slope of the production possibilities
  frontier at any point is called the marginal rate
  of transformation (MRT)
• It measures the opportunity cost of clothing in
  terms of food.
• For the economy we consider, the MRT increases
  when we move to the right. This is always the
  case as long as there are constant or decreasing
  returns to scale.

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Efficiency in product mix

• In order for an economy to be efficient in terms
  of production mix, the MRS for each consumer has
  to be equal to the MRT

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General equilibrium and efficiency in product mix

• Let PF and PC denote the equilibrium prices for
  food and clothing.
• As we have seen for the simple exchange economy,
  in equilibrium, the MRS of every consumer will be
  equal to the ratio of these prices PC / PF.
• In order to show that the general equilibrium is
  efficient, we need to show that the MRT is also
  equal to PC / PF

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Demonstration

• Lets show that at any point on the production
  possibilities frontier he MRT is equal to the
  ratio of the marginal cost of clothing (MCC) to
  the marginal cost of food (MCF).
• The MRT is given by
• It is the amount of food you have to give up in
  order to get one more unit of clothing.
• In order to produce one more unit of clothing, we
  need to use a bundle of inputs the value of which
  is MCC.

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Demonstration (ctd1)

• In order to get that bundle of input, we need to
  produce less food.
• For each unit of food we give up, we get an input
  bundle which is worth MCF.
• So, in order to get an input bundle worth 1, we
  need to give up 1/ MCF units of food
• In order to get an input bundle worth MCC, we
  need to give up MCC / MCF units of food.
• So,

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Demonstration (ctd2)

• The equilibrium condition for food and clothing
  producers is that product prices be equal to the
  corresponding marginal costs.
• PF MCF and PC MCC
• So,
• So, an economy in competitive general equilibrium
  is simultaneously efficient (i.e. Pareto optimal)
  in consumption, production and in the choice of
  product mix.

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Outline.

• Sources of inefficiency

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Taxes in general equilibrium
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Taxes and inefficiency in the product mix

• Even with the tax on food, consumers have a
  common value of MRS in equilibrium and that
  producers have a common value of MRTS. So, the
  economy is efficient in consumption and
  production.
• The tax causes producers to see a different price
  ratio from the one seen by consumers consumption
  decisions are based on gross prices whereas
  production decisions are guided by net prices.
• So, the MRS and MRT can never be equal in
  equilibrium.
• So, the tax leads to an inefficient production
  mix.

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Minimising Distorsions

• Subsidies, like taxes upset the conditions
  required for efficiency
• The tax system has to be designed in order to
  minimise distorsions
• Taxing food and clothing at the same rate t.
• But in general, comodity taxes will have
  distortionary effects
• Lump-sum taxes
• But generate equity problems
• The best tax tax levied on activities of which
  there would otherwise be too much

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Externalities

• Another source of inefficiency occurs when
  production or consumption activities involve
  benefits or costs for people not directly
  involved in them. Such benefits and costs are
  called externalities
• Example of negative externality pollution
• Example of positive externality flowers
• Externalities create a problem very similar to
  taxes they cause producers and consumers to
  react to a different set of relative prices .

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Externalities (ctd)

• Solution
• Tax negative externalities
• Subsidise positive externalities
• The existence of externalities is a good example
  of market failure
• It is a case in which the outcome generated by
  the working of the market is no optimal.
• This sets the ground for public intervention in
  the economy.

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Public goods

• Pure public goods have 2 characteristics
• They are non-rival the fact that one person uses
  the good does not reduce the amount of good that
  can be used by another person.
• Example radio or TV programs, national defence.
  
• They are non-excludable it is impossible to
  exclude somebody who does not pay from using the
  good.
• Example TV programs before cable TV, radio
  programs, national defence
• There is no reason to presume that private
  markets will supply optimal quantities of pure
  public goods

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Public goods (ctd)

• The problem is less acute with goods that are
  non-rival but excludable.
• Example cable TV. It is possible to exclude
  people from watching programs they do not pay
  for.
• But even here there are likely to be
  inefficiencies Once a TV program has been
  produced, it costs society nothing to let an
  extra person see it.
• Here again, these market failures set the ground
  for public intervention in the economy.