Chapter 34 Externalities

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• Chapter 34 Externalities
• Typically, demand only reflects private marginal
  benefits of consumers and supply private marginal
  costs of producers. These could differ from
  social marginal benefits and social marginal
  costs. Hence the market equilibrium is not
  efficient.
• Government intervention is not the only solution.
  Private bargaining may work. Key is in defining
  the property right.

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• A smoker and a non-smoker who have preferences
  over money and smoke. A smoker would like to
  smoke as much as he could while a non-smoker
  would like the air to be as clean as possible.
• The Edgeworth is only different that we measure
  the amount of smoke in one direction.

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• Look at the case where the smoker has the legal
  right to smoke and another extreme where
  non-smoker has the legal right of clean air.
• Externalities do not cause inefficiency when
  there is a well-defined property right. Moreover,
  with the property right defined, bargaining may
  lead to efficiency.

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Fig. 34.1
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• In the example above, the amount of externality
  will depend on the assignment of property rights.
• There is a special case where the outcome of
  externalities is independent of the assignment of
  property rights. This is the case of quasilinear
  preferences. Since preferences take the form of
  mv(smoke), indifferent curves are parallel to
  each other along the m axis.

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• Hence if we have an efficient allocation, moving
  along the m axis, we get another efficient
  allocation.
• Coase Theorem When parties can bargain without
  cost and to their mutual advantage, the resulting
  outcome will be efficient, regardless of how the
  property rights are specified.

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Fig. 34.2
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• Consider a situation involving production
  externalities. A steel firm produces s and some
  pollutants x. A fishery produces f and is
  adversely affected. Suppose Ss cost is cs(s,x)
  and Fs cost is cf(f,x). Assume that ?cf/?xgt0 and
  ?cs/?x0.
• In the market equilibrium, S max pss-cs(s,x), F
  max pff-cf(f,x). FOCps ?cs(s,x)/?s, 0
  ?cs(s,x)/?x and pf ?cf(f,x)/?f.
  ?cf(f,x)/?xgt0, but S fails to consider this.

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Fig. 34.3
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• Ways to get efficient levels of pollution.
• Internalizing the externalities Consider the
  case where S and F merge. Then they max
  pss-cs(s,x)pff-cf(f,x) and by definition, there
  is no externality anymore. FOC ps
  ?cs(s,x)/?s, 0 ?cs(s,x)/?x ?cf(f,x)/?x
  and pf ?cf(f,x)/?f.
• Taxing Key is to make pollution tax t
  (pss-cs(s,x)-tx) so that t?cf(f,x)/?x.

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• Sometimes if the government has a pretty good
  idea about how much pollution to reduce, then the
  problem becomes to find the most cost effective
  way to achieve the targeted reduction. A
  practical measure is the pollution vouchers.
  Suppose two polluting firms, each having emission
  quotas x and x. The cost of achieving the quota
  is c1(x) and c2(x). Hence we need to solve

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• Minx,x c1(x)c2(x) s.t. xxX. So at optimum,
  the marginal cost of each firm should equal.
• If we allow firms to trade pollution vouchers.
  Suppose we first assign some quotas y and y
  where yyX to each firm. If c1(y)gt c2(y),
  then increasing one unit of emission saves the
  cost of firm 1 by c1(y) while reducing one unit
  of emission costs firm 2 by c2(y).

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• Alternatively, if there is a market for the
  emission quota (say the price is p), then 1
  should compare c1(y) to p. If c1(y)gt p, then
  buying one unit of quota costs only p but saves
  the emission cost by c1(y). Hence worthwhile
  doing. So 1 will be the buyer and 2 will be the
  seller. If market clears, then what 1 is willing
  to buy must equal what 2 must be willing to
  supply. Moreover, their MCs both equal to the
  common price.