Efficiency and Equity

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Efficiency and Equity
Efficiency Make the pie as large as
possible. Equity Share out the pie in the most
equitable way.
An efficient outcome could be entirely
inequitable. An equitable outcome could be
grossly inefficient.
The socially optimal outcome is one that is both
efficient and equitable.
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Pareto efficiency
? A Pareto efficient outcome is one that cannot
be changed so as to make someone better off
without also making someone else worse off.
? A Pareto improvement is a change that makes at
least one person better off without also making
anyone else worse off. Any outcome that we can
change to yield a Pareto improvement is said to
be Pareto inefficient.
Pareto improvements are often hard to come by.
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Some examples of Pareto improvements
? Gas Royalties
Federal government royalties force profitable oil
wells to close down.
? Tradable SO2 emissions permits
Introduction of tradable SO2 permits enabled
plants to reduce emissions at lowest possible
industrial cost.
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Allocations and the utility possibility frontier
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Compensation criteria
As a society we may prefer efficient allocation
y to inefficient allocation x, but moving from x
to y is not a Pareto improvement. We may also
prefer a more egalitarian allocation b to the
allocation y, but moving from y to b is also not
a Pareto improvement.
When there are losers as well as winners from a
policy change we need some criteria that can help
us decide whether the change is desirable.
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• Kaldor criterion. Implement a policy if, with
  the policy change, it is possible to fully
  compensate the losers while still leaving the
  gainers better off.
• ? Hicks criterion. Implement a policy if the
  potential losers cannot compensate the potential
  winners for not having the policy change, while
  still leaving themselves better off than they
  would be with the policy change.

The criteria do not require that compensation
actually be made it only needs to be
hypothetically possible to make the compensating
payments.
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Compensation criteria explained graphically
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Both criteria always rank a Pareto efficient
distribution of utility over a Pareto inefficient
distribution.
The compensation criteria therefore justify moves
from inefficient allocations to efficient
allocations, even when they are not Pareto
improvements.
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Neither criterion can rank two Pareto efficient
distributions of utility.
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Neither criterion can rank two Pareto inefficient
distributions of utility.
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• In summary
• A policy that yields a Pareto improvement is
  always desirable.
• A policy that moves us from any Pareto
  inefficient allocation to any Pareto efficient
  allocation is always desirable under the
  compensation criteria,
• The compensation criteria cannot compare two
  Pareto efficient or two Pareto inefficient
  allocations.
• ? Even when the compensation criteria work,
  compensation is only hypothetical. if we know
  that compensation is not actually going to be
  made, do we really want to make a move that makes
  people worse off?

To address these concerns, we need to develop
some tools to think about how as a society we
might feel about inequality.
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Equity and the social welfare function
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The SWF and utility possibilities
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The SWF and utility possibilities
The SWF is usually drawn this way because we
favor less inequality to some degree
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Benthamite social preferences (utilitarianism)
Bills Utility
Joes Utility
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Bills Utility
Rawlsian social preferences (egalitarianism)
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Joes Utility
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Does democracy reveal the SWF?
Example A vote for three different tax policies
A, B, and C, each of which impose different rates
of income taxes on the poor, the middle class,
and the rich. The population is evenly divided
between the three income levels. Policies are
offered in pairs, and the voting rule is to
choose the policy that the majority prefers.
The voting scheme creates an endless cycle of
votes indicating a preference to switch.
This is an example of the Arrow Impossibility
Theorem