Ec355, lecture 3: Equity and Efficiency, Social Welfare

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Ec355, lecture 3 Equity and Efficiency, Social
Welfare
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This week

• (first finish last weeks notes)
• Altruism and the Equity-efficiency tradeoff
• Social choice, social welfare functions
• Philosophical justifications and critiques
• Distortionary taxation and the cost of public
  funds
• CBA and the criterion of Potential Pareto
  improvements
• Reading MC, ch. 2, 7.1-7.2

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Equity-efficiency tradeoff?

• Lump-sum transfers infeasible ? distortionary
  effects of taxation (see later
• But (extreme) inequality may bring
  inefficiencies...

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Altruism

• Altruistic utility function U(x,V) where V is
  consumption (or utility) of another individual.

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(Aside what motivates altruistic behavior?)

• Allowing a private warm glow we may have
  U(x,g,V) where g is my own contribution this
  can explain voluntary donations to large-scale
  charities, but it is a bit of a black box.
  There are alternative models, such as Impact
  altruism and Kantian behavior.
• Altruistic utility U(x1,x2,V), where
  VV(y1,y2,..)
• Paternalism (e.g.) U(x1,x2,y1,y2)

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Equality and Efficiency Altruism argument

• Depict Fig 3.1 The UPF with altruism.
• UPF with altruism Pareto Improvements along the
  frontier

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Poverty relief as a public good.

• Note V can be a public good (non-rival and
  non-excludable).
• I benefit from others contributions towards V
  (as much as from my own) in fact, my marginal
  benefit may be less than one, hence not
  justifying a contribution even at V0.

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The provision of poverty relief as a prisoners
dilemma
(We will model this more fully when we discuss
public goods)
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• Instrumental arguments for redistribution
• Crime
• Class question Why is crime inefficient?
• How does it waste (and not just transfer)
  resources?
• Social insurance
• Need argument for failures in insurance market
  (Ch 16), and how the government could do better
• Imperfect capital markets
• A potential side benefit of redistribution, but
  CM need further justification for a profitable
  government role here. See, e.g., Ch 6 on
  asymmetric information.

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Social choice

• How do we as society choose a (desired) point
  along the UPF?
• (Most policies and redistributions involve
  tradeoffs of one utility for another)
• We need a social choice function (SCF), an
  ordinal ranking of the alternatives.
• What criteria should such a function have?
• How do we choose which function is the right one?

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Arrows delicious PUDI

• Pareto principle If at least one individual
  prefers option x to option y and no one strictly
  prefers y to x then society prefers x to y
• Universal domain The SCF should work for any set
  of individual preferences (no matter how weird).
• non-Dictatorship The SCF should not depend
  solely on the rankings of one individual
• Independence of irrelevant alternatives The
  ranking of x and y should only depend on
  individual rankings of x and y and not on the
  preferences of individuals over x and z (nor y
  and z).
• Arrow Any SCF should be complete and transitive
  and satisfy these four criteria.
• Economists of the world That sounds nice
• Arrow Also, I proved that no SCF can satisfy
  these four criteria.
• Economists of the world Wow, lets give you a
  Nobel prize!

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Condorcets Paradox (as an illustration of
Arrows Impossibility Theorem)

• Rankings of alternatives, example
• Liberals Green Park gt Public housing gt Private
  housing
• Labour Public housing gt Private Housing gt Green
  Park
• Conservatives Private Housing gt Green Park gt
  Public housing
• Consider majority rule as a social choice
  function When considering two policies, select
  the one that more people prefer. This will
  satistfy PUDI.
• But in the case above, the choice will depend on
  the way these are paired (as in
  Rocks-Paper-Scissors).
• Society prefers Green Park to Public housing,
  Private housing to a Green park, and Public
  housing to Private housing.
• ? Social preferences are not transitive.

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Condorcet with utility numbers, utilitarian rule

• Example on page 45-46 shows that neither our
  standard idea of a utility function (ordinal
  only order of utility matters) nor the expected
  utility restriction (unique up to a linear
  transformation) will be coherent
• Utility must be measured on the same scale for
  everyone we need to be able to make
  interpersonal comparisons.
• Note we can achieve P,I,and D (e.g., via
  majority rule) if we limit ourselves to
  single-peaked preferences unlike those in the
  previous example.

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Social welfare functions (SWFs)

• (A SWF ranks all the options against a common
  scale a SCF selects one of these options)
• Wf( U1, U2,.)
• Three typical properties (PIN)
• Pareto principle W rises in Ui for any i all
  partial derivatives are always positive
• Inequality aversion f is concave
• INdiviualism Only a function of individual
  utilities.

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Types of SWF (URI)

• Utilitarian W U1 U2 ..
• This one is very general. Remember that this is
  not the same as expected income maximising, and
  it can embody a great deal of inequity (risk)
  aversion
• Rawlsian WminU1, U2,
• Isoelastic WSumiUi(1-e)/(1-e)
• A parametrization of all the alternatives in
  between Utilitarian (e0) and Rawlsian (e
  infinite)
• Depict Fig 3.3
• Note 2 and 3 may be more reasonable considered
  in terms of incomes.

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Social justice and the correct SWF

• Consider what do we mean by individual utility
  in this context?
• Simplest view pleasure
• Rawls The veil of ignorance thought experiment
• Probably wouldnt merely maximise expected income
• Might maximise expected utility (Utilitarian
  SWF/Harsanyi argument)
• Some argue we should drop the utility framework
  entirely, and focus on more objective measures

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Other topics in social welfare

• Anti-consequentialism
• Horizontal equity (and fairness)\
• Is this important in itself or is it really based
  on imagined consequences?
• (liberalism skip)

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Marginal cost of public funds

• (Previously assumed) Lump-sum taxation transfers
  do not change incentives.
• But this is often impossible (what if people
  dont have the money to give?)
• It is rare, and politically difficult for various
  reasons (such as inequality aversion and
  unobservable enwdoments, also the political
  desire to tax sin, etc.)
• More typical Distortionary taxation
• Alters incentives (relative prices)
• Of labor (leisure)
• Of consumption (savings/ deferred consumption)
• Of one good or service relative to another

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Pizza taxation example

• Depict Fig. 3.4
• (Like-for-like comparison of lump sum tax and tax
  on pizza.)
• M income
• p pizza price (before tax)
• (price of all else normalised to one consider
  why this is without loss of generality)
• x Pizza consumption y consumption of all else
• T revenue (needed to be) raised
• Lump-sum tax yields parallel budget constraint to
  original
• Pizza tax shifts price slope (note same amount
  achievable if no pizza purchases)
• Optimal choices, B.C. tangent to convex
  indifference curve.
• E0 original choice, E1 with Lump sum tax (note
  relative shifts possible because of income
  effects), E2 with pizza tax (note shift away
  from pizza)
• Note lower welfare with pizza tax then with
  lump-sum tax

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Pizza algebra

• Original budget constraint pxym
• With lump-sum tax px y m-T
• With pizza tax (pt)x2 y2 m
• Same revenue ? tx2T ? t T/x2
• (p T/x2)x2 y2 m
• px2 y2 m-T
• Bundle chosen with pizza tax is also on the B.C.
  for lump-sum tax (but not vice/versa)

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Excess burden/ MCPF

• After imposing a tax, how much would we have to
  compensate the individual to make her as well off
  as before? (Compensating variation) TAB in
  the diagram
• AB is the excess burden (the burden over and
  above the tax itself.
• Marginal cost of public funds (TEB)/T
• How inefficient is the tax?
• (Note alternate measure is the difference in
  revenue raised see fig 3.5)

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The MCPF the equity/efficiency tradeoff

• Consider utilitarian SWF.
• With lump-sum transfers
• Max W(R-T) W(PT)
• (rich guy pays tax, poor guy gets transfer)
• Set MWRMWP
• (FOC for interior optimum)
• With distortionary taxes
• Max W(R-C(T)) W(PT)
• Set MWR MCPFMWP
• (FOC for interior optimum)
• See fig 3.6 (assumes utility linear in income,
  but allows isoelastic welfare function) higher
  MCPF ? less redistribution is optimal
• Estimates of the MCPF vary

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Last weeks questions

• MC 2.3 Why are Pareto improvements possible if
  producers current use of factors is not on the
  production contract curve?
• Off the contract curve can increase production
  of one good without decreasing production of
  another. Graphically, consider a point off the CC
  and move along one isoquant (towards CC) note
  increase in production of other good (higher
  isoquant).
• With greater production of one good, assuming
  nonsatiation, utility for one or both consumers
  can be increased.
• Movement to PPF ? Wider consumption EB,
• Depict as moving one consumer to higher
  indifference curve while keeping other consumer
  on same indifference curve ? Pareto improvement.
• MC 2.4 Why is it that an efficient outcome may
  also be unfair?
• Unfair is a subjective measure, but it could
  certainly lead to extremely unequal outcomes.
  Consider if one consumer is endowed with all
  capital and labour, the other with none will
  lead one to starve and the other to consume all.
  This would seem unfair to many
• Because the endowments are unfair

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New homework

• MC exercises 3.2 3.6
• Read ch. 14 articles mentioned (at least
  download and skim these)

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Bonus the window tax (distortion) 1696-1851
When the window tax was introduced, it consisted
of two parts a flat-rate house tax of 2
shillings per house and a variable tax for the
number of windows above ten windows. Properties
with between ten and twenty windows paid a total
of four shillings, and those above twenty windows
paid eight shillings.