Economics of Policy Issues
EC3060
Spring 2010
Tutorial 1
Revision
Michael King
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Outline
Purpose of Tutorial
• Opportunity to ask questions
• Revision
Contents
1. Condorcet Winner
2. Logrolling
3. Political Competition with Multiple Issues
4. Risk Aversion
5. Rawls v’s Bentham: The Limiting Cases
6. Game Theory
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1. Condorcet Winner
•
•
The Condorcet winner defeats all other proposals in pair-wise majority
voting
Voter rankings of alternative public projects (X<Y<Z) based on knowledge
of own benefits and their increased tax payment
Case A: Single-peaked preferences
•
•
Y is the Condorcet winner: {Y P X}, {Y P Z}
Case B: Not single peaked preferences
•
There is no Condorcet winner: {X P Y}, {Z P X}, {Y P Z}
•
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•
•
Why might preferences not be single-peaked?
– Minimal effective spending (e.g. National Security)
– Different projects rather than different quantities
If the projects can be ranked to provide single-peaked preferences, a
Condorcet winner exists
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2. Logrolling
• Definition: Logrolling is vote trading
• All projects (D, E and F) can in principle be
financed
• Does logrolling ensure that majority voting
results in efficient public spending
decisions?
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•
•
•
Logrolling with efficient projects
Suppose each proposal only benefits one region
With majority voting all three proposals will be rejected, despite
satisfying the cost-benefit criterion.
V12 (D, E ) = (90,80,−60 )
V13 (D, F ) = (80,−50,70)
V 23 (E , F ) = (− 50,70,70 )
•
•
Logrolling has resulted in acceptance for two of three proposals
V(1,2) maximises total and individual benefit for 1 and 2.
Politician 3’s constituency pays taxes but does not benefit
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• Logrolling with inefficient proposals
V12 (D , E ) = (10,10,−60 )
V13 (D , F ) = (10,−70,−10 )
V23 (E , F ) = (− 80,20,−10 )
• Logrolling can result in majority support for
proposals for which public finance is not justified
by CB analysis (V12(D,E)).
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3. Political competition with
multiple issues
• Two publicspending choices
(X, Y) with
personal taxes
required to finance.
• Concentric
indifference
curves.
• Also derived utility
from private
spending Z.
• Candidate can
guarantee support
if point 1 is chosen.
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• Initially, person 2
want more of both
goods.
• The contract curve
(CC) joins the
preferred points 1
and 2 of voters 1
and 2 (all points
are pareto
efficient).
• All candidates will
chose a point on
the CC.
• Policy proposals
on CC defeat
others. B>>A
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•
Now consider, three
voters required for
majority voting
– Candidate E gets
votes from 1 and 3
– Candidate S gets
votes from 1 and 2
– Candidate F gains
votes from 2 and 3.
•
•
•
There is no stable
outcome of political
competition.
No Nash Equilibrium.
2 candidates and 2 +
policies, there is also
no Nash equilibrium.
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• Principled
political
behavior
• Voter 1 and 3
are principled
about low
spending and
won’t defect
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4. Risk Aversion
• People are usually risk-averse
• Risk-aversion can be calculated by the level of
unwillingness to accept a fair gamble
– Risk neutral not willing to pay anything to avoid a fair
gamble
• For risk-averse people, the marginal utility of
income is declining (value additions to incomes
less than avoidance of income losses)
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• Behind the veil of ignorance would you
prefer the average income (with its
associated utility) or an an expected
average of the utility associated with high
and low income?
– Diminishing utility of income suggests that we
prefer the average income with its associated
income.
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• Expected utility and
the fair gamble
• Note: expected utility
from fair gamble (EU)
< expected utility
from average income
(U(Ey))
• The income yC is the
certainty-equivalent
income that gives
expected utility EU
with certainty.
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• Price prepared to pay to avoid gamble and
be at the low end of ex post inequality
• The positive value of ρ confirms risk
aversion
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5. Rawl’s v’s Bentham
• Two limiting social welfare functions:
– Jeremy Bentham
– John Rawls
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• Jeremy Bentham (1748–1832): “the greatest good for the
greatest number” or equal weights to all (dist. does not matter).
• For two people and with diminishing marginal utility.
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•
John Rawls (1921–2002) and the weakest link
•
The Rawls objective is not equality but maximization of the utility of
the worst-off person
Rawls social welfare function provides complete insurance.
Because of the Laffer curve and limitations of tax revenue, complete
insurance and ex-post equality are not necessary consequences
•
•
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•
Bentham and Rawls as limiting cases
•
•
Bentham and Rawls are limiting cases of aversion to inequality
Intermediate welfare function: Two peoples social weights equal at 45o line.
Otherwise the person with lower utility has a higher weight.
Social aversion to inequality is measured by the amount of utility that can be
taken from a high utility person and transferred to a low utility person while
keeping social welfare constant (i.e. the slope of the welfare contour).
•
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Chosen social welfare function will
depend on
1. A societies aversion to inequality (risk
aversion)
2. Degree of work ethic
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6. Game Theory: Social Justice
without Government
1. Sharing of Incomes (with personal cost to
effort)
2. Private Income Transfers (when each person
prefers that the other give)
3. Exploitation of Charity
4. Strategy for Donor to Overcome Exploitation of
Charity
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• The sharing of incomes and the personal cost of effort
give rise to a prisoners’ dilemma
• In the Nash equilibrium with moral hazard, the likelihood
is maximized that everyone will have low income
• People “free ride” by choosing low effort
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• The prisoners’ dilemma of private income transfers when
each person prefers that the other give
• Nash Equilibrium is that no person gives.
• Free rider problem is introduced
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• The exploitation of charitable feelings
• The Nash equilibrium is (3, 4)
• The donor is unhappy with the outcome
• What can the donor do?
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•
•
•
•
•
•
Misrepresented preference:
– Donor declares that she has the highest utility 4 when recipient makes no effort
and the donor does not give.
– Donors new preferences give utility 3 when the recipient makes the effort and
money given.
The recipient starves at 4,1 and wants to avoid it.
No dominant strategy for donor or the recipient and no Nash equilibrium in pure
strategies
The recipient does not want to die of starvation and recipient adopts a maxi-min
strategy (makes the decision that results in the least potential self-harm)
The outcome is at (3,3)
For the change in outcome, the recipient must believe that the donor will indeed let
him starve. In repeated game he might learn that (4,1) is not possible. Rules, not
discretion can help.
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Questions?
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