Micro 2: Welfare Economics Flashcards
What, formally, does it mean for an allocation to (weakly) Pareto dominate another?
An allocation x weakly Pareto dominates another allocation y if x is weakly preferred to y for all agents, and y is strictly preferred to x for at least one agent. That is, the change must make no-one worse off, and some people better off.
What is Pareto efficiency? How does it relate to the UPF?
An allocation is Pareto efficient if no change could make any agent better off without making some other agent worse off. The utility possibilities frontier is the set of Pareto efficient outcomes; any allocation on the interior of the UPF has some feasible Pareto-dominant outcomes.
Is Pareto efficiency a good social welfare rule?
- Requires few ethical assumptions - seems undeniable that it is always better to make everyone at least weakly better off.
- Does not require cardinal, ratio or absolute utility values.
- Cannot always compare two outcomes in terms of Pareto-dominance (eg two points on the UPF).
- In combination with IIA and unrestricted domain, the Pareto principle implies the only possible complete, transitive SWF is a dictatorship.
- Sen: the Pareto (1970) principle may conflict with a weak sense of liberalism.
- Although, Blau (1975) argued that this problem is avoided if ‘nosy’ preferences are disallowed.
What is a Kaldor-Hicks improvement?
A reallocation is a Kaldor-Hicks improvement if those that are made better off could hypothetically compensate those that are made worse off and lead to a Pareto improvement. The compensation does not actually have to occur.
What is a preference aggregation rule?
A preference aggregation rule takes a set of preferences and produces a preference ordering for society.
What is the difference between ordinal and cardinal utility?
Ordinal utility simply requires preference orderings. Any monotonic increasing function can be applied to these utility functions and preferences are preserved. However, cardinal utility also requires a sense of preference intensity; the only permissible transformations are those of addition and multiplication by scalars.
What are the four premises of Arrow’s Impossibility Theorem?
- Unrestricted domain - agents can report any preferences.
- Pareto principle - if everyone prefers x to y, then x > y.
- IIA: if the individual preference orderings over x and y do not change, ordering between x and y should not change, even if other preferences do.
- Non-dictatorship: there is no agent such that x >i y implies x>y, irrespective of others’ preferences.
What does Arrow’s Impossibility Theorem state?
If there are at least 3 social states, there is no preference aggregation function that satisfies the four above rules and generates a complete and transitive preference ordering for society.
What does the Gibbard-Satterthwaite theorem state?
Suppose there are at least 3 social states. Then, there are no social choice functions that are strategy-proof and respect sovereignty.
What are single-peaked preferences? Why does the Median Voter Theorem hold for them?
Preferences are single-peaked iff the options can be placed in some order such that all agents have a ‘bliss point’, and all options further from this point are ranked below ones closer to the point. Then, the Median Voter states that majority rule induces a transitive social preference ordering. The median alternative is selected; any point to the left or right does not gain a majority.
What is a Condorcet cycle? When are these preferences likely to be a problem?
Consider the following options:
(1) A gets £3, B gets £7, C gets £0
(2) A gets £7, B gets £0, C gets £3
(3) A gets £0, B gets £3, C gets £7.
Preferences are not single-peaked here; B will prefer 1>3>2, A prefers 2>1>3, C prefers 3>2>1. These are in a cycle, and so majority rule will not provide a transitive social ordering. There is a majority for 1>3, and for 3>2, and for 2>1, but transitivity would imply 1>2. These are especially likely to be a problem in rival distribution problems like this.
Is majority rule strategy-proof?
Under single-peaked preferences, Moulin (1980) proved that simple majority rule is strategy-proof. In general, no.
What informational relaxations on utility do we require to allow a Rawlsian SWF? What about utilitarian or weighted utilitarian SWFs?
A Rawlsian SWF requires full comparability of utility, but no more than ordinal scales. Utilitarian SWFs require a cardinal utility scale. Even partial interpersonal comparison metrics can allow some SWFs.
Should we allow informational relaxations that permit utilitarian SWFs?
Inferring interpersonal welfare comparisons through subjective wellbeing surveys, expenditure patterns or access to primary goods are all imperfect and require ethical assumptions. However, social choice is an inescapably ethical issue, and so it may be necessary to explicitly acknowledge axioms such as hedonism to make progress with social choice.
