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Show informal proof of the 2nd FWT

1. Choose point on contract curve
2. x* = Pareto-efficient, so MRSa = MRSb
3. Draw tangential budget line (i.e. fix prices)
4. Pick any point w on the budget line as endowment
5. Agents will trade to x*, if they take prices as given
6. SEE NOTES FOR DIAGRAM (informal proof of 2nd FWT)


Implications of 2nd FWT?

1. Any efficient can be implemented as market outcome
2. Efficiency and equity concerns can be separated


Why won't tatonnement converge on competitive equilibrium?

1. ‘anything goes’ theorem
2. (i) Take reasonable individual demands, derived from utility maximisation and aggregate them
(ii) Cannot tell anything about properties of aggregate demand
3. May have multiple equilibria with no convergence


2 possible restrictions that can be placed on aggregate demand for tatonnement to converge on competitive equilibrium price?

1. Weak axiom of revealed preference (WARP)
2. Gross substitutes


What is the weak axiom of revealed preference (WARP)?

if prices and incomes change, consumer should not choose a bundle which they could previously afford


Definition of the core?

1. Core = set of allocations that cannot be blocked
2. Coalition of agents blocks an allocation x, if its members can improve (increase utilities) on the allocation by trading only amongst themselves


What points does the core consist in (Edgeworth box)?

3. Core consists of points on contract curve which give both agents higher utility than reservation utility (utility from endowment)


Is competitive equilibrium of exchange economy in the core? Always? Why?

1. Yes always
2. No possible coalition can block this competitive equilibrium allocation (it’s within core)


What condition required for the only core outcome to be the competitive equilibrium outcome?

Sufficiently large market


Arrow's impossibility theorem:

1. no complete and transitive social choice rule exists which satisfies all the following conditions (UPID):
(i) Unrestricted domain
(ii) Pareto principle
(iii) Independence of irrelevant alternatives
(iv) Non-Dictatorship


Restriction needed for majority voting to produce consistent social ordering which fulfils Arrow's 4 criteria for social choice rule?

1. Relax unrestricted domain (single-peaked preferences)


Theorem (impossibility of a Paretian liberal)

1. if there are at least 3 social states/options, then there’s no social choice rule which satisfies:
(i) Unrestricted domain
(ii) Pareto principle
(iii) Liberalism


Theorem (tactical voting)

1. If there are at least 3 social states/options, no social choice function both:
(i) Strategy proof; and
(ii) Respects citizens’ sovereignty


Restriction needed for majority voting to be strategy proof?

Agents have single-peaked preferences


Feasible allocation x is in the core if......

it can't be improved on by any coalition


What does concept of the core assume?

1. Agents:
(i) can coordinate and bargain costlessly
(ii) have access to necessary information


Key assumptions of 1st FWT:

1. Markets perfectly competitive
2. No externalities
3. Agents are price-takers


Value judgements made when writing social welfare as a function of individual welfare?

-pareto principle


Why redistribute income?

-reduces inequality and so improves social welfare (assuming concave SWF)
-social insurance and income smoothing
-poverty relief


What can social planner NOT observe (but would like to)?

-inter-personal comparisons of utility
-lifetime income


Examples of when there is no trade-off between equity and efficiency:

1. social insurance (market failure of private insurance market)
2. Imperfect capital markets
3. externalities (e.g. altruism, crime)


What is required to create a coherent social welfare function that meets Arrow's 4 minimally demanding conditions?

common scale to measure well-being, so that inter-personal comparisons of relative well-being can be made


Theoretically, how would social planner go about implementing optimal lump-sum taxation?

1. Construct contract curve of Pareto-efficient allocation (to select social optimum)

2. Predict equilibrium that will emerge for all possible income levels (so incomes needed to decentralise chosen allocation can be determined)

3. Know value of each consumer’s endowment (to calculate pre-tax incomes and hence lump-sum taxes that must be imposed)


SWF is consistent if....

it ranks social states in same way for all permissible transformations of utility functions


What sort of comparability (of utility functions) does ordinal level comparability allow?

Allows ranking of consumers by utility level


What information about preferences does the Pareto principle require?

Ordinal information about individuals' utility


What sort of comparability does a Rawlsian SWF require?

Full ordinal level comparability


What sort of comparability does a utilitarian SWF require? why?

1. Cardinal unit comparability
2. so we can compare the loss of 1 individual against the gain of another individual


Who said?

"a society or economy can be Pareto-optimal and still be perfectly disgusting"



Sen quote to show limitation of Pareto efficiency?

"a society or economy can be Pareto-optimal and still be perfectly disgusting"