Welfare Economics

Question 1

Show informal proof of the 2nd FWT

Answer 1

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)

Question 2

Implications of 2nd FWT?

Answer 2

1. Any efficient can be implemented as market outcome

2. Efficiency and equity concerns can be separated

Question 3

Why won’t tatonnement converge on competitive equilibrium?

Answer 3

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

Question 4

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

Answer 4

1. Weak axiom of revealed preference (WARP)

2. Gross substitutes

Question 5

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

Answer 5

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

Question 6

Definition of the core?

Answer 6

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

Question 7

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

Answer 7

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

Question 8

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

Answer 8

1. Yes always

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

Question 9

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

Answer 9

Sufficiently large market

Question 10

Arrow’s impossibility theorem:

Answer 10

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

Question 11

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

Answer 11

1. Relax unrestricted domain (single-peaked preferences)

Question 12

Theorem (impossibility of a Paretian liberal)

Answer 12

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

Question 13

Theorem (tactical voting)

Answer 13

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

Question 14

Restriction needed for majority voting to be strategy proof?

Answer 14

Agents have single-peaked preferences

Question 15

Feasible allocation x is in the core if……

Answer 15

it can’t be improved on by any coalition

Question 16

What does concept of the core assume?

Answer 16

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

Question 17

Key assumptions of 1st FWT:

Answer 17

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

Question 18

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

Answer 18

• individualism
• pareto principle
• consequentialism

Question 19

Why redistribute income?

Answer 19

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

Question 20

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

Answer 20

• utility
• inter-personal comparisons of utility
• lifetime income
• ability

Question 21

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

Answer 21

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

Question 22

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

Answer 22

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

Question 23

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

Answer 23

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)

Question 24

SWF is consistent if….

Answer 24

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

Question 25

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

Answer 25

Allows ranking of consumers by utility level

Question 26

What information about preferences does the Pareto principle require?

Answer 26

Ordinal information about individuals’ utility

Question 27

What sort of comparability does a Rawlsian SWF require?

Answer 27

Full ordinal level comparability

Question 28

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

Answer 28

1. Cardinal unit comparability

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

Question 29

Who said?

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

Answer 29

Sen

Question 30

Sen quote to show limitation of Pareto efficiency?

Answer 30

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