2. Inequality and Welfare

Intergenerational mobility

Parental income/education affects children’s outcomes due to environment quality, investment in education, role models etc.

Inequality of opportunity

Ouctomes depend on two factors, circumstances (gender, family etc) and effort, inequality during to effort is seen to be acceptable but that caused by circumstances is unfair

Libertarian view on Inequality (Nozick)

Inequality itself is not a problem what merges is how it arose

Policies to correct causes of inequality

early childhood intervention

health and nutrition policies

equal access to quality education

health and nutrition policies

labour market policies that target discrimination

social welfare function

an aggregation of individual utilities in a society

consequences of inequality

Interpersonal comparability of utility

make meaningful comparisons of the utility of different individuals

Pareto improvement

a change in one economic state to another that makes at least one person better off without making any individual worse off

Pareto efficiency

the economic state from which no further Pareto improvements can be made

Pareto preferred

an outcome created by a Pareto improvement is said to be Pareto preferred to the original outcome

advantage Pareto concepts

makes minimal assumptions, requiring very little information about individual preferences only ordinal utility (is the person better/worse off or unchanged)

disadvantage of Pareto concepts

an allocation that does not waste resources is Pareto efficient, this could be 1 person with 100% income

Pareto preference can only rank some cases, precludes majority of policy decisions

Arrow’s impossibility theorem:

Assuming only ordinal utility and no interpersonal comparability no complete, reflexive and transitive Social Choice Rule exists which satisfies the basic properties we would want from such rule because of too few assumptions

SWF =

F(u₁, u₂, … uₙ)

society of individuals i = 1 to n

Each of them maximizes their utility given their income constraints, makes choices inside their choice set Ci and reaches individual welfare Ui

how to work out how much importance is given to each individual by the SWF

Partial derivative → dSWF/dUi = Wi

Wi ← welfare wight ← how an increase in Ui (a single persons utility) impacts the social welfare (note Wi is usually positive)

Assumptions for a general SWF

individuals maximise their utility

interpersonal comparability of utility

preferential relationships assumptions (transitive, compete etc)

each individual has a welfare weight

normative choices to decide aggregation rule

Utilitarian SWF

SWF = ∑ Ui

Objective of utilitarian social welfare

maximise the sum of utilities of all members of society

Additional assumptions of utilitarian SWF

cardinal utility

equal welfare weights

is utilitarianism egalitarian

Not inherently egalitarian however due to diminishing marginal utility it can lead to egalitarian outcomes as in order to maximise the sum of utilities, you redistribute income to those with higher marginal utility

Limitations of utilitarian SWF

Nozick’s utility monster

depends on utility productivity so doesn’t care about the distribution

behavioural economic issues

Nozick’s utility monster

under a utilitarian social welfare function, an individual who derives more utility from each init of resources than others would receive most/all the resources since this maximised total utility

Rawlsian SWF

= min(u₁, u₂, … uₙ)

is rawlsian

Rawls’ veil of ignorance

if individuals had to choose the principles that govern society without knowing what position they would take in society eg rich or poor, they would choose to protect the least advantage leading to the Rawlsian SWF

assumptions of the rawlsian SWF

cardinal utility

normative values - very strong aversion to inequality

limitations of the rawlsian SWF

• extreme inequality aversion → ignores every one except the worst off → too extreme

• non differentiable

inequality aversion

one is averse to inequality if they believe that a transfer from a richer to poorer household which preserves the ranking between the households is a good thing

Pigou-Dalton Principle of Transfers

Any measure of inequality should decrease if there is a transfer from a richer to poorer household which preserves the ranking in income distribution and does not change the total income

axis for the Lorenz curve

y = % of income/wealth

x = cumulative % of population (ranked by income)

limitation of the Lorenz curve as a measure for inequality

if curves cross different inequality averse SWF would rank them differently because one distribution is more equal for some parts of the population and less equal for others - only a partial ordering

two equivalent expressions for GIni coefficient

A/(A+B)

where A is the area between the curve and the line of perfect equality and B is the area under the curve

1 - 1/(µN²) x ∑∑min(M,M’)

where N is the population size and

explain how the Gini is calculated with this equation 1 - 1/(µN²) x ∑∑min(M,M’) using words

one minus the mean incomes x square of the number of people x the sum of the minimum between each pair of incomes including pairs of the same income and repeats

explain why 1 - 1/(µN²) x ∑∑min(M,M’) is more informative

low incomes appear more often showing how the bottom of the distribution gets a higher weightage showing the normative value judgment included in this SWF whereas the geometric formula masks it

problem with Gini coefficient

assumes impact SWF, which conveys normative values

functional distribution of income

how national income is split between factors of production, labour income and capital income